[GAP Forum] The other intersection

[Thomas Breuer]

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