sol6_3:= [ 
    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2 ]
        /* order = 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0,
        0, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0 ]
        /* order = 14 = 2 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2,
        2, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2,
        2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 14 = 2 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0,
        0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0 ]
        /* order = 21 = 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1,
        1, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1,
        1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2 ]
        /* order = 26 = 2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2,
        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0,
        2, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0 ]
        /* order = 28 = 2^2 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0,
        1, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        1, 1, 2, 1, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2 ]
        /* order = 28 = 2^2 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 1, 1, 1 ]
        /* order = 28 = 2^2 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 1 ]
        /* order = 42 = 2 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
        0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1,
        0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
        /* order = 42 = 2 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0 ]
        /* order = 48 = 2^4 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
        /* order = 48 = 2^4 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 48 = 2^4 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2,
        2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 1,
        2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2 ]
        /* order = 52 = 2^2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0 ]
        /* order = 52 = 2^2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
        0, 0, 1, 1, 2, 2, 1, 0, 1, 0, 0, 2, 1, 2 ]
        /* order = 52 = 2^2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 0,
        2, 2, 2, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 0 ]
        /* order = 56 = 2^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1,
        2, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 2, 1,
        1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2 ]
        /* order = 56 = 2^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1,
        2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 ]
        /* order = 56 = 2^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0,
        1, 1, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0,
        2, 1, 0, 1, 0, 0, 0, 0, 2, 1, 2, 1, 2, 0 ]
        /* order = 78 = 2 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1,
        1, 2, 0, 2, 2, 2, 2, 1, 0, 2, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
        2, 2, 1, 1, 1, 1, 0, 1, 2, 0, 0, 0, 0, 0 ]
        /* order = 84 = 2^2 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 1, 1, 1 ]
        /* order = 84 = 2^2 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 0, 2, 2, 2, 1, 2, 1, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 1 ]
        /* order = 84 = 2^2 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 1, 2, 0, 1, 2, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 2, 1, 1,
        2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 2, 1, 2, 1 ]
        /* order = 91 = 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1,
        0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0,
        0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2,
        0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0,
        0, 0, 0, 1, 2, 0, 2, 1, 1, 1, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1,
        0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 1, 0, 0,
        0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 1, 1, 2, 1,
        2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 0,
        0, 1, 0, 1, 0, 2, 1, 0, 1, 2, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1,
        2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1,
        0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0,
        0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 0,
        2, 2, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0,
        0, 1, 0, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 1,
        2, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2,
        0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 1, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2,
        2, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 0,
        0, 2, 1, 0, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1,
        1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1,
        2, 1, 0, 1, 1, 1, 0, 1, 2, 0, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1,
        0, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 0, 2, 1 ]
        /* order = 104 = 2^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0,
        1, 1, 2, 0, 2, 0, 1, 0, 0, 0, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0,
        2, 0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 2, 0 ]
        /* order = 104 = 2^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0 ]
        /* order = 104 = 2^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 1 ]
        /* order = 104 = 2^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2,
        1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 1, 1, 2, 1 ]
        /* order = 112 = 2^4 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0 ]
        /* order = 156 = 2^2 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 ]
        /* order = 156 = 2^2 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 0, 1 ],
        \[ 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2,
        2, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 1 ]
        /* order = 156 = 2^2 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1,
        1, 2, 0, 0, 1, 1, 1, 2, 1, 2, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0,
        1, 1, 1, 1, 1, 2, 1, 1, 0, 0, 0, 2, 2, 0 ]
        /* order = 168 = 2^3 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2,
        1, 2, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1,
        1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1 ]
        /* order = 168 = 2^3 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2,
        1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 1, 0,
        1, 0, 2, 0, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1 ]
        /* order = 168 = 2^3 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1,
        0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1,
        0, 2, 0, 1, 1, 2, 2, 2, 0, 1, 2, 1, 1, 1 ]
        /* order = 182 = 2 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0,
        0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 2, 0, 0 ]
        /* order = 182 = 2 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0,
        2, 2, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 1,
        0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,
        1, 2, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        2, 1, 0, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1,
        1, 1, 0, 0, 2, 1, 1, 0, 1, 2, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 2,
        1, 1, 0, 1, 0, 0, 1, 1, 2, 0, 2, 2, 2, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 1,
        1, 0, 0, 1, 2, 2, 0, 1, 2, 1, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1,
        1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 2, 2, 2, 0, 0,
        2, 2, 0, 0, 0, 2, 1, 2, 2, 2, 1, 2, 2, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1,
        0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2,
        0, 0, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0,
        0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0,
        0, 0, 1, 2, 1, 2, 2, 0, 2, 1, 1, 2, 0, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 1,
        2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1,
        0, 0, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
        0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2,
        0, 2, 1, 1, 0, 2, 0, 2, 1, 0, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 1, 0,
        2, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 0, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2,
        1, 0, 2, 2, 0, 0, 2, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0,
        2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 1, 2, 2, 0, 0, 0,
        0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 2, 0, 2, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 2,
        0, 0, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1,
        1, 0, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2,
        1, 0, 1, 1, 0, 0, 0, 2, 1, 1, 2, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1,
        2, 0, 2, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 0,
        0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 2 ]
        /* order = 208 = 2^4 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 1, 2, 1, 0, 2,
        0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2 ]
        /* order = 273 = 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0,
        0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 1, 2, 1, 1 ]
        /* order = 288 = 2^5 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0,
        1, 2, 0, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0 ]
        /* order = 288 = 2^5 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0,
        1, 0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2,
        0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 2, 2, 1 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 1, 0, 0, 0, 2, 2,
        1, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0,
        2, 1, 2, 2, 1, 1, 0, 1, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0,
        0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1,
        0, 0, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 1, 0 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1,
        0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 0 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0,
        2, 2, 0, 0, 0, 2, 2, 1, 2, 0, 1, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2,
        0, 0, 0, 1, 2, 0, 1, 0, 2, 1, 1, 2, 1, 0 ]
        /* order = 312 = 2^3 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 2,
        1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 0, 1 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0,
        1, 2, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 1,
        0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 1, 0, 2, 2 ]
        /* order = 338 = 2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2,
        1, 2, 0, 0, 1, 0, 2, 2, 2, 1, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 0, 1, 1, 0, 1, 2,
        1, 0, 1, 0, 0, 0, 2, 0, 1, 2, 2, 1, 0, 0 ]
        /* order = 364 = 2^2 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1,
        0, 0, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 1 ]
        /* order = 364 = 2^2 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1 ]
        /* order = 364 = 2^2 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0,
        2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
        0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2,
        0, 2, 1, 2, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 1, 1,
        2, 1, 0, 2, 0, 0, 0, 0, 2, 1, 0, 1, 0, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0,
        2, 1, 2, 2, 1, 2, 2, 1, 0, 2, 1, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1,
        2, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 2, 1, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
        0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2,
        0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 2, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 1,
        1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0,
        0, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1,
        2, 0, 2, 2, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        2, 0, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2,
        1, 2, 0, 1, 2, 0, 2, 2, 1, 1, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 2,
        1, 1, 2, 2, 1, 1, 2, 1, 0, 2, 2, 2, 1, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0,
        2, 2, 2, 1, 2, 1, 0, 1, 1, 0, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
        1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 1, 2, 2, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 1,
        1, 1, 0, 1, 1, 0, 2, 1, 2, 2, 0, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0,
        2, 1, 1, 2, 2, 1, 0, 1, 0, 2, 2, 2, 2, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        1, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0,
        2, 1, 0, 1, 0, 1, 0, 2, 1, 1, 1, 2, 0, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2,
        1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        0, 0, 2, 2, 2, 2, 1, 2, 1, 0, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 0, 0, 1, 0, 2,
        2, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0,
        2, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2,
        1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2,
        2, 0, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 1, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2,
        1, 2, 1, 2, 1, 2, 2, 0, 2, 2, 1, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2,
        0, 2, 2, 0, 2, 0, 2, 2, 1, 2, 1, 1, 1, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0,
        0, 2, 1, 2, 0, 2, 1, 2, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 2,
        0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 1, 2, 2, 0, 2,
        1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1,
        0, 0, 1, 0, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 1, 1, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 2, 1, 2, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1,
        2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 0, 2, 1,
        0, 1, 0, 0, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1,
        0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 2, 1, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2,
        0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1,
        2, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 2, 1, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 2, 1, 0, 0, 2, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1,
        2, 2, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 0, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 1, 0, 2,
        2, 2, 1, 2, 2, 1, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0,
        1, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
        0, 0, 2, 2, 1, 2, 2, 1, 0, 1, 0, 0, 0, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 2, 2, 2, 1, 2, 2, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 1, 2, 1,
        2, 1, 2, 1, 0, 2, 1, 2, 2, 0, 2, 0, 0, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 1, 0, 2, 1, 1, 0,
        2, 0, 0, 1, 0, 0, 2, 1, 1, 2, 2, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 1,
        1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 1, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1,
        0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 2,
        1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 0, 0, 0,
        0, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1,
        0, 1, 2, 1, 2, 2, 2, 1, 1, 2, 0, 2, 2, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0,
        0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 2,
        0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 2,
        2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1,
        0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0,
        0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 0,
        1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        0, 0, 1, 1, 1, 1, 1, 0, 1, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 0, 0, 1,
        1, 0, 2, 1, 2, 2, 1, 1, 2, 1, 0, 0, 0, 0 ]
        /* order = 546 = 2 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2,
        1, 2, 0, 0, 1, 2, 1, 1, 2, 0, 2, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1,
        2, 0, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1 ]
        /* order = 546 = 2 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 1, 2, 0, 1, 2, 2, 0,
        2, 0, 2, 1, 0, 2, 1, 1, 0, 1, 2, 2, 2, 1 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 2, 2, 0, 1, 1, 1, 1, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 1, 1, 1, 2,
        2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 2, 0, 1, 2,
        2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 1, 0,
        2, 0, 2, 1, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 2, 1,
        0, 1, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, 1, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0, 1,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 1, 2, 1,
        2, 0, 1, 2, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0,
        0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0,
        2, 1, 2, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 2 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0,
        1, 1, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0,
        1, 2, 0, 1, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2,
        2, 1, 2, 2, 1, 2, 1, 2, 0, 0, 1, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0,
        0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 0, 1, 2, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2,
        1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
        0, 0, 1, 1, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 1,
        0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1,
        0, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 2, 2,
        0, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 0 ]
        /* order = 624 = 2^4 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 2, 0,
        0, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 2, 0, 1, 0, 2, 1, 0, 1, 0, 1 ]
        /* order = 624 = 2^4 * 3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 0,
        0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0 ]
        /* order = 676 = 2^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0, 1,
        0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2,
        1, 0, 2, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0, 0 ]
        /* order = 676 = 2^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2,
        1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 0, 2, 1, 1, 2, 2, 2, 1, 2, 1 ]
        /* order = 728 = 2^3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        2, 1, 0, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2, 1, 1, 1, 2,
        0, 2, 2, 0, 2, 2, 0, 2, 1, 1, 0, 1, 0, 0 ]
        /* order = 728 = 2^3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1,
        2, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 2, 2,
        2, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 1 ]
        /* order = 728 = 2^3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2,
        0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 1, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 0, 0, 2, 1, 2, 2, 0, 1, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 1,
        1, 2, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        2, 0, 2, 1, 2, 0, 0, 1, 1, 1, 0, 1, 1, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 0, 1, 2, 0, 0, 2, 2, 0, 2, 1, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 1, 1, 2, 0,
        1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 0, 2, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2,
        2, 0, 2, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1,
        0, 1, 2, 0, 2, 1, 2, 2, 0, 1, 2, 2, 0, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 1, 0, 2, 0,
        0, 2, 0, 1, 1, 0, 1, 2, 2, 1, 2, 1, 0, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1,
        0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0,
        0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2,
        0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 1,
        0, 1, 1, 0, 0, 2, 1, 2, 1, 1, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2,
        1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 2, 2, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 1, 0, 1, 0, 0, 0,
        1, 0, 2, 1, 0, 2, 0, 1, 1, 2, 2, 2, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0,
        2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 0, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 2, 2, 2,
        1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0,
        1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        2, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1,
        0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0,
        2, 0, 1, 2, 1, 1, 1, 2, 0, 2, 0, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1,
        1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 1, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2,
        0, 2, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 2, 0, 0, 1, 0, 1,
        0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 2, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 1, 1, 0,
        1, 0, 2, 1, 0, 2, 1, 1, 1, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2,
        2, 1, 2, 2, 1, 0, 0, 0, 2, 1, 1, 0, 0, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 1,
        0, 1, 0, 1, 0, 2, 2, 2, 0, 1, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 2,
        0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 1, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2, 0,
        2, 2, 0, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1,
        1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 2, 0, 2, 0,
        2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0,
        0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 2, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 1, 0, 1, 0, 2, 0,
        2, 0, 2, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0,
        0, 1, 2, 1, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2,
        1, 1, 1, 0, 0, 2, 2, 1, 1, 0, 0, 0, 1, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 1,
        2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0,
        1, 1, 1, 2, 1, 2, 2, 0, 0, 2, 2, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 2, 0, 1,
        2, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 0, 2, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1,
        2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 1, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0,
        0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 2, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0,
        2, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 1, 2, 2,
        2, 1, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 2, 1, 0, 0, 2,
        1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 0, 2,
        1, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2,
        0, 0, 2, 0, 2, 1, 0, 1, 1, 2, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2,
        0, 1, 2, 2, 2, 0, 2, 2, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2,
        0, 1, 0, 0, 2, 0, 0, 2, 1, 1, 1, 1, 0, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2,
        0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 2, 0, 2,
        1, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 2, 0, 1, 0, 0,
        0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 2, 1, 2,
        2, 2, 0, 0, 1, 2, 1, 1, 0, 2, 0, 0, 0, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1,
        0, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 2,
        0, 0, 0, 2, 1, 2, 0, 2, 2, 0, 1, 1, 0, 1 ],
        \[ 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 2, 2,
        1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 1, 1, 0, 1 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1,
        0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 1 ]
        /* order = 936 = 2^3 * 3^2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 1, 1, 1,
        2, 0, 2, 2, 2, 0, 0, 1, 1, 2, 0, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2,
        2, 2, 1, 1, 2, 2, 1, 0, 1, 0, 0, 0, 0, 0 ]
        /* order = 1014 = 2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2,
        1, 0, 2, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 1, 0, 1, 0, 0, 2, 1, 2, 2, 2 ]
        /* order = 1014 = 2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2,
        1, 2, 1, 1, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0,
        2, 1, 1, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2 ]
        /* order = 1092 = 2^2 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0,
        2, 0, 1, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0,
        1, 2, 2, 2, 0, 2, 2, 1, 2, 0, 1, 2, 1, 0 ]
        /* order = 1092 = 2^2 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 1, 1, 2, 2, 1, 1, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 1,
        1, 1, 1, 0, 1, 0, 2, 0, 1, 2, 1, 2, 2, 0 ]
        /* order = 1092 = 2^2 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
        2, 1, 1, 0, 0, 1, 2, 2, 2, 2, 2, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0,
        1, 0, 1, 0, 2, 0, 2, 1, 0, 2, 2, 0, 1, 2 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2,
        2, 1, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 2, 2, 0,
        0, 2, 0, 2, 0, 1, 2, 1, 1, 1, 2, 2, 2, 2 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1,
        0, 0, 2, 2, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 2, 1, 1, 0, 1,
        2, 1, 1, 1, 1, 2, 0, 0, 1, 0, 1, 2, 2, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0,
        0, 0, 2, 2, 2, 2, 0, 0, 1, 1, 2, 2, 1, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0,
        1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2,
        0, 1, 0, 1, 1, 2, 2, 0, 2, 1, 2, 0, 2, 2 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0,
        2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1,
        1, 0, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1,
        2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 1, 0,
        2, 0, 1, 1, 1, 2, 2, 2, 2, 1, 0, 2, 0, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        0, 2, 1, 0, 2, 2, 1, 1, 2, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 2,
        0, 0, 2, 2, 1, 1, 2, 0, 1, 0, 2, 2, 1, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 1,
        1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0,
        0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2,
        0, 0, 0, 2, 2, 1, 1, 1, 0, 1, 0, 0, 0, 0 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        2, 0, 2, 0, 2, 2, 0, 0, 1, 1, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,
        2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
        0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0,
        0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 0, 2, 0, 0, 2,
        0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 0, 2, 0, 1 ]
        /* order = 1352 = 2^3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2,
        2, 2, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1,
        0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2 ]
        /* order = 1456 = 2^4 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0,
        2, 2, 1, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0,
        0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 0, 1, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2,
        2, 0, 0, 1, 2, 0, 0, 0, 2, 1, 2, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 2,
        0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 1, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2,
        0, 1, 2, 2, 0, 2, 0, 1, 0, 2, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        0, 0, 1, 1, 0, 2, 0, 0, 2, 1, 1, 0, 2, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 2, 0, 2,
        0, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2,
        0, 1, 2, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 2,
        2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 2, 0,
        1, 0, 1, 1, 1, 1, 2, 2, 0, 2, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0,
        1, 2, 2, 2, 1, 2, 0, 0, 2, 1, 2, 2, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0,
        1, 1, 1, 1, 2, 0, 0, 2, 0, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 1,
        1, 0, 2, 2, 2, 0, 0, 2, 1, 1, 2, 1, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 2, 0, 1, 0,
        0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 0, 2, 0, 2, 1, 2,
        2, 2, 1, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 1, 2, 1, 1, 0, 0, 1, 0, 0, 2, 1,
        0, 1, 0, 2, 2, 1, 1, 1, 2, 1, 0, 0, 2, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2,
        1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1,
        2, 0, 2, 0, 2, 0, 0, 0, 1, 1, 2, 1, 2, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1,
        1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 0, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 1, 2, 1, 0,
        0, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 1,
        0, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
        0, 1, 2, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
        0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 1, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 2, 2, 0,
        1, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2,
        2, 0, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 0, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
        1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 2, 1, 1,
        1, 1, 0, 2, 1, 1, 0, 2, 0, 0, 0, 1, 0, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1,
        0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2,
        2, 2, 1, 2, 2, 0, 1, 2, 2, 0, 0, 1, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0,
        1, 0, 0, 1, 2, 1, 1, 0, 1, 2, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0,
        1, 2, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0,
        2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2,
        0, 0, 0, 2, 2, 1, 1, 1, 1, 2, 2, 0, 0, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 2,
        0, 0, 1, 1, 1, 1, 1, 0, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1,
        1, 0, 1, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1,
        2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 1, 1, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
        2, 2, 0, 2, 0, 0, 2, 1, 2, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 2,
        2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 1, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2,
        2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0,
        0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 2, 1, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2,
        1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 1, 2, 0, 2, 0,
        1, 0, 2, 2, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 2, 1, 0,
        1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2,
        1, 1, 2, 1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 2, 1, 0, 1, 1, 1, 2,
        2, 0, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2,
        2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 1, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 2, 1, 1, 0,
        0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 2,
        0, 1, 1, 1, 2, 1, 2, 2, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2,
        2, 2, 0, 1, 0, 2, 2, 2, 2, 0, 1, 1, 1, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        2, 1, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1,
        1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 2, 2, 2, 0,
        2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 1, 1, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2,
        2, 0, 1, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2,
        1, 2, 1, 0, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1,
        1, 0, 1, 2, 1, 1, 2, 0, 2, 2, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0,
        1, 1, 1, 0, 2, 0, 0, 1, 1, 0, 2, 0, 1, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 2, 2, 1, 0, 0,
        0, 2, 0, 2, 1, 1, 1, 0, 1, 0, 2, 2, 0, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0, 1,
        0, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0,
        2, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
        0, 1, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2,
        0, 0, 0, 2, 0, 0, 0, 0, 2, 1, 1, 0, 1, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2,
        1, 0, 1, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0, 0, 2,
        2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 1,
        0, 0, 1, 0, 2, 1, 2, 1, 2, 0, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2,
        2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 1, 0, 1, 0, 0,
        2, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 1, 2, 2 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0 ]
        /* order = 1536 = 2^9 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 2, 1, 0,
        1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 0, 2 ]
        /* order = 1872 = 2^4 * 3^2 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1,
        2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 2, 2, 1,
        2, 2, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 0, 0 ]
        /* order = 2028 = 2^2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0,
        0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 2,
        1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 1, 1 ]
        /* order = 2028 = 2^2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2,
        0, 1, 0, 0, 1, 1, 1, 2, 2, 0, 1, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 0, 2, 2, 1, 1, 0,
        0, 1, 2, 2, 2, 2, 2, 0, 1, 0, 1, 2, 1, 2 ]
        /* order = 2028 = 2^2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 2,
        0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 2, 0, 0 ]
        /* order = 2028 = 2^2 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 1,
        1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 1, 1, 2, 1, 2, 0, 2, 2 ]
        /* order = 2184 = 2^3 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1,
        2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 1, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 1, 1,
        1, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, 2, 0 ]
        /* order = 2184 = 2^3 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1,
        1, 1, 2, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 0, 0, 1,
        0, 1, 1, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 0 ]
        /* order = 2184 = 2^3 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2,
        0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 1, 0, 0, 2, 0,
        2, 1, 1, 1, 0, 1, 1, 2, 1, 0, 0, 1, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1,
        1, 0, 0, 2, 1, 0, 2, 2, 2, 2, 0, 2, 0, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0,
        2, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1,
        0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 2, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2,
        1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1,
        0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 2, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2,
        0, 2, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0, 0,
        0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1,
        2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 0, 1, 0, 2 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1,
        0, 0, 1, 0, 2, 1, 2, 0, 2, 0, 1, 1, 1, 2 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 1, 2, 1, 0, 2, 1, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2,
        0, 0, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 2, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 1, 0,
        2, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 1, 1, 2, 2, 1, 0, 0,
        1, 2, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0,
        0, 0, 2, 2, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 1, 0, 2, 1,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1 ]
        /* order = 3042 = 2 * 3^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2,
        2, 0, 0, 2, 1, 0, 2, 2, 0, 1, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 0, 2,
        0, 2, 1, 2, 1, 0, 1, 0, 0, 2, 1, 2, 2, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 0,
        0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0,
        0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 0, 0,
        2, 2, 1, 0, 2, 1, 1, 1, 0, 2, 1, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2,
        2, 2, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 1, 1, 1,
        0, 2, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 1, 2, 1, 1, 0,
        2, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 2, 0, 0, 0,
        1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 0,
        1, 2, 1, 0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1,
        0, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2,
        2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 0, 0, 0, 1,
        2, 1, 1, 2, 0, 0, 2, 1, 1, 1, 0, 0, 2, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2,
        1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
        0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0,
        2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 1, 0, 1, 2, 2,
        1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 1, 1, 1, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 2,
        0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 1, 0, 2, 1, 0, 0,
        1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0,
        2, 1, 2, 0, 1, 2, 0, 0, 1, 0, 0, 2, 2, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0,
        1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
        0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 1, 0, 0, 2, 2, 1, 2, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 1,
        2, 2, 0, 1, 2, 1, 2, 0, 0, 1, 1, 1, 0, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0,
        2, 0, 1, 0, 0, 2, 0, 2, 1, 1, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 1,
        0, 2, 0, 2, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 1,
        0, 1, 1, 0, 1, 2, 2, 0, 0, 2, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 0, 1, 1, 1,
        0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0,
        2, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 1, 2, 0, 1,
        0, 0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2,
        2, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 1, 1, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 2,
        2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 1, 0, 1, 1, 0,
        2, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 1, 2, 2, 0, 1,
        1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 1, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0,
        0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 1, 1, 1, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1,
        2, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 0, 0,
        2, 1, 2, 1, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 2,
        2, 0, 0, 2, 2, 0, 2, 1, 0, 1, 0, 0, 2, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0,
        0, 2, 1, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, 1,
        0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 1, 1, 2, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1,
        1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 0, 2 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2,
        0, 1, 1, 0, 1, 2, 2, 1, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 1, 0,
        2, 2, 2, 2, 1, 2, 0, 0, 1, 0, 1, 0, 2, 1 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2,
        1, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 2, 1,
        1, 0, 0, 2, 0, 2, 1, 1, 2, 1, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2,
        0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
        0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2,
        0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
        /* order = 3072 = 2^10 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
        0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2 ]
        /* order = 4056 = 2^3 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2,
        0, 1, 1, 2, 2, 1, 0, 0, 1, 2, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 2, 2, 2, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0 ]
        /* order = 4056 = 2^3 * 3 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,
        2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 1, 1, 0,
        0, 2, 1, 2, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0 ]
        /* order = 4368 = 2^4 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 0, 1, 1, 1,
        2, 2, 2, 1, 2, 0, 2, 1, 1, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0,
        1, 2, 1, 0, 2, 2, 0, 0, 1, 1, 2, 1, 2, 0 ]
        /* order = 4608 = 2^9 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ]
        /* order = 4608 = 2^9 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1,
        0, 0, 1, 2, 0, 1, 1, 0, 1, 1, 2, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1,
        0, 2, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 2 ]
        /* order = 4608 = 2^9 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 2, 1,
        1, 0, 1, 2, 0, 0, 1, 0, 2, 2, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 2, 1,
        0, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 0, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 1, 2, 0, 2, 2, 2, 1, 1,
        0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 0 ]
        /* order = 4608 = 2^9 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1,
        2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0,
        2, 1, 2, 1, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0 ]
        /* order = 6084 = 2^2 * 3^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 2, 0, 1,
        0, 1, 2, 2, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2,
        2, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 1, 1 ]
        /* order = 6084 = 2^2 * 3^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0,
        2, 0, 2, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 1, 1,
        1, 2, 1, 0, 1, 0, 2, 2, 2, 1, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1,
        0, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1,
        1, 1, 0, 2, 2, 1, 0, 2, 2, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 0, 1,
        0, 0, 2, 0, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 1, 1,
        0, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 1, 1, 1, 2, 0,
        1, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 1, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2,
        1, 1, 0, 2, 2, 2, 0, 1, 2, 2, 0, 1, 2, 2 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 0, 2, 0, 0, 0, 1, 0,
        0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 2, 2, 1, 1, 1, 0,
        0, 2, 1, 2, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0,
        0, 0, 2, 1, 2, 1, 1, 0, 2, 0, 0, 0, 1, 1 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1,
        0, 0, 1, 2, 2, 1, 1, 0, 2, 1, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 2, 2, 0, 2, 0, 0,
        2, 0, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1,
        0, 0, 0, 0, 2, 0, 2, 1, 1, 2, 0, 0, 2, 0 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1,
        1, 2, 2, 2, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0,
        1, 2, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1,
        2, 0, 2, 0, 1, 1, 2, 0, 2, 2, 0, 1, 2, 1 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0,
        0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1,
        0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0,
        1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 1,
        0, 2, 0, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1,
        2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 1, 0, 0, 2, 1, 2, 2, 0, 2, 1, 0,
        1, 0, 2, 2, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2 ]
        /* order = 6144 = 2^11 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0,
        1, 0, 2, 0, 0, 2, 1, 1, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 1, 1, 2, 1, 0, 0, 0,
        1, 0, 0, 2, 1, 0, 1, 2, 1, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 1, 0, 1,
        1, 0, 1, 1, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2 ]
        /* order = 9216 = 2^10 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2,
        0, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2 ]
        /* order = 9216 = 2^10 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1,
        2, 1, 0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 1, 1, 1, 2, 0,
        0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 2, 1, 2 ]
        /* order = 9216 = 2^10 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2,
        1, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 0, 1, 1, 0, 0, 2, 1, 2, 2, 0 ]
        /* order = 9216 = 2^10 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 2, 2, 0, 2,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 0, 1, 2, 2, 1,
        2, 0, 2, 1, 1, 0, 2, 2, 1, 2, 2, 2, 0, 0 ]
        /* order = 12168 = 2^3 * 3^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 2, 2, 2,
        1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0,
        2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 2, 2, 1, 0,
        1, 2, 2, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 2 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0, 2, 1, 0,
        2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2,
        2, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1,
        0, 2, 0, 0, 0, 0, 1, 2, 0, 2, 2, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 0, 2, 1, 2,
        0, 2, 0, 0, 1, 1, 0, 2, 2, 2, 2, 1, 0, 1 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0,
        1, 2, 1, 1, 0, 1, 0, 0, 1, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2,
        2, 2, 1, 2, 2, 2, 2, 0, 1, 0, 1, 2, 2, 2 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0,
        1, 2, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2,
        1, 2, 0, 1, 1, 0, 1, 0, 0, 2, 2, 1, 0, 1 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        1, 2, 2, 0, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 1, 0, 0, 0, 0, 0,
        0, 2, 2, 0, 1, 0, 1, 1, 2, 2, 2, 2, 1, 0 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 2, 2,
        2, 2, 2, 2, 1, 1, 2, 2, 2, 0, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2,
        2, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 2, 2, 0 ]
        /* order = 12288 = 2^12 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2,
        0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 ]
        /* order = 13824 = 2^9 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2,
        1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 0, 1, 2, 2, 0, 2, 1, 2, 0, 2 ]
        /* order = 13824 = 2^9 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1,
        0, 1, 1, 0, 2, 2, 2, 0, 2, 1, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1,
        0, 1, 2, 2, 0, 2, 2, 2, 2, 0, 1, 1, 2, 0 ]
        /* order = 18432 = 2^11 * 3^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 1, 1, 0, 1, 0,
        2, 0, 0, 0, 2, 1, 1, 1, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 0, 1, 2, 0, 1, 1,
        1, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 2, 2, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 1, 2, 0, 0, 2,
        0, 2, 2, 1, 1, 2, 1, 2, 1, 2, 0, 2, 0, 0 ]
        /* order = 24576 = 2^13 * 3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1,
        0, 0, 2, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0,
        0, 1, 2, 0, 0, 0, 1, 2, 1, 1, 0, 1, 2, 2 ]
        /* order = 27648 = 2^10 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0,
        0, 2, 1, 1, 1, 2, 0, 1, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 2,
        1, 0, 2, 2, 1, 2, 2, 2, 1, 1, 2, 0, 1, 2 ]
        /* order = 27648 = 2^10 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 0, 2, 0, 1, 2, 2, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1,
        1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2 ]
        /* order = 27648 = 2^10 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2,
        1, 0, 0, 0, 2, 2, 1, 1, 1, 1, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 0,
        2, 2, 1, 2, 2, 1, 2, 1, 2, 0, 1, 0, 0, 1 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 0, 0, 2,
        2, 1, 2, 0, 0, 1, 0, 2, 2, 1, 0, 1, 2, 2 ]
        /* order = 27648 = 2^10 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0,
        0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0 ]
        /* order = 41472 = 2^9 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 1, 0, 0, 2,
        1, 2, 2, 2, 2, 1, 2, 0, 1, 0, 2, 1, 1, 2 ]
        /* order = 55296 = 2^11 * 3^3 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1,
        1, 0, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2, 1, 0, 1, 2, 2, 0,
        1, 0, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2,
        0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 1 ]
        /* order = 82944 = 2^10 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0,
        2, 2, 0, 1, 2, 2, 2, 1, 1, 0, 2, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0,
        2, 0, 1, 1, 1, 2, 1, 0, 2, 1, 2, 2, 1, 2 ]
        /* order = 82944 = 2^10 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1,
        0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 2, 2, 0,
        0, 1, 0, 1, 1, 1, 2, 2, 0, 1, 0, 1, 2, 0 ]
        /* order = 82944 = 2^10 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 1, 2, 0, 2, 0, 0, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 1, 1,
        2, 2, 1, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0 ]
        /* order = 165888 = 2^11 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 2, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2,
        1, 0, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2, 1, 0 ]
        /* order = 165888 = 2^11 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1,
        1, 1, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 1, 1, 1, 2, 1,
        1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2 ]
        /* order = 331776 = 2^12 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 1, 0,
        2, 1, 2, 0, 0, 0, 2, 1, 0, 2, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0,
        2, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 1, 1 ]
        /* order = 331776 = 2^12 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
        0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0,
        0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 331776 = 2^12 * 3^4 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 0, 2, 1, 1, 2, 0, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 2, 2, 1, 0,
        2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2 ]
        /* order = 663552 = 2^13 * 3^4 */ >
];