"Source: Text/Group/GrpGPC.text";
"Line: 2209";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpGPC.text, line: 2209
// Example: H81E12 ()
print "Example: H81E12";
ei := GetEchoInput();
SetEchoInput(true);
F<t, a,b, c,d> := FreeGroup(5);
G<t, a,b, c,d> := quo<GrpGPC: F | a^2, b^16, b^a=b^15,
                                  c^2, d^16, d^c=d^15,
                     t^2, a^t=c, b^t=d, c^t=a, d^t=b>;
IsNilpotent(G);
assert $1;
D1 := sub<G|a,b>;
D2 := sub<G|c,d>;
D3<u,v> := sub<G|a*c, b*d>;

IsConjugate(G, D1, D2);
IsConjugate(G, b, d^-1);
IsConjugate(D3, D1, D2);
assert not $1;
IsConjugate(D3, b, d^-1);
assert not $1;
SetEchoInput(ei);
