[GAP Forum] Groups of order 192

[Stefan Kohl]

On Thu, September 11, 2014 6:22 pm, hadi Hooshmand wrote:
> Dear All,
>
> Let $G$ be a group of order 192 and $d$ a positive divisor of it . Is it
> true
> that there exists a subgroup of $G$ with order or index $d$?
>
> Is there any GAP code to check the question by an ordinary computer?
> Does anyone know the answer?

Just enter

gap> check := n->ForAll(AllGroups(n),
>                    G->ForAll(DivisorsInt(n),
>                              d->Intersection([d,n/d],
>                                              List(ConjugacyClassesSubgroups(G),
>                                                   cl->Size(Representative(cl))))<>[]));;
gap> check(192);

and have some patience.

Hope this helps,

    Stefan Kohl

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