[GAP Forum] Orbits for subgroups of S_n

[Matthew Fayers]

Dear GAP forum,

I have a calculation that I want to carry out (repeatedly with the data 
varying) without running into memory difficulties.

Let S_n denote the symmmetric group on {1,...,n}.  I have subgroups H <= 
K <= S_n; these subgroups are defined by (small) generating sets.  I 
have an element g in S_n.  When subgroups of S_n act on S_n by 
conjugation, the K-orbit containing g is partitioned into H-orbits.  I'd 
like to find representatives for these H-orbits (ideally, the 
representatives which are smallest in the usual GAP order for 
permutations).  In practice, K is so large that computing the whole of 
the K-orbit containing g exceeds the available memory.

Does anyone have any idea how I can accomplish this?

Best wishes,
Matt Fayers.

_______________________________________________________________
Matthew Fayers
School of Mathematics
Queen Mary University of London
Mile End Road
London
E1 4NS
020 7882 5479