G:=MatrixGroup<24, IntegerRing() |
    \[ -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, -1 ],
    \[ 1, -1, -1, -1, 1, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    -1, 0, 0, -1, -2, -2, 1, 0, 0, -1, 0, 0, -1, 0, 1, -1, 0, 1, 0, -1, 1, -1, 
    0, -1, -1, 1, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 
    0, 0, -1, 1, 1, -1, 0, 2, 2, 0, -1, 0, 1, 0, -2, 1, 1, 0, -1, 1, 1, 1, 0, 
    -1, 0, -1, 0, 2, 0, -1, 1, 0, -1, 1, 1, -1, 0, -1, -1, 1, 1, 0, -1, 0, 0, 1,
    0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -1, 0, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 
    0, -1, 0, 0, 0, 0, -1, 0, -1, 1, -2, -1, 0, 0, -1, -1, 0, 1, 0, 1, 0, -1, 0,
    0, 0, -1, 0, 0, 0, -1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 2, 0, 0, -1, 1, 0,
    -1, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, -2, -1, 1, -2, 1, -1, 1, -1, -1, 0, 1,
    -2, 1, 1, 0, -1, -1, 0, 0, -1, 0, 1, 1, 0, -2, -3, 1, 1, -1, -1, 0, 0, -1, 
    0, 0, 0, -1, 0, 0, 0, 1, 0, 1, -1, -1, 0, -1, 1, 1, 1, 1, 0, -1, 1, 0, -1, 
    1, 1, 0, -1, 1, 0, 1, 0, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 0, -1, 0, 0, 1, 1,
    0, 0, -1, 1, 0, -1, 0, 1, -1, 1, 0, 1, -1, 0, 1, -1, 3, 1, 1, 0, -1, 2, 1, 
    -1, 1, 0, -1, 1, 0, 0, 1, 2, -1, 1, 0, 1, 1, -1, 0, 0, 1, 1, 0, 0, 1, 0, -1,
    0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, -1, -1, 1, -1, -1, 2, -1, 0,
    2, -1, -1, 0, 1, 0, -1, -1, 0, 0, 0, 0, 1, -1, 0, 1, 0, -2, -2, 0, 1, 0, -1,
    0, 1, -2, -1, 1, 0, -1, 0, -1, -1, 2, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 
    0, 1, 1, -1, 0, -1, 1, -1, -1, 0, 1, 0, 0, 0, 0, -1, -1, -2, 1, 0, 1, -1, 
    -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, 0, 0, 0,
    -1, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -1, -1, -1, 1, 1, 0, 0, 2,
    2, -1, -1, 0, 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 1, -1, 1, 0, 0, 2, 0, 1, -1, 
    -2, -2, 0, 1, 2, -1, 0, 1, -2, -2, 1, 1, -1, -1, -1, 0, 1, -1, 1, 0, -2, 1, 
    1, 0, -2, -3, 1, 1, 0, -1, 0, 1, -1, 0, 0, 1, -1, -1, 0, 0, 1, 0, 1, 0, -2, 
    0, 0, -1, -1, -1, 0, -1, 1, -1, 0, -1, 0, 0, 1, -1, 1, 1, 0, -1, 0, 0, 0, 
    -1, 1, 1 ],
    \[ 0, -1, -1, -2, 0, -1, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 
    0, 1, 1, -2, 2, 0, 1, -1, -1, 1, 1, -1, 1, 0, -1, 0, 0, 1, 1, 1, -1, 1, 0, 
    1, 1, 0, 0, 0, 1, 2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 1, 0, 0,
    1, -1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 1, 1, -1, -1, 1, -1, 0, 
    -1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, -1, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, -1, 1,
    0, -1, 0, 1, -1, -1, -3, 0, -1, -1, 0, 1, 0, -1, -1, -1, 1, -2, -1, 0, 1, 0,
    0, 0, 0, -1, 1, 1, 0, -1, -1, 0, 1, 1, -1, -1, 0, 0, -1, 0, 1, -1, -1, 0, 1,
    -1, 1, 1, 1, -1, 0, 1, 0, -1, -1, -1, 0, 1, -1, -1, 1, 0, -1, 0, 1, -1, -1, 
    -1, 0, 0, 0, 0, 1, -1, 1, 1, -2, 0, -1, 1, -1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 
    1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 1, 0, 1, -1, -1, 1, 
    -1, -1, 0, 2, -1, 1, 0, 1, 1, 0, -1, 1, 0, 2, -1, 1, 1, 0, -1, 1, 1, 1, 0, 
    0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2, 0, 0, -1, -1, 0, 1, 0, 0, 
    -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 1, 2, -1, -1, -1, 1, 1, 1, 1,
    1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 2, 2, 1, 1, -1, 1, 0, 0, 1, 
    2, 0, -1, 1, 2, 1, -1, 1, -1, -1, 0, 0, -1, 0, -2, 1, -1, 2, -1, -2, 1, 1, 
    0, 1, 2, -1, 0, 0, 1, 2, 0, 0, 1, -1, 1, 0, 0, 1, 0, 2, 0, 0, 0, -1, 1, 0, 
    -1, 1, 0, -1, 1, -1, 0, 1, 1, -1, 1, 0, 1, 1, -1, 0, -2, 3, 3, 0, -2, -1, 2,
    2, 0, 1, 1, -1, 0, 1, 1, 1, 1, -1, 1, -1, 1, 2, -1, 0, 0, 0, -1, 0, 0, -1, 
    1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, 1, 0, 1, 0, 0, 0, 0, -1, 0, 1, 1, 2,
    -1, -1, -1, -1, 0, 2, -1, 1, 1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0, -1, -1, 0, 
    0, 2, -1, 0, -1, -2, -2, 2, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 1, 3, 
    0, -1, 0, 0, 0, 1, 1, 2, 0, -1, 2, 1, 0, -1, 0, 1, -1, 0, 1, -1, 1, -1, 0, 
    -2, 1, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
    -1, -3, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, -2, -1, 0, 1, 0, -1, 0, 0, -1, 2, 
    1, -2, 2, 1, 0, -2, -1, 1, 2, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, 0, -1, 0, 1, 0 
    ]
        /* order = 7056 = 2^4 * 3^2 * 7^2 */ >;

F:=MatrixAlgebra(RationalField(), 24) ! [ RationalField() | 4, 2, -2, -1, -1, 2, 1,
2, 2, 2, 0, 2, 1, -2, 1, 1, 1, 2, -2, -2, -1, 1, 2, 1, 2, 4, 0, -1, 0, 1, 2, 1, 
2, 2, -1, 0, -1, -1, 1, 2, 2, 1, 0, 0, -1, 1, 1, 2, -2, 0, 4, 0, 0, -1, 0, -2, 
0, 0, -1, -1, 0, 0, -1, -1, 1, -2, 1, 2, 1, -1, -2, 1, -1, -1, 0, 4, 2, -2, -2, 
-2, 0, -2, 2, -2, 1, 2, -2, -2, 1, -2, 2, 1, 2, -2, -2, 1, -1, 0, 0, 2, 4, -2, 
0, -1, -1, 0, 2, -2, 0, 2, -2, -1, 0, -1, 1, 0, 0, -2, 0, 0, 2, 1, -1, -2, -2, 
4, 1, 2, 2, 1, -2, 2, -1, -2, 2, 1, -1, 1, -2, 0, -2, 2, 2, 1, 1, 2, 0, -2, 0, 
1, 4, 2, 1, 2, 0, 1, -2, -2, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 2, 1, -2, -2, -1, 2,
2, 4, 0, 2, -1, 2, -1, -2, 1, 2, -1, 2, -2, -1, -1, 1, 2, 0, 2, 2, 0, 0, -1, 2, 
1, 0, 4, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, -2, 0, 1, 2, 2, 
0, 4, -1, 1, 0, -2, 0, 2, 1, 2, -2, -1, -1, 0, 2, 1, 0, -1, -1, 2, 2, -2, 0, -1,
0, -1, 4, -1, 1, 1, -2, -1, 0, 0, 1, -1, 1, -2, -1, -1, 2, 0, -1, -2, -2, 2, 1, 
2, 1, 1, -1, 4, 1, -2, 1, 0, -1, 2, -2, -2, 0, 2, 2, 0, 1, -1, 0, 1, 0, -1, -2, 
-1, 0, 0, 1, 1, 4, 0, -1, -2, 1, 0, -1, -2, 1, 0, 0, 0, -2, -1, 0, 2, 2, -2, -2,
-2, -1, -2, 1, -2, 0, 4, 0, -1, 0, -2, 1, 0, 1, -1, -1, 0, 1, 1, -1, -2, -2, 2, 
0, 1, 1, 0, -2, 1, -1, 0, 4, 1, 0, 1, -1, -1, -1, 2, 1, 0, 1, 2, -1, -2, -1, 1, 
2, 2, 0, 2, -1, 0, -2, -1, 1, 4, 0, 2, -1, 0, -1, 1, 1, 0, 1, 2, 1, 1, 0, -1, 0,
-1, 1, 1, 0, -1, 1, 0, 0, 0, 4, 0, 1, 0, 1, -1, -1, 2, 2, 1, -2, -2, -1, 1, 2, 
2, 0, 2, 0, 2, 0, -2, 1, 2, 0, 4, -1, -2, -1, 1, 2, -1, -2, 0, 1, 2, 1, -2, 0, 
-2, 0, -2, 1, -2, -1, 1, -1, -1, 1, -1, 4, 2, 1, -1, -2, 0, -2, 0, 2, 1, 0, 0, 
0, -1, 0, -1, -1, -2, -2, 0, -1, 0, 0, -2, 2, 4, 0, -1, -2, 1, -1, -1, 1, 2, 0, 
-2, -1, -1, 0, -1, 1, 0, 1, 1, -1, -1, 1, -1, 1, 0, 4, -1, -2, 1, 1, 1, -1, -2, 
-2, 2, 0, 1, 1, 0, -2, 2, 0, -1, 2, 1, -1, 1, -1, -1, -1, 4, 2, 0, 2, 1, -2, -2,
0, 2, 1, 2, 0, 2, -1, 2, 0, -1, 1, 1, -1, 2, -2, -2, -2, 2, 4, 0, 1, 2, 1, 1, 0,
1, 0, 0, 2, 1, -1, 0, 0, 0, 0, 0, 2, -1, 0, 1, 1, 0, 0, 4 ];
w7:=MatrixAlgebra(RationalField(), 24) ! [ RationalField() | -1, 0, -4, -2, 2, 2, 2,
-4, -2, 0, -4, 0, 2, -4, 0, 2, -4, -2, 4, -6, 0, -2, -4, 4, 2, -3, 2, -2, 4, 0, 
-2, 2, 2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 1, 0, -2, -4, 
0, 2, 2, 0, 2, 0, 0, 2, 0, -2, 2, 0, -2, 4, 0, 2, 4, -2, -2, 2, -4, -1, 0, 0, 2,
-2, -2, -2, 0, 0, 2, -4, 2, 0, 0, -4, -2, 0, 0, -2, 0, 2, 0, 2, -4, -2, 1, 6, 4,
-2, -2, 0, -2, -4, 4, 0, 0, -2, 0, -2, 0, 0, 4, 0, -2, -2, 2, -2, 4, 0, 2, 3, 
-2, 0, -2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, -2, 0, 0, 0, 0, 4, -2, 0, -2, 0, 4, 3, 
0, 0, 2, -4, -4, 4, 4, -2, 0, -4, 0, 6, -2, 2, 0, -2, 0, 4, -2, 2, 2, 0, 0, 2, 
-1, 0, 2, -4, -2, 0, 2, 0, 0, -4, 2, 2, -2, 0, 0, -2, 0, 0, -2, 0, -2, 2, 2, -2,
0, -1, 0, 0, 2, 0, -2, 0, 2, 0, -2, 4, -2, 0, 0, 0, 2, 2, 0, -2, -2, 0, 0, 4, 
-2, 0, -1, -6, -6, 2, 0, -2, -2, -4, 2, 2, -4, 2, 0, -2, 2, -2, 2, -6, -2, 0, 4,
4, -2, -2, 2, -1, -2, 4, 0, 0, -2, -2, -2, 0, 0, 2, 0, -4, 2, -2, 0, 0, 6, -2, 
0, 2, -2, -2, 4, 0, 3, 0, 0, 2, 2, -2, -2, 2, -2, -2, 0, 0, 0, -6, 2, -4, 4, -2,
-4, 2, -2, 0, 0, 0, 2, -1, -4, 2, 0, 0, -2, -4, -2, -2, 0, 0, 2, 0, 2, 2, 2, 0, 
2, -4, 2, 0, 2, 4, 2, -4, 1, 0, -2, 4, 0, -2, 2, 0, 2, 0, -4, 2, -4, 8, 4, 0, 
-2, -6, 4, 2, 2, 4, 4, -8, 2, -1, 0, 4, 4, 0, 0, -4, 4, 0, -2, 4, -2, 0, -6, 4, 
0, -2, 0, 2, -2, -4, -2, 0, 0, -2, 1, -2, 2, 4, -2, 2, -2, -2, 2, 0, 0, 0, 0, 
-2, -4, 0, 2, 2, -2, -2, -2, -2, -2, -2, -2, -1, 0, 0, -4, -2, 0, 0, 2, 0, -2, 
2, 4, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, -2, 1, 2, -4, -2, 0, -2, 2, 0, -2, 2,
0, 0, -2, -2, 4, 2, -2, 2, 0, 0, 0, 0, 0, 2, 0, -1, 2, -2, 0, 2, 0, 2, -2, 2, 
-4, 2, -2, -2, 2, 2, -4, 0, 0, 2, 0, 0, 2, 2, 0, 0, 3, 0, -2, 4, 0, 0, 2, -4, 2,
-4, -4, 4, -2, -2, 2, 0, 0, 0, 0, 2, -4, -2, -2, -2, 2, -1, 0, 0, 2, 0, -2, 0, 
-2, 4, 0, -4, 0, 0, -2, 0, 4, -2, -2, 0, 4, 2, 0, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0,
2, 6, 2, -2, -4, 0, -2, -2, 2, 0, 0, 2, -2, 0, 4, -4, 2, 0, -3, 0, 2, 0, 0, -2, 
2, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, 0, 0, -2, 2, -2, 0, 0, 0, 1 ];
load constnebe;

