[GAP Forum] StructureDescription

[Robert Heffernan]

On 2/26/06, Nilo de Roock <ndroock1 at gmail.com> wrote:> The issue I have here is that "C5:C4" occurs twice in the list. What I am> looking for is a command that would recognize that the Frobenius group> <s,t; s^4 = t^5 = 1, ts = st^2> is in there somewhere.
The semidirect product of two groups is not unique, this is why C5:C4occurs twice.  You can ask GAP to construct an explicit isomorphismbetween F and one of the two C5:C4 groups:
gap> F:=FreeGroup(2);;gap> s:=F.1;; t:=F.2;;gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1];;gap> StructureDescription(G);"C5 : C4"gap> IsomorphismGroups(G,SmallGroup(20,1));failgap> IsomorphismGroups(G,SmallGroup(20,3));[ f1, f2 ] -> [ f1, f3 ]
So, as you can see, F is isomorphic to SmallGroup(20,3).
I hope this helps.