-- Dear Gap Forum,
Alex Trofimuk asked:
How to find a split extensions G of group H by group N, i.e. G/N is
isomorphic to H?
So I define group H:
gap> F:=FreeGroup("a","b","c");
<free group on the generators [ a, b, c ]>
gap> a:=F.1;b:=F.2;c:=F.3;
a
b
c
gap> rels:=[a*(b*c)^-1,b^3*(a*b*c)^-1,a*b*(c^-1)^3];
[ a*c^-1*b^-1, b^3*c^-1*b^-1*a^-1, a*b*c^-3 ]
gap> H:=F/rels;
<fp group on the generators [ a, b, c ]>
gap> Size(H);
48
So I define group N:
N:=ExtraspecialGroup(125,5);
<pc group of size 125 with 3 generators>
Alex Trofimuk.
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