[GAP Forum] Generating the total number of distinct permutations in the set UG

[Marco Costantini]

Dear Dursun Bulutoglu and Gap forum,

> 	I was able to generate two permutation groups U and G in GAP.  U
> has order 480 and G has order 185794560. Let elements of U be u_1, u_2,
> ...u_480. I am interested in the cosets
> u_1G, u_2G,...u_480G. I would like to be able to compute the number of
> distinct such cosets of G. (Here there may be repeated cosets.) I was
> wondering how I could do this  efficiently in GAP.

Try something like the following:

I := Intersection( U, G );
rc := RightCosets( G, I );
Length ( rc );

Best regards,
Marco Costantini