insol6_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,
        0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 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, 0, 0, 0, 1 ]
        /* order = 60 = 2^2 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1,
        2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 120 = 2^3 * 3 * 5 */ >,

    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, 2, 0, 2, 2, 2, 1, 0, 1, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2,
        2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 0, 1 ]
        /* order = 120 = 2^3 * 3 * 5 */ >,

    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,
        0, 1, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0 ],
        \[ 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1,
        2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1 ]
        /* order = 120 = 2^3 * 3 * 5 */ >,

    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, 2, 0, 0, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 1, 0, 1, 1, 1, 2,
        1, 2, 2, 1, 1, 2, 0, 2, 2, 1, 1, 1, 2, 2 ]
        /* order = 168 = 2^3 * 3 * 7 */ >,

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

    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, 1, 0, 1, 2, 2, 1, 0, 2, 1, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 2, 2,
        1, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0 ]
        /* order = 240 = 2^4 * 3 * 5 */ >,

    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, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0,
        2, 2, 0, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0 ]
        /* order = 240 = 2^4 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 1, 0, 0, 2,
        2, 0, 1, 2, 0, 1, 0, 1, 2, 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, 0, 0,
        0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2 ]
        /* order = 240 = 2^4 * 3 * 5 */ >,

    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, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 2, 0, 0,
        2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1 ]
        /* order = 240 = 2^4 * 3 * 5 */ >,

    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, 1, 1, 2, 0, 2, 1, 2, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2,
        0, 0, 0, 2, 2, 1, 2, 0, 0, 1, 1, 2, 0, 2 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

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

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

    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, 0,
        0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2,
        2, 2, 0, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 0 ]
        /* order = 360 = 2^3 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2,
        1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 1, 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, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0,
        0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        1, 1, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2,
        1, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 1,
        2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    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,
        2, 1, 0, 2, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1,
        1, 1, 0, 2, 0, 1, 2, 2, 0, 0, 2, 2, 1, 2 ]
        /* order = 672 = 2^5 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2,
        1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1,
        0, 2, 2, 1, 0, 1, 2, 2, 0, 1, 2, 0, 1, 1 ]
        /* order = 672 = 2^5 * 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, 2, 0, 2,
        0, 0, 2, 1, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 1, 1,
        2, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0 ]
        /* order = 672 = 2^5 * 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, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1,
        2, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0 ]
        /* order = 672 = 2^5 * 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, 0, 1, 1,
        1, 2, 1, 2, 2, 1, 2, 1, 0, 1, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 2, 0, 2, 1,
        1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 0, 2, 1 ]
        /* order = 720 = 2^4 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 2, 1, 2, 1, 2, 2, 2, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0,
        0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 2, 0, 0 ]
        /* order = 720 = 2^4 * 3^2 * 5 */ >,

    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, 0, 0, 2, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0,
        0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 1 ]
        /* order = 720 = 2^4 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2,
        0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,
        1, 1, 1, 1, 2, 2, 2, 2, 1, 0, 0, 0, 0, 0 ]
        /* order = 720 = 2^4 * 3^2 * 5 */ >,

    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, 1, 1, 0, 1, 2, 0, 1, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2,
        2, 1, 1, 1, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0 ]
        /* order = 720 = 2^4 * 3^2 * 5 */ >,

    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, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 2,
        1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 2, 2, 0, 1 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0,
        2, 1, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 1, 2, 2, 2, 2, 1,
        2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 0, 2, 2 ]
        /* order = 1320 = 2^3 * 3 * 5 * 11 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 0, 1, 1, 2, 1, 2, 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,
        1, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2 ]
        /* order = 1344 = 2^6 * 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, 0, 1, 1,
        2, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2,
        1, 1, 2, 1, 1, 2, 0, 2, 1, 2, 2, 2, 0, 1 ]
        /* order = 1344 = 2^6 * 3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1,
        0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1,
        1, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 0, 2, 1 ]
        /* order = 1344 = 2^6 * 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, 2, 0,
        2, 2, 1, 2, 1, 2, 1, 2, 0, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0,
        1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 0, 2, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1,
        0, 1, 2, 0, 0, 1, 1, 2, 2, 0, 2, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 2, 0, 2, 2, 1, 0,
        2, 2, 2, 1, 2, 0, 0, 0, 1, 2, 2, 1, 1, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    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,
        0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1, 1, 2,
        2, 2, 1, 2, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0,
        0, 1, 1, 2, 0, 1, 0, 2, 0, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1,
        1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2,
        1, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        2, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 2, 1, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    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, 0,
        0, 1, 2, 2, 0, 1, 2, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 1, 2, 1,
        1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    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, 1, 1, 2, 2, 2, 0, 0, 0, 2, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 1, 0, 1,
        0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 1, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    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, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 1, 2, 0, 2, 2, 1,
        0, 1, 1, 2, 1, 0, 1, 0, 2, 2, 0, 2, 0, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 1, 1,
        2, 1, 1, 0, 0, 1, 1, 0, 2, 0, 2, 0, 1, 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, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 2, 2, 2, 2,
        2, 1, 1, 2, 0, 0, 1, 2, 1, 2, 0, 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, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    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, 2,
        2, 0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 0,
        2, 1, 0, 2, 1, 2, 1, 0, 2, 2, 2, 1, 1, 0 ]
        /* order = 2184 = 2^3 * 3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 0,
        2, 0, 2, 1, 0, 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, 1, 0, 1, 2, 1,
        2, 1, 1, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0 ]
        /* order = 2520 = 2^3 * 3^2 * 5 * 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, 1, 2,
        2, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0,
        0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 1, 1 ]
        /* order = 2688 = 2^7 * 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, 1,
        0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 1, 2, 0,
        2, 2, 1, 0, 2, 2, 0, 0, 0, 1, 1, 0, 2, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 2, 0, 0, 0, 1, 1, 2, 2, 0, 1, 2, 2, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0,
        0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 0, 0, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 0, 0, 1, 2, 1, 1,
        0, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 2, 0, 2, 0, 2, 1, 0, 2, 1, 1, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 0, 2, 1, 2, 0,
        0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 2, 2, 2, 2, 2, 2, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,
        2, 2, 2, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 0, 1, 2, 2, 1, 2, 2, 2, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 0, 2, 1, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0,
        0, 1, 0, 0, 2, 0, 2, 0, 1, 1, 0, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1,
        2, 2, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 2, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 2, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 1, 2, 0,
        0, 0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 2, 1, 1 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2,
        1, 2, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2,
        1, 1, 0, 2, 1, 2, 2, 0, 1, 1, 0, 2, 1, 2 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 2, 1, 2, 2, 2, 1, 2, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 1,
        1, 1, 0, 1, 2, 2, 0, 2, 0, 2, 1, 1, 1, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2,
        2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2, 2, 2, 2, 1,
        0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 2, 0, 2, 2, 0, 1, 0, 2, 1, 0, 1, 1,
        2, 0, 0, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    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, 0,
        1, 0, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 0, 2, 1, 2,
        1, 1, 0, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 0 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1,
        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, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1,
        0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 1, 0 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    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, 2,
        0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        1, 0, 2, 1, 2, 0, 0, 0, 1, 2, 1, 2, 0, 2 ]
        /* order = 5040 = 2^4 * 3^2 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0,
        0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        2, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0 ]
        /* order = 5040 = 2^4 * 3^2 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2,
        2, 2, 1, 0, 0, 0, 0, 0, 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, 1, 0, 0,
        0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2 ]
        /* order = 5040 = 2^4 * 3^2 * 5 * 7 */ >,

    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, 2,
        1, 0, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 2, 0, 2,
        0, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 0 ]
        /* order = 5616 = 2^4 * 3^3 * 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, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 2, 2, 0, 1,
        0, 2, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 0 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 1, 1, 2, 1, 1, 2, 2, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 2, 1,
        1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    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,
        1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0,
        0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    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, 2, 0, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 0,
        1, 1, 1, 0, 2, 0, 0, 2, 1, 2, 1, 2, 0, 2 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    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, 0, 0, 1, 0, 2, 2, 2, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 1, 1, 0, 2, 1,
        1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 2, 2 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 0, 1, 1, 1, 1,
        2, 2, 2, 0, 2, 0, 0, 0, 1, 1, 1, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 2, 1, 0, 1, 1, 2, 2,
        0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2,
        2, 2, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2,
        0, 1, 2, 1, 1, 2, 1, 1, 1, 2, 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, 0,
        0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 1, 0, 0, 2,
        0, 0, 2, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 1 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    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, 0,
        0, 1, 2, 2, 0, 2, 2, 0, 2, 1, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 1, 0, 1, 1, 1,
        1, 1, 2, 2, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2 ]
        /* order = 6048 = 2^5 * 3^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 0, 1, 0,
        1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2,
        0, 1, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 2, 1 ]
        /* order = 7680 = 2^9 * 3 * 5 */ >,

    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, 2, 1, 0, 1, 1, 0, 2, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2,
        0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 1 ]
        /* order = 10080 = 2^5 * 3^2 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 0, 0, 2, 0, 2,
        1, 0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0,
        0, 1, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0 ]
        /* order = 11232 = 2^5 * 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, 1, 0, 0,
        2, 2, 1, 1, 2, 2, 0, 1, 1, 0, 2, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1,
        0, 2, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1 ]
        /* order = 11232 = 2^5 * 3^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 2, 1,
        1, 0, 2, 2, 0, 0, 0, 0, 2, 1, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1,
        0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 2, 1, 1, 1, 0,
        1, 0, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 1, 1 ]
        /* order = 11520 = 2^8 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 0, 1,
        0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0,
        1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 2, 1, 2 ]
        /* order = 11520 = 2^8 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 1,
        2, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2,
        1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2 ]
        /* order = 12096 = 2^6 * 3^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1,
        1, 0, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1 ],
        \[ 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1,
        0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 2 ]
        /* order = 12096 = 2^6 * 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, 0, 0, 1,
        2, 2, 1, 0, 0, 2, 1, 1, 1, 2, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 1, 1, 1, 0,
        0, 1, 1, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0 ]
        /* order = 19656 = 2^3 * 3^3 * 7 * 13 */ >,

    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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0,
        0, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 2, 1, 0 ]
        /* order = 22464 = 2^6 * 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, 1, 0, 1,
        0, 0, 2, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0,
        2, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0 ]
        /* order = 22464 = 2^6 * 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, 1, 2, 0,
        0, 2, 0, 0, 2, 1, 1, 0, 2, 0, 0, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1,
        2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 22464 = 2^6 * 3^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0,
        2, 0, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0,
        1, 2, 2, 0, 0, 0, 1, 2, 2, 2, 1, 2, 1, 1 ]
        /* order = 23040 = 2^9 * 3^2 * 5 */ >,

    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, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 2, 1, 0, 2, 2,
        0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 0, 2, 1 ]
        /* order = 23040 = 2^9 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2,
        2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1,
        1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 0, 0, 1 ]
        /* order = 23040 = 2^9 * 3^2 * 5 */ >,

    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, 0,
        2, 0, 1, 2, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2,
        0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 0 ]
        /* order = 24192 = 2^7 * 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, 0, 2, 2, 0,
        0, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 2, 1, 2,
        0, 0, 2, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 2 ]
        /* order = 24192 = 2^7 * 3^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 2, 2,
        1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2,
        1, 0, 0, 2, 0, 2, 1, 1, 1, 0, 2, 1, 2, 0 ]
        /* order = 24192 = 2^7 * 3^3 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 2,
        1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1,
        0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 1 ]
        /* order = 39312 = 2^4 * 3^3 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1,
        0, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2,
        2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 1, 0, 0, 2 ]
        /* order = 40320 = 2^7 * 3^2 * 5 * 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, 0,
        1, 0, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 2, 1,
        2, 1, 0, 0, 2, 1, 1, 1, 0, 2, 0, 2, 2, 0 ]
        /* order = 44928 = 2^7 * 3^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2,
        2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2,
        2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 2, 0, 0, 0 ]
        /* order = 44928 = 2^7 * 3^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1,
        2, 1, 0, 0, 0, 2, 0, 1, 2, 1, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1,
        2, 0, 0, 2, 2, 1, 0, 1, 2, 2, 2, 2, 1, 2 ]
        /* order = 44928 = 2^7 * 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, 1, 2,
        1, 0, 1, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 0,
        2, 2, 2, 1, 2, 0, 1, 2, 2, 0, 0, 1, 1, 1 ]
        /* order = 44928 = 2^7 * 3^3 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 2, 2, 1,
        0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2,
        1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 2 ]
        /* order = 46080 = 2^10 * 3^2 * 5 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1, 2, 2,
        0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1,
        0, 1, 0, 2, 0, 1, 0, 2, 1, 0, 0, 2, 0, 2 ]
        /* order = 48384 = 2^8 * 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, 0, 2, 1, 1,
        1, 1, 0, 0, 2, 1, 0, 1, 1, 2, 0, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1,
        2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 1 ]
        /* order = 48384 = 2^8 * 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, 1, 0, 2,
        1, 0, 0, 0, 0, 2, 1, 0, 1, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 1, 2, 2,
        0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 1, 0, 0, 2 ]
        /* order = 48384 = 2^8 * 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, 2, 2, 0, 1,
        1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 1, 1, 2, 0,
        2, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 2, 1, 1 ]
        /* order = 58968 = 2^3 * 3^4 * 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, 2, 1, 2,
        2, 2, 0, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2,
        2, 0, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 1, 1 ]
        /* order = 80640 = 2^8 * 3^2 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2,
        2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 2, 0, 1, 2, 1, 2, 1, 2, 2, 0, 0 ]
        /* order = 80640 = 2^8 * 3^2 * 5 * 7 */ >,

    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, 2,
        2, 0, 1, 2, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 1,
        0, 1, 1, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 1 ]
        /* order = 80640 = 2^8 * 3^2 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 2, 0, 1, 1, 0, 0, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0,
        1, 1, 2, 0, 1, 2, 2, 2, 0, 1, 1, 2, 0, 1 ]
        /* order = 89856 = 2^8 * 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, 2, 2, 1,
        0, 2, 1, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 1, 1, 0, 1, 2, 2,
        1, 1, 2, 1, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2 ]
        /* order = 96768 = 2^9 * 3^3 * 7 */ >,

    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, 2, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0,
        2, 0, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1 ]
        /* order = 117936 = 2^4 * 3^4 * 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, 0,
        0, 0, 1, 1, 1, 2, 1, 2, 1, 2, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 0, 0, 1, 1,
        2, 1, 0, 1, 0, 1, 1, 1, 0, 2, 2, 1, 2, 2 ]
        /* order = 134784 = 2^7 * 3^4 * 13 */ >,

    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 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0,
        0, 2, 2, 1, 2, 0, 2, 2, 2, 1, 1, 2, 0, 2 ]
        /* order = 161280 = 2^9 * 3^2 * 5 * 7 */ >,

    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, 0,
        2, 0, 2, 2, 0, 2, 0, 0, 1, 1, 1, 1, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 0, 0,
        2, 2, 1, 0, 1, 1, 2, 1, 2, 2, 1, 0, 0, 2 ]
        /* order = 190080 = 2^7 * 3^3 * 5 * 11 */ >,

    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, 0,
        1, 2, 0, 2, 2, 2, 0, 1, 2, 1, 2, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 0,
        1, 2, 0, 2, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0 ]
        /* order = 255528 = 2^3 * 3^3 * 7 * 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, 1, 0, 2,
        2, 0, 0, 1, 1, 0, 1, 2, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 1, 1, 2, 1,
        2, 1, 0, 0, 0, 1, 1, 2, 2, 2, 0, 1, 1, 1 ]
        /* order = 269568 = 2^8 * 3^4 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0,
        0, 1, 0, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 1, 2, 0, 0, 0, 0,
        0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1 ]
        /* order = 511056 = 2^4 * 3^3 * 7 * 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, 1, 1, 2,
        2, 2, 0, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 2, 0,
        2, 2, 1, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 1 ]
        /* order = 766584 = 2^3 * 3^4 * 7 * 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, 2, 0, 2,
        0, 1, 2, 1, 1, 2, 0, 0, 0, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 1,
        2, 1, 1, 1, 2, 0, 1, 0, 1, 2, 0, 2, 2, 1 ]
        /* order = 1533168 = 2^4 * 3^4 * 7 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 1, 0, 0,
        1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1,
        0, 1, 1, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1 ]
        /* order = 6065280 = 2^7 * 3^6 * 5 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2,
        1, 2, 2, 0, 2, 1, 0, 0, 1, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2,
        0, 1, 2, 2, 2, 2, 1, 2, 2, 1, 0, 1, 1, 2 ]
        /* order = 6531840 = 2^8 * 3^6 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2,
        0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0,
        0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 1 ]
        /* order = 12130560 = 2^8 * 3^6 * 5 * 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, 2,
        0, 2, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0,
        0, 2, 0, 2, 1, 0, 1, 2, 2, 0, 0, 0, 0, 2 ]
        /* order = 12130560 = 2^8 * 3^6 * 5 * 13 */ >,

    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, 1,
        2, 2, 1, 0, 1, 2, 1, 2, 0, 2, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2,
        2, 0, 0, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 2 ]
        /* order = 12130560 = 2^8 * 3^6 * 5 * 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, 0,
        1, 0, 2, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 2,
        1, 2, 0, 2, 1, 1, 1, 2, 0, 1, 0, 0, 0, 0 ]
        /* order = 13063680 = 2^9 * 3^6 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 1, 0, 2, 1,
        0, 2, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2,
        2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0 ]
        /* order = 13063680 = 2^9 * 3^6 * 5 * 7 */ >,

    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, 0, 1, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2,
        0, 0, 0, 1, 1, 2, 2, 1, 1, 0, 2, 2, 1, 1 ]
        /* order = 13063680 = 2^9 * 3^6 * 5 * 7 */ >,

    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,
        1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0,
        0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 1, 1, 1, 1 ]
        /* order = 24261120 = 2^9 * 3^6 * 5 * 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, 0, 0,
        0, 2, 0, 0, 2, 1, 1, 0, 1, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2,
        1, 0, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0 ]
        /* order = 24261120 = 2^9 * 3^6 * 5 * 13 */ >,

    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, 1, 2, 1, 0, 1, 2, 2, 1, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 2, 1, 2,
        1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 2, 1 ]
        /* order = 24261120 = 2^9 * 3^6 * 5 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1,
        0, 0, 0, 2, 0, 2, 0, 1, 2, 1, 2, 0, 0, 1 ]
        /* order = 26127360 = 2^10 * 3^6 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2,
        2, 1, 0, 2, 2, 1, 0, 2, 0, 2, 2, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2,
        0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 1, 0, 2, 2 ]
        /* order = 26127360 = 2^10 * 3^6 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0,
        1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2,
        1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 2, 0, 0, 1 ]
        /* order = 26127360 = 2^10 * 3^6 * 5 * 7 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0,
        0, 1, 1, 1, 0, 1, 2, 0, 0, 2, 2, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 0, 0, 0, 1, 1, 0,
        1, 1, 2, 1, 2, 2, 1, 0, 0, 2, 2, 2, 1, 1 ]
        /* order = 42456960 = 2^7 * 3^6 * 5 * 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, 2,
        2, 2, 1, 0, 2, 2, 0, 1, 2, 0, 1, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 1, 2, 1, 2,
        2, 2, 1, 2, 2, 2, 0, 1, 2, 0, 2, 0, 1, 1 ]
        /* order = 48522240 = 2^10 * 3^6 * 5 * 13 */ >,

    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, 2, 0, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0, 0,
        0, 2, 1, 2, 0, 1, 2, 2, 1, 1, 2, 1, 0, 0 ]
        /* order = 52254720 = 2^11 * 3^6 * 5 * 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, 1, 0,
        0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 0, 0,
        0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 63078912 = 2^9 * 3^6 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 1, 0, 2,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2,
        0, 0, 2, 0, 0, 2, 1, 1, 0, 1, 1, 2, 1, 1 ]
        /* order = 84913920 = 2^8 * 3^6 * 5 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2,
        2, 0, 2, 2, 0, 2, 1, 2, 1, 1, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
        2, 2, 2, 2, 2, 2, 0, 0, 1, 0, 1, 0, 0, 0 ]
        /* order = 84913920 = 2^8 * 3^6 * 5 * 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, 1, 1, 1, 1, 0, 0, 0, 2, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 0, 0, 1, 2, 2,
        0, 2, 0, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0 ]
        /* order = 126157824 = 2^10 * 3^6 * 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, 0, 2,
        2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 0, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2,
        2, 0, 0, 2, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1 ]
        /* order = 126157824 = 2^10 * 3^6 * 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, 2, 0,
        2, 0, 2, 2, 0, 2, 0, 2, 1, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 1, 2, 2, 0, 1,
        2, 2, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 2, 2 ]
        /* order = 169827840 = 2^9 * 3^6 * 5 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 1, 1,
        0, 0, 1, 2, 1, 0, 0, 1, 2, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0,
        2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 0 ]
        /* order = 169827840 = 2^9 * 3^6 * 5 * 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, 0, 0, 2,
        1, 0, 2, 2, 2, 1, 0, 0, 1, 0, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 1, 2,
        0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0 ]
        /* order = 169827840 = 2^9 * 3^6 * 5 * 7 * 13 */ >,

    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,
        1, 0, 1, 2, 2, 1, 1, 2, 0, 2, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 2, 2,
        1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 1, 1, 1 ]
        /* order = 252315648 = 2^11 * 3^6 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 1,
        2, 2, 0, 2, 2, 2, 1, 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, 0, 2, 2, 2,
        0, 0, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 2, 2 ]
        /* order = 339655680 = 2^10 * 3^6 * 5 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0,
        0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 2,
        0, 1, 1, 1, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2 ]
        /* order = 339655680 = 2^10 * 3^6 * 5 * 7 * 13 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2, 2, 0,
        1, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1,
        1, 1, 1, 0, 1, 1, 1, 2, 0, 2, 1, 0, 0, 1 ]
        /* order = 339655680 = 2^10 * 3^6 * 5 * 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, 2, 0, 2,
        1, 2, 1, 2, 1, 2, 2, 0, 1, 1, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 1, 1, 1,
        0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2, 2, 0, 2 ]
        /* order = 679311360 = 2^11 * 3^6 * 5 * 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, 2, 2, 2,
        2, 2, 0, 1, 1, 0, 1, 2, 2, 0, 1, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1,
        1, 2, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2 ]
        /* order = 2^10 * 3^9 * 5 * 7 * 13 */ >,

    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, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1,
        0, 2, 0, 1, 2, 1, 2, 1, 1, 1, 2, 0, 0, 0 ]
        /* order = 2^11 * 3^9 * 5 * 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, 1, 2,
        0, 0, 2, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 2, 0,
        1, 0, 0, 2, 2, 2, 1, 2, 1, 2, 0, 1, 0, 1 ]
        /* order = 2^12 * 3^15 * 5 * 7 * 11^2 * 13^2 */ >,

    MatrixGroup<6, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
        0, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 1,
        0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 2, 0 ]
        /* order = 2^13 * 3^15 * 5 * 7 * 11^2 * 13^2 */ >
];