Direct product of S3 and S3

Definition
This group is defined as the defining ingredient::external direct product of two copies of the symmetric group of degree three.

It can alternatively be defined as the subgroup of the symmetric group on $$\{ 1,2,3,4,5,6 \}$$ generated by the elements $$(1,2,3), (1,2), (4,5,6), (4,5)$$.

Other descriptions
The group can be constructed using GAP's DirectProduct and SymmetricGroup functions:

DirectProduct(SymmetricGroup(3),SymmetricGroup(3))