"Source: Text/Group/GrpGPC.text";
"Line: 1473";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpGPC.text, line: 1473
// Example: H81E8 ()
print "Example: H81E8";
ei := GetEchoInput();
SetEchoInput(true);
F<a,b,c> := FreeGroup(3);
rels := [ b^a=b*c, b^(a^-1)=b*c^-1 ];
G<a,b,c> := quo<GrpGPC: F | rels>;

S := sub<G|(a*b)^3, c^7, b^21>;
Index(G, S);
assert $1 eq 441;
pi, P, K := CosetAction(G, S);
P;
K;
Index(G, K);
assert $1 eq 3087;
{@ G!x : x in PCGenerators(K) @};
pi(S);
Index(P, pi(S));
assert $1 eq 441;
SetEchoInput(ei);
