[GAP Forum] Fixed point free permutations of specific order

[Aner Ben-Efraim]

Dear Forum,
I am interested in getting all permutations of order n (order 2 is also good) in the group SymmetricGroup([2..m]), which keep no point in place.
I have tried to use Filtered(SymmetricGroup([2..m]),x->Order(x)=n and NrMovedPoints(x)=m-1), but this gets extremely slow when m is double digit. I was wondering if there is a way to do this in reasonable time on my PC, at least for m up to say 17, or even 33 if possible.
Thanks,Aner