"Source: Text/Group/GrpPC.text";
"Line: 373";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 373
// Example: H70E2 ()
print "Example: H70E2";
ei := GetEchoInput();
SetEchoInput(true);
G<a,b,c,d,e> := PolycyclicGroup<a, b, c, d, e |
             a^2 = c, b^2, c^2 = e, d^5, e^2,
             b^a = b*e, d^a = d^2, d^c = d^4 >;
F<a,b,c,d,e> := FreeGroup(5);
rels := { a^2 = c, b^2 = Id(F), c^2 = e, d^5 = Id(F), e^2 = Id(F),
     b^a = b*e, d^a = d^2, d^c = d^4 };
G<a,b,c,d,e> := quo< GrpPC : F | rels >;
G;
Order(G);
assert $1 eq 80;
IsAbelian(G);
assert not $1;
SetEchoInput(ei);
