[GAP Forum] How many elements of SymmetricGroup can be represented by GAP ?

[Marco Costantini]

Dear Kang ByoungKwan and dear forum members,

> I met the problem about limit # of representing elements of symmetric
> group.
> This is my partial code for using all elements of symmetric group
>
> gap>idx:=10;
> gap>G:=SymmetricGroup(idx);
> gap>sub:=Elements(G);
>
> gap: cannot extend the workspace any more
> gap: Press <Enter> to end program

There are 3628800 element in SymmetricGroup(10) and these are too much,
not only for Gap to store all them in memory (at least on your computer),
but also for you, to consider all of them.

The standard suggestion in this case is to consider only the conjugacy
classes.

idx := 10;
G := SymmetricGroup( idx );
cc := ConjugacyClasses( G );

For further information, see the Gap help about this topic, with the
command

?Conjugacy Classes

Best regards,
Marco Costantini