Direct product of A5 and S3

Definition
This group can be defined in a number of equivalent ways:


 * 1) It is the direct product of the alternating group of degree five and the symmetric group of degree three. In other words, it is $$A_5 \times S_3$$.
 * 2) It is the member of family::outer linear group $$OL(2,4)$$, i.e., it is the semidirect product of the general linear group:GL(2,4) by a two-element cyclic group acting via the transpose-inverse map.

Group ID
This group has ID $$121$$ among the groups of order $$360$$. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(360,121)

Other definitions
The group can be defined using the DirectProduct function:

DirectProduct(AlternatingGroup(5),SymmetricGroup(3))