The following variables are predefined as according permutation groups
with a default smallest set of generators:
C2, C3, C4, V4, C5, C6, S3,
C7, C8, C2xC4, C2xC2xC2, D8, Q8,
C9, C3xC3, C10, D10, C11, C12,
C2xC6, D12, A4, T, C13, C14,
D14, C15.
gap> S3; S3 gap> Elements( S3 ); [ (), (2,3), (1,2), (1,2,3), (1,3,2), (1,3) ] gap> IsPermGroup( S3 ); true gap> S3.generators; [ (1,2), (1,2,3) ]
GAP 3.4.4