/*
2"S5+ as 4 x 4 matrices over Z[w].
Rep chi_8 in the ATLAS.
*/

F<w>:=CyclotomicField(3);i3:=2*w+1;
// F<i3>:=QuadraticField(-3);w:=(-1+i3)/2;

G<x,y>:=MatrixGroup<4,F|[
1,0,0,0,
0,1,0,0,
w,-1,-1,0,
1,w+1,0,-1]
,\[
0,1,0,0,
0,0,1,0,
0,0,0,1,
-1,0,0,0]
>;

C:=x;D:=y;