"Source: Text/Group/GrpFP.text";
"Line: 6728";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 6728
// Example: H80E52 ()
print "Example: H80E52";
ei := GetEchoInput();
SetEchoInput(true);
G<x, y> := DihedralFPGroup(6);
C, V, E := CayleyGraph(G);  C;
d := Diameter(C);  d;
p := DiameterPath(C);  p;
word := &* [ Label(E![p[i], p[i+1]]) : i in [1..d]];
word;
D := UnderlyingGraph(C);  D;
A := AutomorphismGroup(D);  A;
subs := Subgroups(A);
P := PermutationGroup(G);
exists(j){ i : i in [1..#subs] | IsIsomorphic(P, subs[i]`subgroup)};
j;
SetEchoInput(ei);
