insol3_7:= [ 
    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 0, 5, 2, 4, 4, 5 ],
        \[ 0, 0, 1, 0, 5, 5, 4, 5, 5 ]
        /* order = 168 = 2^3 * 3 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 6, 4, 4, 5, 3, 0 ],
        \[ 0, 0, 1, 3, 2, 6, 3, 0, 5 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 1, 0, 1, 6, 1, 5 ],
        \[ 0, 0, 1, 0, 2, 5, 3, 2, 1 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 5, 3, 0, 6, 4, 4 ],
        \[ 0, 0, 1, 0, 2, 6, 4, 6, 1 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 5, 6, 3, 1, 6, 6 ],
        \[ 0, 0, 1, 5, 1, 1, 3, 5, 3 ]
        /* order = 504 = 2^3 * 3^2 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 0, 6, 2, 3, 3, 0 ],
        \[ 0, 0, 1, 0, 1, 0, 1, 0, 0 ]
        /* order = 672 = 2^5 * 3 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 0, 0, 1, 6, 0, 0 ],
        \[ 2, 4, 0, 0, 4, 0, 0, 5, 1 ]
        /* order = 1008 = 2^4 * 3^2 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 0, 0, 1, 1, 3, 4 ],
        \[ 0, 2, 0, 1, 1, 1, 0, 0, 3 ]
        /* order = 1008 = 2^4 * 3^2 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 6, 5, 2, 3, 2, 2 ],
        \[ 0, 0, 1, 0, 6, 0, 6, 6, 4 ]
        /* order = 1008 = 2^4 * 3^2 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 5, 0, 0, 2, 2, 0, 4, 0, 2 ],
        \[ 0, 1, 0, 0, 0, 1, 1, 2, 5 ]
        /* order = 2016 = 2^5 * 3^2 * 7 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 3, 4, 5, 4, 3, 4 ],
        \[ 0, 0, 1, 1, 6, 2, 2, 6, 4 ]
        /* order = 5630688 = 2^5 * 3^3 * 7^3 * 19 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 3, 5, 0, 0, 0, 5 ],
        \[ 0, 0, 1, 2, 3, 2, 0, 4, 1 ]
        /* order = 11261376 = 2^6 * 3^3 * 7^3 * 19 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 2, 5, 0, 3, 2, 6 ],
        \[ 1, 3, 0, 0, 0, 1, 5, 6, 2 ]
        /* order = 16892064 = 2^5 * 3^4 * 7^3 * 19 */ >,

    MatrixGroup<3, GF(7) |
        \[ 0, 1, 0, 2, 3, 2, 3, 1, 4 ],
        \[ 0, 0, 1, 3, 4, 1, 0, 2, 4 ]
        /* order = 33784128 = 2^6 * 3^4 * 7^3 * 19 */ >
];