"Source: Text/Group/GrpPC.text";
"Line: 665";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 665
// Example: H70E4 ()
print "Example: H70E4";
ei := GetEchoInput();
SetEchoInput(true);
E := PolycyclicGroup<a1,a2,b1,b2,z|a1^3,a2^3,b1^3=z,b2^3=z,
  z^3,b1^a1=b1*z,b2^a2=b2*z>;
FactoredOrder(E);
Exponent(E);
assert $1 eq 9;
D3 := DihedralGroup(GrpPC, 3);
#D3;
assert $1 eq 6;
IsNilpotent(D3);
assert not $1;
SetEchoInput(ei);
