[GAP Forum] The other intersection

[Motalane, John]

Thank you very much.

On Tue, Sep 22, 2020 at 11:09 AM Thomas Breuer <sam at math.rwth-aachen.de>
wrote:

> Dear GAP Forum, dear John,
>
> the group Sp(6,2) has maximal subgroups of the orders 2^6 * 168 and
> 504 * 3; there is one class of each of these orders.
>
>     gap> g:= SP( IsPermGroup, 6, 2 );
>     Perm_Sp(6,2)
>     gap> mx:= MaximalSubgroupClassReps( g );;
>     gap> m1:= Filtered( mx, x -> Size(x) = 2^6 * 168 );
>     [ <permutation group of size 10752 with 2 generators> ]
>     gap> m2:= Filtered( mx, x -> Size(x) = 504 * 3 );
>     [ <permutation group of size 1512 with 2 generators> ]
>
> For possible intersections of members of these classes,
> one can fix one representative, and consider conjugates of the other.
>
>     gap> Size( Intersection( m1[1], m2[1] ) );
>     12
>     gap> repeat inter:= Intersection( m1[1], m2[1]^Random(g) );
>     >    until Size( inter ) <> 12;
>     gap> Size( inter );
>     168
>
> All the best,
> Thomas
>
>
> On Tue, Sep 22, 2020 at 10:33:51AM +0200, Motalane, John wrote:
> > Dear All
> >
> > Hoping that you are all well.
> >
> > I am working on the Symplectic group Sp(6,2).
> >
> > I am having a problem to get the other intersection, for an example the
> > intersection of the maximal subgroups 2^6:L3(2) and L2(8):3 is having two
> > candidates which are A_4 and PSL(3,2). In GAP, I am able to get A_4 only.
> > Please help me to get the other candidate using GAP.
> >
> > Thanks in advance
> >
> > Warm regards John
>
>

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