sol4_3:= [ 
    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0 ]
        /* order = 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 0, 0 ]
        /* order = 10 = 2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 2, 2, 2 ]
        /* order = 10 = 2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0 ]
        /* order = 16 = 2^4 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 16 = 2^4 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ]
        /* order = 16 = 2^4 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 ]
        /* order = 16 = 2^4 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 16 = 2^4 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 2 ]
        /* order = 20 = 2^2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0 ]
        /* order = 20 = 2^2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 2, 0, 2, 1, 0, 2, 1, 1, 2, 1, 1, 1 ]
        /* order = 20 = 2^2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]
        /* order = 20 = 2^2 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 1, 0, 1 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 1 ],
        \[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 0, 0, 1, 0, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 0 ],
        \[ 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 0 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1 ]
        /* order = 32 = 2^5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2 ]
        /* order = 40 = 2^3 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 2, 1 ]
        /* order = 40 = 2^3 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0 ]
        /* order = 40 = 2^3 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 2 ]
        /* order = 40 = 2^3 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 2, 0, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0 ]
        /* order = 40 = 2^3 * 5 */ >,

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

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

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 1, 2, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 1, 2, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 2 ],
        \[ 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1 ],
        \[ 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 2, 1, 1, 2, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 0, 0 ],
        \[ 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 1, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 2, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 2, 0, 2 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2 ],
        \[ 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 2, 2 ]
        /* order = 64 = 2^6 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1 ]
        /* order = 80 = 2^4 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 2, 2, 1, 1, 2 ]
        /* order = 80 = 2^4 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 0 ],
        \[ 1, 2, 0, 0, 0, 2, 0, 0, 2, 1, 1, 1, 2, 2, 0, 2 ]
        /* order = 80 = 2^4 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 1 ]
        /* order = 80 = 2^4 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 1, 1, 2, 1 ]
        /* order = 80 = 2^4 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 2, 2, 2, 1, 2, 0, 1, 0, 0, 0, 0, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 2, 2, 0, 1, 1, 2, 2, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 1 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 1 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 2, 0, 2, 2, 2, 1, 1, 2, 1, 2, 1, 0 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 2, 1, 1, 2, 0, 1, 0, 0, 0, 1, 0, 2 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 2, 1, 0, 1, 2 ],
        \[ 1, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 1, 0, 0, 2, 1 ]
        /* order = 96 = 2^5 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 1, 1 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 1 ],
        \[ 2, 0, 2, 0, 1, 1, 0, 2, 0, 1, 2, 0, 1, 2, 1, 1 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0 ],
        \[ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 1, 0, 1, 1, 0 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1 ],
        \[ 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 1, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1 ],
        \[ 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 1, 2, 0, 0, 0 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 2, 0, 0, 0, 1 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 ],
        \[ 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0 ]
        /* order = 128 = 2^7 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 1, 0, 2, 1, 0, 0 ]
        /* order = 160 = 2^5 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 1, 1, 2, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 0, 2 ]
        /* order = 160 = 2^5 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1 ]
        /* order = 160 = 2^5 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
        \[ 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 0, 2, 1, 2, 2, 1 ]
        /* order = 160 = 2^5 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2 ],
        \[ 0, 0, 1, 0, 1, 2, 2, 2, 0, 2, 1, 1, 2, 2, 1, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 0, 0, 1, 2, 1, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 1 ],
        \[ 2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 1, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 1, 0, 0 ],
        \[ 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 2, 0, 2 ],
        \[ 0, 0, 2, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 2, 0, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 1, 1, 1, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2 ],
        \[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ]
        /* order = 192 = 2^6 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0, 1, 2, 1 ],
        \[ 2, 2, 1, 0, 0, 2, 1, 1, 1, 2, 2, 1, 0, 1, 2, 0 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 2 ],
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1, 1 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 0, 1, 0 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1 ],
        \[ 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 1, 2, 1, 1, 0, 0 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 1, 2, 1, 1, 1, 2 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0 ],
        \[ 0, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 2, 2, 1, 0, 0 ]
        /* order = 256 = 2^8 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 1, 1, 1 ]
        /* order = 288 = 2^5 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 0, 1, 1, 1 ],
        \[ 2, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 2 ]
        /* order = 320 = 2^6 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 0, 1, 1, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1 ]
        /* order = 320 = 2^6 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 0, 2 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 0, 1, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 1 ],
        \[ 0, 0, 0, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 0, 0 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1 ]
        /* order = 384 = 2^7 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2 ],
        \[ 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 2 ]
        /* order = 512 = 2^9 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 2, 0, 1, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 1, 0, 0, 0, 2 ],
        \[ 0, 0, 0, 1, 2, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 1 ]
        /* order = 576 = 2^6 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 1, 0, 2 ]
        /* order = 640 = 2^7 * 5 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2 ]
        /* order = 768 = 2^8 * 3 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 1, 1 ],
        \[ 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 1 ],
        \[ 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 0 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0 ],
        \[ 2, 2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 1 ]
        /* order = 1152 = 2^7 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2 ],
        \[ 0, 0, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 0, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0 ]
        /* order = 2304 = 2^8 * 3^2 */ >,

    MatrixGroup<4, GF(3) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1 ],
        \[ 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 1, 1, 1, 1 ]
        /* order = 4608 = 2^9 * 3^2 */ >
];