# S_3 as dihedral group:
f := FreeGroup("a","b"); a := f.1;; b := f.2;;
rels := [a^2,b^3,a*b*a*b];
g := f/rels;
Size(g);
Elements(g);
d := DerivedSubgroup(g);
Size(d);
iso := IsomorphismFpGroup(d);
dd := Image(iso);
RelatorsOfFpGroup(dd);
Index(g,d);
q := g/d;
Size(q);
iso := IsomorphismFpGroup(q);
qq := Image(iso);
RelatorsOfFpGroup(qq);
# A bigger example:
f := FreeGroup("a","b"); a := f.1;; b := f.2;;
rels := [a^2,b^3,(a*b)^11,Comm(a,b)^6,(a*b*a*b*a*b^-1)^6];
g := f/rels;
Size(g);
iso := IsomorphismPermGroup(g);
p := Image(iso);
DisplayCompositionSeries(p);
IsSimple(p);
# Even worse:
f := FreeGroup("a","b","c","d");
a := f.1;; b := f.2;; c := f.3;; d := f.4;;
rels := [a^2,b^3,a*b*a*b,a*c*a/d,a*d*a/c,b*c*b^2*d,b*d*b^2/(c/d),Comm(c,d)];
g := f/rels;
Size(g);   # this is not going to work
AbelianInvariants(g);
l := LowIndexSubgroupsFpGroup(g,6);
List(l,AbelianInvariants);