"Source: Text/Group/GrpMatGen.text";
"Line: 1243";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatGen.text, line: 1243
// Example: H66E8 ()
print "Example: H66E8";
ei := GetEchoInput();
SetEchoInput(true);
K<w> := FiniteField(4);
GL34 := GeneralLinearGroup(3, K);
x := GL34 ! [w,0,1, 0,1,0, 1,0,1];
x;
Degree(x);
assert $1 eq 3;
Determinant(x);
Trace(x);
Order(x);
assert $1 eq 15;
m<t> := MinimalPolynomial(x);
m;
Factorization(m);
c<t> := CharacteristicPolynomial(x);
c;
SetEchoInput(ei);
