[GAP Forum] Checking if permutation action has self-paired orbitals

[Frederic Vanhove]

Dear forum,

suppose you have a group acting on a set.  The orbitals are the orbits 
on ordered pairs of elements of that set, and their number
can be computed in GAP using
RankAction(groupname,setname);

But I would like to know if these orbitals are self-paired, i.e. that 
(x1,x2) and (x2,x1) are always in the same orbit.
What is the easiest way to check this?

More generally, I would like to check if the permutation character is at 
least multiplicity-free.

Many thanks,
Kind regards,
Frédéric