"Source: Text/Group/GrpGPC.text";
"Line: 2486";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpGPC.text, line: 2486
// Example: H81E13 ()
print "Example: H81E13";
ei := GetEchoInput();
SetEchoInput(true);
F<a,b,c,d,e> := FreeGroup(5);
G<a,b,c,d,e> := quo< GrpGPC : F | c^6 = F!1, e^3 = F!1,
                                  d^c=d*e, e^c=e^2,
                                  b^a=b^-1,
                                  b^(a^-1)=b^-1,
                                  c^b=c*e,
                                  c^(b^-1)=c*e,
                                  d^b=d^-1,
                                  d^(b^-1)=d^-1,
                                  e^b=e^2,
                                  e^(b^-1)=e^2 >;
H := sub< G | c,d,e >;
IsNormal(G, H);
assert $1;
GModulePrimes(G, H);
M, pi := GModule(G, H, 3);
M;
submod := Submodules(M);
nsgs := [ m @@ pi : m in submod ];
[ PCGenerators(s, G) : s in nsgs ];
SetEchoInput(ei);
