G:=MatrixGroup<24, IntegerRing() |
    \[ 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 1, -1, 1, -1, -1, 2, 3, 0, 1, -2, 1, 0, -1, 0, -1, -1, 0, 1, 0, 1, 0, 0, 
    1, 0, 3, -3, -1, 0, 1, 1, 1, -1, 0, 0, 1, 0, -1, 1, 1, -1, 1, 0, 0, -1, -1, 
    -1, 1, -1, 4, -3, 0, 0, 0, 3, 2, -1, 1, -1, 2, 1, -1, 1, 0, -1, 1, 0, 0, 0, 
    -1, 0, 2, 0, -1, 3, -1, 2, 0, -2, -3, 1, -1, 2, -1, 1, 2, 0, 1, 2, 0, -1, 0,
    0, 1, 1, 0, 0, 1, -2, 0, 0, 0, 1, 1, -1, 1, -1, 0, 0, -2, 0, 0, -1, 0, 0, 
    -1, 1, 0, -1, 0, 1, -4, 2, 1, -1, 1, -2, -2, 0, 0, 1, -2, -2, 1, -1, 0, 1, 
    -1, 0, -1, 0, 0, 0, -2, 0, 2, -1, -1, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 
    0, 1, 0, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 1, -1, 
    0, 0, 1, -1, -1, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
    0, 1, 1, 1, -1, -1, 0, 1, -1, -1, 0, 0, 3, -3, 1, -2, 0, 3, 3, -1, 1, -3, 1,
    0, -1, 1, -1, -2, 1, 1, 0, 0, -1, 0, 1, 0, 3, -2, 0, 0, 0, 2, 2, -1, 1, -1, 
    1, 0, -2, 0, 0, -2, 1, 1, 0, 0, 0, 0, 1, -1, 1, -2, -1, 1, 0, 0, -1, 0, -1, 
    1, 1, 1, 0, 1, 1, 0, 0, -1, 1, -1, -1, -1, 0, 0, -2, 4, 0, 1, 0, -2, -2, 1, 
    -1, 1, -1, 0, 2, -1, 0, 2, -1, 0, 0, 0, 1, 1, -1, -1, 4, -4, -1, -1, 0, 2, 
    3, -2, 1, -2, 1, 1, -2, 1, 0, -1, 1, 0, -1, 0, 0, -1, 2, 0, -1, 1, 0, 0, 1, 
    -1, -1, 0, 0, 1, 0, -1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1,
    0, 1, 1, -1, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 2, -1, -2, 
    1, 0, 0, -1, 0, -1, 1, 1, 1, 0, 1, 0, 0, 1, -1, 1, -2, 0, 0, 0, -1, 2, -1, 
    -1, 0, -1, 1, 1, 0, 0, -1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, -1, -1,
    2, -2, 0, 2, 2, -1, 2, -2, 0, -1, -1, 0, -1, -1, 0, 1, -1, 2, -1, 0, 0, 0, 
    1, 1, 2, -1, -1, 2, 2, 0, 1, -3, 0, -1, -1, -1, -2, -2, 1, 2, 0, 1, 1, 1, 0,
    0, 0, 0, 2, -1, 0, 2, 2, -1, 2, -2, 0, -1, -1, -1, -1, -1, 0, 1, -1, 2, 0, 
    0, 0, 1, -2, 0, 1, -1, 0, -1, 0, 0, 0, 0, -1, -1, 0, -1, -1, -1, 0, 0, -1, 
    0, 1, 0, -1, 0, 0, 0, -1, 1, 1, -1, -2, 0, -1, 2, 0, 1, 1, 1, 1, 1, 0, -1, 
    1, -1, -1, 0, 0 ],
    \[ 0, 0, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 
    0, 0, 4, -3, 0, 0, -1, 3, 3, -1, 1, -2, 1, 1, -2, 1, -1, -2, 1, 0, -1, 1, 1,
    0, 2, 0, 0, -1, -1, 0, 2, -1, -1, -1, -1, 1, -1, 0, 0, 1, 1, 1, 0, -1, 0, 
    -1, -1, -1, 0, -1, 3, -2, 1, 0, 0, 2, 2, -1, 2, -2, 1, 0, -2, 0, 0, -1, 1, 
    0, -1, 1, 0, 0, 1, 0, -1, 2, 1, 0, -1, 0, 0, 1, 1, -1, 0, -1, 0, -1, 0, 0, 
    0, 1, 0, 1, 0, 1, 0, -1, -3, 2, -1, 0, 0, -3, -2, 1, -1, 2, 0, 0, 2, -1, 0, 
    2, -1, -1, 1, -2, 0, 0, -2, 1, -2, 2, 0, 1, 1, -1, -2, 1, -1, 2, 0, 0, 2, 0,
    1, 1, -1, 0, 1, 0, -1, 0, -1, 2, -3, 1, 0, -1, 2, -2, -1, 0, -1, 1, -2, -1, 
    1, 0, 1, 1, -1, 0, 0, 0, -1, -1, -1, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 
    0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, -2, 1, -1, -1, 3, 3, -1, 3, -3,
    1, 0, -2, 0, -1, -2, 1, 1, -1, 2, 0, 0, 1, 1, 1, -2, 1, -1, 0, 2, 2, 0, 0, 
    -1, 0, 0, -1, 1, 0, -2, 0, 0, 0, 1, 0, -1, 1, -1, -2, 0, -2, 0, 1, -3, -2, 
    -1, -1, 2, -1, 0, 0, 0, 1, 2, -1, -1, 0, -2, 0, -1, -1, -1, 0, 1, 0, 1, 1, 
    -1, -2, 1, -1, 1, 0, 0, 1, 0, 1, 1, 0, -1, 1, -1, -1, 0, -1, 1, 1, 0, 0, 0, 
    0, 1, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0, 1, 0, 2, -2, 0, -2, 
    0, 2, 3, -2, 2, -3, 0, 0, -2, 0, -1, -1, 1, 1, -1, 1, 0, 0, 1, 1, -2, 1, -2,
    1, 2, -3, -3, 0, -2, 3, -1, 1, 2, 1, 2, 2, -1, -1, 1, -1, -1, -1, -1, 1, 0, 
    -1, 1, -1, 0, 1, 2, -1, 2, -1, 0, -1, -2, -1, -1, -1, 0, 1, -2, 1, 1, 0, 0, 
    1, -2, 0, 0, -1, 1, -1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 
    -1, -1, 0, 1, 0, 0, 0, -1, 1, 1, 1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, 
    1, 0, 1, 0, 0, -2, 1, -1, -1, 1, 2, -1, 2, -1, 1, 0, -1, 0, -1, -1, 0, 0, 
    -1, 1, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, -1, 0, 
    0, 0, -1, 1, 0, 0, 0, 1, -1, -1, 0, 0, 0, 1, -1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, -3, -3, 1, -1, 2, -1, 0, 3, -1, 0, 2, 
    -1, 0, 1, -1, 0, 1, -2, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, -1, 0, 
    0, 0, 0, -1, 0, 0, 0, 0 ],
    \[ 0, 1, 1, 0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 
    0, 2, 0, 1, 0, 0, 2, 1, 0, 1, -1, 1, 0, 0, 0, -1, -1, 1, 0, 0, 1, 0, 1, 1, 
    -1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    -1, 0, -2, 3, 1, 0, 0, -1, -1, 1, 0, 0, -1, -2, 0, -2, -1, 0, 0, 1, 0, 0, 1,
    1, -1, 0, 1, 3, 0, 3, 0, 0, -2, 2, -2, 1, 0, 1, 2, 0, 1, 1, 0, 0, 2, 0, 0, 
    1, 0, 0, -1, -1, 0, -1, 0, -1, 1, -1, 1, 0, -1, -1, -1, -1, 0, 0, 0, 0, -2, 
    0, 1, -1, 0, 1, -1, -2, -2, 0, 1, -2, 0, 0, -1, 2, 0, 1, 0, 1, 2, 1, -2, -1,
    0, -1, -1, -2, 0, -1, 0, -1, -1, 1, -1, 0, -1, 1, -1, 1, 1, 1, 0, 1, 1, 0, 
    0, -1, 1, -1, 0, -1, 0, 0, -1, 0, 1, -1, -1, 0, 1, 0, 1, 0, 0, -1, 0, -1, 
    -1, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, -1, 
    -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, -2, 1, -2, 0, 2, 2, -1, 2, -2, 1, -1, -1, 
    0, -1, -2, 1, 1, -1, 0, 0, 0, 1, 0, 1, -1, 1, -1, 0, 1, 1, -1, 1, -2, -1, 
    -1, -2, 0, 0, -1, 1, 1, -1, 1, 0, 0, 0, -1, -4, 1, 0, -1, -1, -3, -1, 0, 0, 
    1, -1, -1, 0, -2, -1, 1, -1, 0, -1, -1, 1, 0, -2, 1, 2, -2, -1, 1, 1, 1, 0, 
    0, -1, 1, 1, 2, 1, 2, 1, 0, 0, -1, 1, 0, -1, -1, 1, 0, 0, 2, 2, 0, -1, 2, 0,
    1, 1, -1, 0, -1, 0, -1, -1, -1, 1, 1, 0, 1, 1, 1, 0, 0, -2, -3, -2, -1, 0, 
    -2, 0, -1, 0, 1, 0, 1, -1, 1, 1, 1, -1, -1, 0, -1, -1, -2, -1, 0, 0, 3, 0, 
    1, 0, -1, -1, 2, -1, 1, 0, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 0, -1, -2, 0,
    0, -1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 
    1, 2, -1, 0, 1, 0, 0, 1, -1, 0, -1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 1, 0, 1, 
    1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 
    -3, 1, -2, 0, 3, 3, -2, 2, -3, 1, 0, -1, 1, -1, -2, 2, 1, -1, 1, 0, 0, 2, 1,
    1, -2, -1, -1, 1, 0, 2, -1, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 
    0, 0, -2, 0, -1, 0, 0, 2, -1, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 
    0, 0, -1, 2, 0, 0, 0, -1, -1, 0, -1, 0, -1, -1, 0, -1, -1, 0, 0, 1, 0, -1, 
    1, 1, -1 ]
        /* order = 13824 = 2^9 * 3^3 */ >;
F:=MatrixAlgebra(RationalField(), 24) ! [ RationalField() | 4, 1, 0, 2, 1, -2, -1, 
-2, -2, 1, -2, 1, -1, -1, -1, -1, 2, -1, -2, 2, -2, 0, -1, 2, 1, 4, -1, 1, -1, 
-2, -2, -2, 0, 2, 1, -1, -2, 1, 1, -2, 1, -2, 1, 2, 1, 1, -2, -1, 0, -1, 4, 1, 
-1, 0, -1, 2, -1, -2, 0, 2, 2, -2, 1, 1, -1, 2, -1, -2, -1, -2, -1, 1, 2, 1, 1, 
4, 0, -1, -2, -1, -1, 1, 0, 1, 1, -2, 1, -1, 2, 0, 0, 1, -2, 0, -2, 2, 1, -1, 
-1, 0, 4, -1, 0, 0, -1, 1, -2, -1, -1, 1, 0, -1, 0, -1, 0, 0, -2, -1, 0, 1, -2, 
-2, 0, -1, -1, 4, 1, 1, 2, -1, 0, 1, 2, -1, 0, 1, -1, 1, 0, -1, 1, 1, 2, -1, -1,
-2, -1, -2, 0, 1, 4, 1, 0, -1, 0, -1, 0, 1, -2, 2, 0, 0, -1, 0, 0, 1, 2, -1, -2,
-2, 2, -1, 0, 1, 1, 4, 0, -2, 1, 0, 1, 0, 1, 2, -1, 2, 0, -2, 0, -1, 1, -1, -2, 
0, -1, -1, -1, 2, 0, 0, 4, 1, 1, -1, 1, 0, 1, -1, 0, 1, 2, -1, 1, 0, 0, -1, 1, 
2, -2, 1, 1, -1, -1, -2, 1, 4, 0, -2, -1, 1, 1, -2, 1, -2, 1, 2, -1, 1, -1, 0, 
-2, 1, 0, 0, -2, 0, 0, 1, 1, 0, 4, -1, 0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, -1, 1, 
-1, 2, 1, -1, 1, -1, 0, -1, -2, -1, 4, 1, -2, 0, 1, 0, 1, -1, -1, 0, 0, 0, 1, 
-1, -2, 2, 1, -1, 2, 0, 1, 1, -1, 0, 1, 4, -2, 0, 1, -1, 2, 0, -2, -1, -1, 0, 1,
-1, 1, -2, -2, 1, -1, 1, 0, 0, 1, 0, -2, -2, 4, 0, 0, -1, -2, 1, 0, 1, 1, 0, -2,
-1, 1, 1, 1, 0, 0, -2, 1, 1, 1, 1, 0, 0, 0, 4, -1, 0, 0, 2, -1, 0, 0, -1, -1, 
-1, -2, 1, -1, -1, 1, 2, 2, -1, -2, 0, 1, 1, 0, -1, 4, -1, 1, -1, -1, 0, 1, 2, 
-1, 2, 1, -1, 2, 0, -1, 0, -1, 0, 1, 0, 0, -1, -1, 0, -1, 4, 0, 0, 2, -1, 1, -1,
1, -1, -2, 2, 0, -1, 1, 0, 2, 1, -2, 1, 1, 2, -2, 0, 1, 0, 4, 0, -2, 0, -2, 0, 
1, -2, 1, -1, 0, 0, 0, -1, 0, 2, 1, 2, -1, 0, 1, 2, -1, 0, 0, 4, -1, 1, 0, -1, 
-1, 2, 2, -2, 1, 0, -1, 0, -2, -1, 2, 0, -1, -2, 0, -1, -1, 2, -2, -1, 4, 0, 2, 
0, 0, -2, 1, -1, -2, -2, 1, 0, 0, 1, -1, 2, 0, -1, 1, 0, 0, -1, 0, 1, 0, 4, 1, 
1, -2, 0, 1, -2, 0, -1, 1, 1, -1, 0, 1, 0, 0, -1, 1, 0, 1, 1, -2, 0, 2, 1, 4, 1,
-2, -1, -2, -1, -2, 0, 2, 2, 1, 0, -1, 0, 0, 0, 0, -1, 2, -1, 0, -1, 0, 1, 1, 4,
-1, 2, -1, 1, 2, 1, -1, -1, -1, -1, 0, -1, 1, 1, -2, -1, -1, 1, 1, -1, 0, -2, 
-2, -1, 4 ];
w7:=MatrixAlgebra(RationalField(), 24) ! [ RationalField() | 1, -2, -2, 4, -2, -4, 
4, 4, 0, 2, -4, 0, 0, -4, 0, -2, -2, 0, 2, 0, 4, 0, 0, -2, -2, 1, 8, -4, 10, -2,
-4, -8, 6, -6, 6, 0, 6, 4, 2, 4, 6, -2, -4, 4, 0, 2, 2, 0, 0, -8, 5, 0, 0, 0, 
-4, -6, 0, -2, 4, -2, 0, 4, -2, -2, 2, 0, 0, 2, -2, 0, 0, -4, -2, 0, 4, 3, 6, 
-4, 2, -4, 4, -2, 2, 2, 2, 2, 0, 0, 0, 2, -2, 2, 2, 2, 2, -2, 4, -2, -8, 2, -5, 
0, 2, 6, -2, 4, -2, 0, -2, -4, 2, 0, -4, 0, 0, -2, 2, -2, -2, 0, -2, 4, -2, 0, 
-2, 1, 2, 4, -2, 2, -2, 4, -2, 0, -2, -2, -2, 2, 2, 0, -2, 0, 0, 2, 0, 2, -2, 2,
-6, 2, 3, 6, -4, 4, -6, -2, -6, -4, -2, -4, -4, 2, 4, -4, 0, 2, 0, 2, 0, -4, 0, 
-2, -2, 2, -4, -3, 0, -2, 4, -2, -2, 2, 0, 0, 0, 0, -2, 0, -4, 0, -2, 0, -4, 4, 
-4, -4, 0, 2, 0, 0, -3, 2, 0, 4, 2, 0, 2, 2, 2, 0, -2, 0, -2, -2, -2, 2, 0, 0, 
0, -2, 2, 0, -2, -2, 0, -1, 2, 0, 2, 0, 2, 2, 2, 0, -2, 0, 0, 2, 0, 0, -4, 4, 8,
-2, 6, 0, -2, -8, 4, -4, 3, 0, 2, 6, 0, 2, 4, 2, -2, 2, -2, 2, 4, 2, 0, -2, 0, 
2, -2, -2, 2, 2, -2, 2, -2, 1, 0, 0, -2, -2, 0, 0, 2, 0, 2, -2, 0, -2, -2, 0, 0,
0, 0, 2, 0, -2, -2, 0, 2, 2, -1, 2, -2, -2, 0, 2, 0, 0, -4, 0, 0, -2, 2, 2, -2, 
-6, 2, 2, -4, 0, 0, -2, 4, -2, 2, -1, 2, 2, 2, -2, -4, -2, -2, 2, -2, 2, -2, -6,
4, -4, 4, 0, -8, -8, 2, -4, 8, 0, 4, 6, 1, 2, 6, -2, -6, 2, -2, 0, 0, -2, 4, -2,
0, 0, -4, 4, 0, 0, -2, -2, 0, -4, -4, 0, 0, -1, -2, 0, 2, -2, -2, 0, -2, 0, -4, 
4, -4, 4, 0, -4, 6, 4, 0, 2, -6, 2, 0, -4, 2, 0, -3, 2, 0, 0, 4, 0, 0, 2, -2, 0,
-6, 0, -4, 0, 2, 0, -2, 0, -2, 2, 0, 0, 2, 0, -2, 1, 0, 2, -2, -4, -2, 0, -2, 4,
-2, -4, 4, 2, -2, -4, 0, -2, 4, 2, 4, 4, 4, 4, 4, 0, -5, 0, -2, -2, 0, 2, 0, 2, 
2, 2, 2, -4, 2, 2, 4, -2, -2, 0, 0, -2, 0, 0, -2, 0, 2, 1, 2, 4, 2, 2, -2, 8, 2,
-4, 4, 0, 0, 0, 2, -2, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, -1, 0, 2, 4, 0, 4, 0, -2, 
2, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 3, 0, 2, 2, -2, 2, 4, -6, 
2, 0, 4, 0, 2, -4, -2, -6, 0, -4, -2, -2, 0, 4, -2, 0, 0, 1, 0, 0, 2, -4, 8, -4,
-4, 8, 6, -2, 6, -8, 2, -2, -4, -2, -4, -6, 4, 4, -2, 4, 0, 2, -1 ];
load constnebe;

