/*
G has 160 images of v = V.1.

0        296     0       74      0
-1       17      1/2     4       3/8
1        17      1/2     4       3/8
-i - 1   8       1/2     2       1/8
-i       17      1/2     4       3/8
-i + 1   8       1/2     2       1/8
i - 1    8       1/2     2       1/8
i        17      1/2     4       3/8
i + 1    8       1/2     2       1/8
*/

F<i>:=QuadraticField(-1);

G<x,y>:=MatrixGroup<20,F|[
-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,-i,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,-i,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,i-1,1,-i,-i-1,-1,1,0,-i-1,0,0,-i,i+1,0,0,i-1,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,
-1,-i,0,0,0,1,-i,i,i,0,i,0,0,0,0,1,-i,0,0,0,
0,0,0,-i+1,-i+1,0,0,i-1,0,i-1,0,-i+1,i,i+1,0,-i,0,-i,0,0,
0,i-1,-i+1,-i+1,0,-1,0,0,0,-1,0,-i,i+1,i+1,0,0,0,-i+1,0,0,
0,-i+1,-1,i,i+1,i+1,0,-1,0,0,0,i+1,-i-1,0,0,-i+1,0,0,0,0,
0,-i,i,0,1,-i+1,i-1,1,i+1,0,0,0,0,0,i,-i-1,0,0,-i-1,-i+1,
0,0,0,0,0,0,0,0,0,0,0,-i,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,
0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-i,0,0,0,1,0,0,0,0,1,0,0,-1,0,0,-i-1,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-i,0]
,[
0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,1,0,i-1,0,1,0,0,0,0,1,0,-i,0,-i,0,0,
0,0,0,-i-1,-i-1,0,0,i+1,0,i+1,0,-i-1,1,-i+1,0,-1,0,-1,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-i,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,-1,0,-i,i,-1,1,0,0,0,0,-i,0,0,i,1,i,
0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,0,i,0,-1,1,i,0,0,-1,1,0,i,0,0,0,-i,1,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
i,0,0,0,i-1,0,-i-1,i+1,i,0,1,0,0,0,-1,-i+1,-i-1,0,-i+1,i,
0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,0,0,-i,0,0,0,1,0,0,0,0,1,0,0,-1,0,0,-i-1,1,
0,i+1,-i,-1,i-1,i,-i,0,i-1,0,0,-1,-i+1,0,0,i+1,0,0,0,0,
i+1,0,0,i,i+1,0,i-1,-i,-i+1,0,-i,i+1,-1,0,0,-i,i-1,0,0,0,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]
>;

// Complex conjugates of x and y.
xc:=GL(20,F)![Conjugate(u):u in Eltseq(x)];
yc:=GL(20,F)![Conjugate(u):u in Eltseq(y)];

// Forms: B1 (Hermitian).
// B1 (Hermitian form): Determinant 10871635968 = 2^27.3^4.
B1:=MatrixAlgebra(F,20)![
6,-i,i,-i,-i,0,-i,i,1,-i-1,1,i-1,0,1,0,i+1,-i+1,0,i,1,
i,6,1,1,0,-i,0,1,-i,-i,i+1,-i,i,0,1,-1,-i-1,1,i,0,
-i,1,6,0,1,1,-i,0,0,i,1,i,-i,-i,-1,-i,i+1,-1,0,i,
i,1,0,6,-1,i,-1,0,0,1,1,-1,-i,-i,-1,i,0,-1,i-1,-i,
i,0,1,-1,6,-1,-i+1,1,-1,1,0,-1,1,0,-1,i,-i-1,i,1,i-1,
0,i,1,-i,-1,6,i,-i,-i+1,0,-i+1,0,1,i,0,i,1,1,1,i-1,
i,0,i,-1,i+1,-i,6,1,i+1,1,-i,-1,0,i+1,-1,-i+1,i,-i+1,1,1,
-i,1,0,0,1,i,1,6,-i-1,-1,i,1,-1,i,1,1,i+1,-i,i+1,-1,
1,i,0,0,-1,i+1,-i+1,i-1,6,0,-1,-i+1,1,-1,-1,i,1,i,1,1,
i-1,i,-i,1,1,0,1,-1,0,6,-i+1,0,i,i,i-1,1,-i,-i,-1,-i+1,
1,-i+1,1,1,0,i+1,i,-i,-1,i+1,6,0,i,-i+1,1,i,1,1,0,0,
-i-1,i,-i,-1,-1,0,-1,1,i+1,0,0,6,1,-i,i+1,i,1,-1,1,0,
0,-i,i,i,1,1,0,-1,1,-i,-i,1,6,-1,-i-1,0,-1,0,i+1,-1,
1,0,i,i,0,-i,-i+1,-i,-1,-i,i+1,i,-1,6,i,i,0,i,-i,0,
0,1,-1,-1,-1,0,-1,1,-1,-i-1,1,-i+1,i-1,-i,6,0,0,-i+1,1,1,
-i+1,-1,i,-i,-i,-i,i+1,1,-i,1,-i,-i,0,-i,0,6,i,0,-i-1,1,
i+1,i-1,-i+1,0,i-1,1,-i,-i+1,1,i,1,1,-1,0,0,-i,6,-1,-1,i,
0,1,-1,-1,-i,1,i+1,i,-i,i,1,-1,0,-i,i+1,0,-1,6,0,i,
-i,-i,0,-i-1,1,1,1,-i+1,1,-1,0,1,-i+1,i,1,i-1,-1,0,6,-i+1,
1,0,-i,i,-i-1,-i-1,1,-1,1,i+1,0,0,-1,0,1,1,-i,-i,i+1,6];


// Centralising algebra: Scalars only.
C1:=MatrixAlgebra(F,20)!Eltseq(y^3);