"Source: Text/Group/GrpMatGen.text";
"Line: 5939";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatGen.text, line: 5939
// Example: H66E34 ()
print "Example: H66E34";
ei := GetEchoInput();
SetEchoInput(true);
n := 4;
N := 4*n;
K<z> := CyclotomicField(N);
zz := z^4;
i := z^n;
cos := (zz+ComplexConjugate(zz))/2;
sin := (zz-ComplexConjugate(zz))/(2*i);
gl := GeneralLinearGroup(3, K);
G := sub< gl | [ cos, sin, 0,  
                -sin, cos, 0,  
                   0,   0, 1 ], 
               [  -1,   0, 0,  
                   0,   1, 0,  
                   0,   0, 1 ] >;
 #G;
assert $1 eq 8;
D8 := DihedralGroup(4);
D8;
#D8;
assert $1 eq 8;
bool, iso := IsIsomorphic(G, D8);
bool;
assert $1;
iso;
SetEchoInput(ei);
