[GAP Forum] computing maximal transitive subgroups of a transitive group

[Alexander Hulpke]

Dear Bill, Dear Forum,

This should work reasonably quickly. Given a group G, try

m:=Filtered(MaximalSubgroupClassReps(G),x->IsTransitive(x,MovedPoints(G)));;
List(m,TransitiveIdentification);

If this does not work satisfactory, let me know which group it fails on.

Best,

  Alexander (Hulpke)


Mitto ab tabulariUM meum

> On Nov 9, 2019, at 16:18, Bill Allombert <Bill.Allombert at math.u-bordeaux.fr> wrote:
> 
> Dear GAP forum,
> 
> I need to compute the maximal transitive subgroups of a transitive
> group (grouped by conjugacy classes).
> 
> For example for S4, I should get A4 and two conjugate copies of D4.
> 
> I managed to do the computation for all transitive groups of degree
> <=13, but for 14 it become quite slow.
> 
> Are there good algorithms to solve this problem ?
> 
> Thanks in advance for your help!
> Bill.
> 
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