"Source: Text/Group/GrpPC.text";
"Line: 1128";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 1128
// Example: H70E7 ()
print "Example: H70E7";
ei := GetEchoInput();
SetEchoInput(true);
E := DihedralGroup(GrpPC,5);
A := CyclicGroup(GrpPC,8);
f1 := hom<A->A|A.1->(A.1)^-1>;
f2 := hom<A->A|A.1->A.1>;
H := Extension(A, E, [f1, f2]);
QH := SylowSubgroup(H,2);
t := TrivialModule(QH, FiniteField(5));
B := Induction(t, H);
G := Extension(B, H);
print G;
print DerivedLength(G);
assert $1 eq 3;
P := SylowSubgroup(G,5);
Q := SylowSubgroup(G,2);
print  Maximum({x[2]:x in Classes(G)});
assert $1 eq 1250;
print  Maximum({x[2]:x in Classes(P)});
assert $1 eq 625;
print  Maximum({x[2]:x in Classes(Q)});
assert $1 eq 4;
SetEchoInput(ei);
