insol4_5:= [ 
    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 4, 2, 4, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 3, 1, 4, 0, 1, 1, 4, 1, 0, 2, 3, 1 ]
        /* order = 120 = 2^3 * 3 * 5 */ >,

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

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

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

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 3, 4, 3, 0, 3, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 2, 1, 1, 3, 3, 4, 3, 1, 1, 0 ]
        /* order = 360 = 2^3 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 0, 0, 0, 1, 2, 2, 0, 3, 0, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 3, 3, 2, 1, 2, 4, 0, 3 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 3, 2, 2, 3, 1, 2 ],
        \[ 0, 0, 1, 0, 2, 4, 3, 0, 1, 2, 2, 4, 2, 2, 1, 4 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 3, 0, 0 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 3, 4, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 1, 3, 0, 0, 2, 1, 0, 1, 0, 3, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 4, 3, 0, 1, 4, 1 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 3, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 2, 2, 4, 0, 0, 0, 1, 1, 1, 3 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 0, 4, 3, 3, 2, 2, 1 ],
        \[ 0, 0, 1, 0, 4, 0, 0, 0, 2, 0, 4, 4, 3, 4, 3, 1 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 4, 0, 0, 0, 4, 0, 0 ]
        /* order = 480 = 2^5 * 3 * 5 */ >,

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

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

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

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

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

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

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

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

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 3, 4, 0, 0, 1, 1, 0, 0 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 0, 4, 1, 0 ],
        \[ 0, 0, 1, 0, 4, 4, 4, 4, 0, 4, 4, 1, 0, 4, 1, 2 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 4, 3, 0, 4, 0, 1, 1, 3, 3, 0, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 4, 2, 2, 0, 1, 1 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 1, 4, 3 ],
        \[ 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 4, 1, 2, 2 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 3, 0, 4, 1, 2, 1, 0, 4, 4, 3 ],
        \[ 0, 0, 1, 0, 1, 4, 1, 1, 4, 0, 4, 4, 3, 3, 0, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 3, 0, 4, 2, 2, 2, 1, 0, 3, 2 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 3, 1, 0, 2, 0, 1, 4 ],
        \[ 0, 0, 1, 0, 4, 2, 4, 4, 1, 4, 1, 0, 3, 4, 2, 2 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 4, 1, 0, 0, 1, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 2, 0, 0, 4, 1, 0, 0 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 1, 0, 0, 0, 0, 3, 3, 0, 0, 4, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 3, 3, 0, 0, 1, 4, 0, 0 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 0, 0, 4, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 3 ],
        \[ 3, 3, 2, 0, 4, 2, 1, 4, 3, 1, 4, 2, 1, 1, 0, 1 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 1, 0, 0, 1, 2, 2, 2, 1, 0, 4, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 3, 3, 1, 4, 2, 0, 2 ]
        /* order = 960 = 2^6 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 3, 1, 2, 2, 0, 1, 4 ],
        \[ 0, 0, 1, 0, 2, 1, 4, 3, 0, 0, 4, 2, 2, 2, 3, 1 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 2, 2, 4, 0, 4, 4, 3 ],
        \[ 0, 0, 1, 0, 0, 2, 1, 2, 2, 2, 1, 0, 1, 0, 3, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 3, 4, 1, 3, 4, 1, 1 ],
        \[ 0, 0, 1, 0, 2, 4, 2, 2, 3, 3, 4, 2, 2, 2, 2, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 1, 1, 0, 3, 2, 1, 0, 4, 4, 4, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 4, 3, 3, 0, 4, 4, 4 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 4 ],
        \[ 0, 0, 1, 0, 4, 1, 4, 0, 2, 3, 2, 2, 3, 0, 2, 3 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 2, 2, 3, 3, 2, 0, 4 ],
        \[ 0, 0, 1, 0, 2, 1, 3, 1, 0, 4, 1, 3, 4, 4, 1, 3 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 4, 1, 0, 0, 4, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 4, 2, 0, 2, 1, 3, 2, 3, 1 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0 ],
        \[ 0, 0, 1, 0, 3, 1, 2, 0, 3, 4, 2, 4, 3, 3, 3, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 4, 1, 0, 2, 0, 3, 3, 2, 0, 3, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 0, 3, 0, 0, 4, 0, 3 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 0, 4, 2 ],
        \[ 0, 0, 1, 0, 1, 2, 2, 0, 2, 0, 4, 1, 3, 0, 0, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 4, 2, 4, 1, 4 ],
        \[ 0, 0, 1, 0, 3, 2, 1, 0, 4, 2, 1, 0, 3, 4, 0, 2 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 4, 1, 2, 2, 1, 2, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 3, 1, 0, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 2, 3, 4, 0, 3 ],
        \[ 0, 0, 1, 0, 2, 2, 3, 1, 2, 4, 4, 4, 0, 4, 0, 0 ]
        /* order = 1440 = 2^5 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 4, 4, 3, 0, 3, 2 ],
        \[ 0, 0, 1, 0, 2, 4, 3, 1, 3, 0, 2, 3, 1, 1, 4, 4 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 1, 3, 1, 4, 1, 4 ],
        \[ 0, 0, 1, 0, 1, 1, 4, 4, 3, 4, 0, 3, 2, 1, 2, 1 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 0, 0, 0, 1, 1, 4, 4, 2, 0, 3, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 3, 1, 2, 1, 1, 0, 4 ],
        \[ 1, 1, 4, 0, 3, 2, 2, 3, 1, 2, 2, 0, 2, 2, 0, 0 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 3, 0, 0, 3, 0, 0, 3, 1, 1, 4, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 4, 0, 3, 4, 2, 2, 0 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 4, 1, 4, 4, 3, 1, 4 ],
        \[ 0, 0, 1, 0, 2, 3, 3, 4, 1, 3, 1, 1, 4, 1, 4, 1 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 2, 0, 0, 4, 1, 3, 1, 2, 0, 1, 3 ],
        \[ 0, 0, 1, 0, 3, 0, 3, 0, 2, 4, 4, 1, 1, 2, 4, 1 ],
        \[ 0, 0, 0, 1, 0, 4, 3, 2, 3, 0, 1, 4, 0, 1, 0, 0 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 3, 0, 0, 0, 0, 0, 3, 0, 0, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 2, 3, 0, 0 ],
        \[ 0, 3, 0, 0, 4, 3, 0, 0, 0, 0, 3, 4, 0, 0, 3, 0 ]
        /* order = 1920 = 2^7 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 0, 2, 0, 1, 3, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 3, 3, 0, 4, 2, 1, 0, 3, 4, 3, 2 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 1, 3, 0, 0, 3, 3 ],
        \[ 0, 0, 1, 0, 4, 2, 2, 0, 4, 4, 3, 2, 4, 4, 3, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 4, 4, 1, 1, 1, 4 ],
        \[ 0, 0, 1, 0, 4, 3, 0, 0, 2, 2, 2, 2, 0, 3, 2, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 1, 0, 1, 0, 2, 2, 2, 3, 1, 3, 4, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 0, 1, 0, 1, 4, 1, 4 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 3, 3, 1, 3, 3 ],
        \[ 0, 0, 1, 0, 2, 3, 0, 0, 0, 4, 2, 1, 1, 0, 0, 2 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 1, 0, 3, 4, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 3, 4, 0, 1, 4, 3, 3, 3, 0, 0, 3, 3 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 4, 3, 4, 4, 0, 0, 2, 1, 1, 0, 1 ],
        \[ 0, 0, 1, 0, 1, 4, 0, 3, 2, 4, 2, 4, 3, 1, 4, 2 ],
        \[ 0, 0, 0, 1, 3, 2, 2, 0, 2, 1, 2, 1, 3, 4, 4, 1 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 4, 0, 2, 4, 4, 4, 0 ],
        \[ 0, 0, 1, 0, 3, 2, 4, 0, 1, 4, 2, 3, 1, 0, 2, 3 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 3, 3, 3, 4, 3, 2, 4, 4, 2, 2, 0 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 2, 1, 2, 3, 0, 3, 2 ],
        \[ 0, 0, 1, 0, 2, 0, 4, 0, 1, 0, 4, 3, 1, 4, 4, 1 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 3, 1, 2, 3, 2, 1 ],
        \[ 0, 0, 1, 0, 1, 2, 0, 3, 2, 0, 0, 0, 3, 3, 4, 3 ]
        /* order = 2880 = 2^6 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 4, 2, 4, 1, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 4, 3, 1, 1, 0, 3, 0, 2, 2, 3, 4 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 0, 0, 0, 3, 4, 3, 0, 0, 1, 2, 2 ],
        \[ 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 4, 3, 0, 0, 3, 4 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 4, 0, 0, 2, 1, 0, 0 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 1, 3, 2, 2, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 1, 3, 4, 2, 3, 0, 4, 4, 1, 0, 1, 4 ]
        /* order = 3840 = 2^8 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 0, 0, 0, 3, 4, 1, 4, 1, 2, 4, 4 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 3, 2, 4, 0, 1, 1, 0 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 3, 2, 3, 4, 1, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 3, 3, 3, 0, 0, 3, 2, 1, 2, 2, 3 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 2, 3, 1, 4, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 2, 0, 1, 3, 3, 2, 1, 0, 0, 0 ],
        \[ 0, 0, 0, 1, 3, 4, 2, 1, 0, 1, 1, 4, 3, 0, 0, 0 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 1, 0, 4, 2, 2, 3, 0 ],
        \[ 0, 0, 1, 0, 3, 1, 3, 0, 2, 0, 1, 4, 1, 4, 3, 0 ]
        /* order = 5760 = 2^7 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 3, 1, 3, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 1, 1, 4, 0, 3, 1, 4, 4, 3, 2, 4, 4 ]
        /* order = 7200 = 2^5 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 4, 3, 1, 0, 3, 1 ],
        \[ 0, 0, 1, 0, 0, 4, 4, 2, 1, 4, 4, 1, 2, 1, 2, 2 ]
        /* order = 7680 = 2^9 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 1, 0, 4, 1, 0 ],
        \[ 0, 0, 1, 0, 3, 3, 0, 2, 4, 1, 1, 4, 1, 0, 4, 4 ]
        /* order = 7680 = 2^9 * 3 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 4, 2, 0, 3, 0, 3, 2, 1, 3, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 2, 4, 3, 4, 3, 1 ]
        /* order = 7800 = 2^3 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 3, 4, 0, 1, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 3, 4, 2, 2, 2, 4 ]
        /* order = 11520 = 2^8 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 3, 3, 0, 1, 2, 3, 1, 4, 2, 1, 4 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 3, 4, 1, 0 ]
        /* order = 14400 = 2^6 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 4, 4, 0, 1, 2, 4 ],
        \[ 0, 0, 1, 0, 1, 0, 2, 1, 4, 0, 1, 0, 3, 4, 1, 1 ]
        /* order = 14400 = 2^6 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 1, 1, 1, 3, 1 ],
        \[ 0, 0, 1, 0, 4, 1, 1, 0, 1, 0, 0, 0, 4, 4, 3, 4 ]
        /* order = 14400 = 2^6 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 2, 4, 4, 4, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 3, 2, 4, 4, 4, 4, 0, 0, 1, 0, 1, 3 ]
        /* order = 14400 = 2^6 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 4, 1, 1, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 1, 1, 1, 4, 1, 0, 1, 4, 1, 0, 0, 0 ]
        /* order = 14400 = 2^6 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 3, 3, 2, 4, 3 ],
        \[ 0, 0, 1, 0, 2, 0, 3, 0, 2, 4, 4, 2, 4, 3, 0, 1 ]
        /* order = 15600 = 2^4 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 4, 3, 4, 3, 3, 3, 3 ],
        \[ 0, 0, 1, 0, 0, 4, 2, 2, 3, 3, 0, 2, 3, 4, 3, 2 ]
        /* order = 15600 = 2^4 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 4, 0, 1, 1, 3, 1, 3, 0, 3, 4 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 3, 0, 3, 4, 0, 0 ]
        /* order = 15600 = 2^4 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 4, 3, 1, 3, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 4, 4, 1, 1, 4, 0, 3, 3, 4, 3, 0, 3 ]
        /* order = 23040 = 2^9 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 1, 4, 4, 2, 3, 1 ],
        \[ 0, 0, 1, 0, 0, 4, 4, 2, 1, 2, 3, 3, 2, 0, 0, 0 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 4, 1, 0, 4, 4, 0, 2, 2, 4, 2, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 3, 2, 4, 2, 1, 2 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 3, 4, 2, 4, 0, 0, 0 ],
        \[ 0, 0, 1, 0, 2, 4, 1, 0, 0, 0, 2, 4, 3, 4, 0, 4 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 1, 2 ],
        \[ 0, 0, 1, 0, 3, 1, 3, 1, 1, 3, 3, 1, 3, 0, 2, 4 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 4, 0, 1, 2, 1, 3 ],
        \[ 0, 0, 1, 0, 4, 1, 2, 3, 0, 1, 2, 0, 4, 0, 2, 2 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 4, 0, 1, 1, 4, 4, 3 ],
        \[ 0, 0, 1, 0, 0, 3, 4, 2, 0, 3, 0, 0, 1, 2, 4, 2 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 1, 4, 0, 1 ],
        \[ 0, 0, 1, 0, 1, 4, 0, 1, 1, 1, 3, 4, 2, 1, 4, 2 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 3, 3, 3, 3, 1, 0, 2 ],
        \[ 0, 0, 1, 0, 3, 1, 1, 1, 1, 0, 0, 1, 1, 3, 4, 4 ]
        /* order = 28800 = 2^7 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 1, 2, 0, 0, 4, 2, 3, 1, 0, 2, 1 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 4, 0, 4, 2, 4, 3, 0 ]
        /* order = 31200 = 2^5 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 0, 0, 0, 0, 4, 0, 3, 2, 0, 4, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 0, 3, 4, 0, 4, 2, 3 ]
        /* order = 31200 = 2^5 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 4, 2, 2, 0, 1, 3 ],
        \[ 0, 0, 1, 0, 3, 3, 1, 4, 3, 0, 2, 1, 0, 0, 3, 4 ]
        /* order = 31200 = 2^5 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 4, 3, 1, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 4, 1, 0, 0, 0 ]
        /* order = 31200 = 2^5 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 3, 2, 2, 3, 0 ],
        \[ 0, 0, 1, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 4, 1, 1 ]
        /* order = 31200 = 2^5 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 4, 0, 4, 0, 0, 1, 4 ],
        \[ 0, 0, 1, 0, 0, 1, 2, 3, 0, 2, 4, 3, 2, 1, 4, 2 ]
        /* order = 46080 = 2^10 * 3^2 * 5 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 3, 0, 0, 4, 2, 2 ],
        \[ 0, 0, 1, 0, 3, 0, 2, 2, 4, 3, 3, 1, 0, 3, 0, 4 ]
        /* order = 46800 = 2^4 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 3, 2, 0, 3, 4, 4, 3, 4, 1, 2, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 4, 3, 1, 4, 3, 0, 4 ]
        /* order = 57600 = 2^8 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 4, 2, 0, 0, 4 ],
        \[ 0, 0, 1, 0, 0, 0, 3, 3, 3, 3, 3, 4, 0, 1, 4, 4 ]
        /* order = 57600 = 2^8 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 3, 1, 1, 4, 4, 0, 4 ],
        \[ 0, 0, 1, 0, 0, 3, 0, 2, 2, 0, 0, 4, 4, 2, 4, 0 ]
        /* order = 57600 = 2^8 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 3, 4, 0, 3 ],
        \[ 0, 0, 1, 0, 4, 4, 2, 3, 4, 2, 3, 1, 4, 1, 2, 3 ]
        /* order = 57600 = 2^8 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 4, 1, 1, 1, 2, 2, 3, 3, 1, 0, 4 ],
        \[ 0, 0, 1, 0, 3, 4, 3, 0, 1, 0, 0, 0, 0, 0, 0, 4 ],
        \[ 0, 0, 0, 1, 3, 3, 0, 4, 1, 3, 4, 1, 2, 0, 0, 4 ]
        /* order = 57600 = 2^8 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 4, 4, 4, 1, 1, 1 ],
        \[ 0, 0, 1, 0, 4, 0, 2, 3, 3, 2, 1, 0, 3, 0, 0, 4 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0, 3, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 1, 2, 1, 3, 2, 2 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 3, 0, 0, 0, 4, 3, 0, 3, 2, 2, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 4, 0, 3, 1, 0, 1, 3, 4 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 4, 2, 0, 0 ],
        \[ 0, 0, 1, 0, 3, 0, 2, 0, 3, 1, 0, 4, 2, 4, 0, 4 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 3, 4, 3, 0 ],
        \[ 0, 0, 1, 0, 4, 3, 3, 0, 0, 2, 3, 2, 4, 2, 2, 1 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 1, 4, 4, 0, 3, 3, 0 ],
        \[ 0, 0, 1, 0, 4, 1, 0, 3, 0, 1, 1, 4, 2, 4, 3, 4 ]
        /* order = 62400 = 2^6 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 4, 0 ],
        \[ 0, 0, 1, 0, 4, 3, 4, 0, 4, 2, 2, 4, 2, 3, 1, 0 ]
        /* order = 93600 = 2^5 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 2, 1, 3, 4, 2, 2, 3 ],
        \[ 0, 0, 1, 0, 1, 2, 4, 0, 4, 1, 4, 3, 2, 1, 1, 4 ]
        /* order = 93600 = 2^5 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 4, 4, 1, 1, 2, 4, 4 ],
        \[ 0, 0, 1, 0, 3, 4, 4, 0, 0, 1, 4, 3, 3, 1, 4, 4 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 3, 4, 1, 3 ],
        \[ 0, 0, 1, 0, 0, 2, 1, 4, 2, 2, 1, 2, 0, 3, 1, 2 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 3, 2, 2, 1, 0, 3, 3 ],
        \[ 0, 0, 1, 0, 0, 1, 3, 4, 3, 4, 4, 3, 0, 3, 3, 0 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 3, 4, 4, 1, 0 ],
        \[ 0, 0, 1, 0, 3, 3, 0, 4, 1, 2, 3, 4, 0, 1, 2, 4 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 3, 1, 1, 3, 1, 2 ],
        \[ 0, 0, 1, 0, 3, 0, 4, 4, 0, 3, 2, 1, 1, 4, 2, 0 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 4, 3, 4, 1, 1, 3, 2 ],
        \[ 0, 0, 1, 0, 3, 2, 4, 4, 1, 2, 3, 1, 3, 2, 4, 0 ]
        /* order = 115200 = 2^9 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 3, 2, 4, 4, 2, 2 ],
        \[ 0, 0, 1, 0, 4, 3, 2, 0, 2, 0, 4, 0, 1, 3, 3, 1 ]
        /* order = 124800 = 2^7 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 2, 0, 3, 1, 0 ],
        \[ 0, 0, 1, 0, 1, 2, 3, 0, 2, 3, 3, 2, 0, 3, 3, 0 ]
        /* order = 124800 = 2^7 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0, 2, 4, 2, 0 ],
        \[ 0, 0, 1, 0, 1, 2, 4, 4, 2, 0, 0, 0, 0, 2, 4, 3 ]
        /* order = 124800 = 2^7 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 3, 3, 4, 1, 4, 4 ],
        \[ 0, 0, 1, 0, 3, 3, 1, 1, 4, 4, 1, 0, 2, 1, 3, 4 ]
        /* order = 124800 = 2^7 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 3, 1, 0, 4, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 3, 2, 1, 2, 4, 4, 1, 0, 2, 0, 3 ]
        /* order = 187200 = 2^6 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 4, 3, 1, 0, 3, 1, 2 ],
        \[ 0, 0, 1, 0, 4, 2, 3, 3, 0, 1, 3, 0, 3, 2, 3, 0 ]
        /* order = 187200 = 2^6 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 4, 0, 3, 2, 4, 3, 3 ],
        \[ 0, 0, 1, 0, 3, 3, 0, 0, 0, 3, 2, 2, 1, 1, 4, 1 ]
        /* order = 187200 = 2^6 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 4, 4, 2, 4, 3 ],
        \[ 0, 0, 1, 0, 0, 0, 1, 4, 0, 2, 2, 1, 4, 2, 2, 3 ]
        /* order = 230400 = 2^10 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 1, 4, 0, 0, 1, 2, 0, 1, 0, 3, 3 ],
        \[ 0, 0, 1, 0, 4, 0, 4, 3, 0, 3, 3, 1, 3, 2, 1, 2 ],
        \[ 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 4, 2, 1, 4, 0, 0 ]
        /* order = 230400 = 2^10 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 4, 2, 4, 2, 3 ],
        \[ 0, 0, 1, 0, 3, 1, 0, 0, 4, 1, 2, 0, 3, 4, 4, 2 ]
        /* order = 249600 = 2^8 * 3 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 2, 4, 2, 0, 0, 1, 1, 2, 3, 0, 1, 0 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 3, 0, 0, 4, 0, 1 ]
        /* order = 374400 = 2^7 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 3, 0, 2, 2, 1, 2 ],
        \[ 0, 0, 1, 0, 0, 1, 4, 4, 2, 4, 1, 3, 0, 0, 1, 3 ]
        /* order = 374400 = 2^7 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 4, 3, 2, 4, 3, 2, 0 ],
        \[ 0, 0, 1, 0, 0, 2, 2, 0, 2, 3, 1, 2, 1, 2, 4, 2 ]
        /* order = 374400 = 2^7 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 2, 1, 1, 2, 0, 2 ],
        \[ 0, 0, 1, 0, 2, 1, 4, 0, 4, 4, 2, 4, 4, 4, 2, 2 ]
        /* order = 460800 = 2^11 * 3^2 * 5^2 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 4, 1, 0, 3, 1, 1, 4, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 1, 3, 3, 1, 2, 4, 0, 2, 1, 2 ]
        /* order = 748800 = 2^8 * 3^2 * 5^2 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 1, 0, 4 ],
        \[ 0, 0, 1, 0, 0, 1, 2, 2, 4, 0, 4, 0, 0, 0, 1, 1 ]
        /* order = 9360000 = 2^7 * 3^2 * 5^4 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 4, 0, 0, 0, 3, 4, 3, 0, 2, 0, 2, 2 ],
        \[ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 4, 0, 1, 3 ]
        /* order = 18720000 = 2^8 * 3^2 * 5^4 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 4, 2, 1, 3, 4, 4 ],
        \[ 0, 0, 1, 0, 4, 4, 3, 2, 2, 2, 4, 2, 0, 1, 3, 4 ]
        /* order = 37440000 = 2^9 * 3^2 * 5^4 * 13 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 2, 4, 4, 1, 1, 3, 4, 4 ],
        \[ 0, 0, 1, 0, 0, 4, 0, 3, 1, 0, 3, 4, 2, 4, 0, 2 ]
        /* order = 2^9 * 3^2 * 5^6 * 13 * 31 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 3, 3, 4, 1, 1, 1, 0, 4 ],
        \[ 0, 0, 1, 0, 3, 0, 2, 1, 2, 1, 4, 0, 3, 3, 1, 2 ]
        /* order = 2^10 * 3^2 * 5^6 * 13 * 31 */ >,

    MatrixGroup<4, GF(5) |
        \[ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 4, 4, 0, 4, 2, 1 ],
        \[ 0, 0, 1, 0, 2, 4, 0, 4, 0, 0, 0, 3, 0, 2, 1, 1 ]
        /* order = 2^11 * 3^2 * 5^6 * 13 * 31 */ >
];