? Wang asked:
> Hi Forum,
> Given a finite group G and one of its maximal subgroup M. I want
> to know the lengths of the M-orbits on the set {Mx | x in G}.
> The moset simple way I know is
> List(DoubleCosets(G,M,M),x->Size(x)/Size(M));
> However, while the index |G:M| is quite large, say 10^6, the above
> method failed. Are there any other methods to get the lengths of
> M-orbits? I also tried to calculate the cosets set of M in G, but
> it didn't work either.

I am afraid the chances are not very good for any *general* methods
that do not depend on the way, the group is given, and may not be very
good anyhow. But could you just tell how your group is given
(permutation, matrix, fp group, character table?). Maybe in certain
cases somebody has an idea.

Joachim Neubueser