Elements of the group with largest degree

Question

I want to find the elements of the Alternating group of some largest degree, but when I try

g:=Elements(AlternatingGroup(31));

it always gives an error of exceeded the permitted memory. Is there anyway to check the elements of the altenating group of largest degree?

Answer 1

Presumably (from the comments) you are looking for the largest order. The GAP command to do so from class representative would be (for a group $G$):

 Maximum(List(ConjugacyClasses(G),x->Order(Representative(x)));

but for the alternating groups of course this either can be calculated from partitions

par:=Filtered(Partitions(31),x->IsEvenInt(Number(x,y->IsEvenInt(y))));;
Maximum(List(par,Lcm));

or even looked up in OEIS: https://oeis.org/A051593 .