"Source: Text/Group/GrpPC.text";
"Line: 2082";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 2082
// Example: H70E13 ()
print "Example: H70E13";
ei := GetEchoInput();
SetEchoInput(true);
G<a,b,c,d> := PolycyclicGroup<a,b,c,d| a^3, b^5, c^5, d^5,
  b^a = c, c^a = d, d^a = b>;
H := sub<G| b,c>;
Order(H);
assert $1 eq 25;
IsAbelian(H);
assert $1;
IsNormal(G, H);
assert not $1;
N := ncl<G| b,c>;
IsNormal(G, N);
assert $1;
Order(N);
assert $1 eq 125;
SetEchoInput(ei);
