[GAP Forum] StructureDescription

[Nilo de Roock]

Hello GAP forum,

Forgive for yet another question (...) on this command, perhaps I am using  
the wrong command for my purpose. When I execute the following command.

gap> List(AllGroups(20),StructureDescription);

GAP responds with
[ "C5 : C4", "C20", "C5 : C4", "D20", "C10 x C2" ]

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.


Even if I do...

gap> F:=FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> s:=F.1;
f1
gap> t:=F.2;
f2
gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1];
<fp group on the generators [ f1, f2 ]>
gap> Size(G);
20
gap> str(G);
"C5 : C4"
gap>

the answer is "C5:C4".


I am getting lost on this command, and thus on GAP. Please help.

-- 
met vriendelijke groet,
Nilo de Roock