Direct product of S5 and V4

Definition
This group is defined in the following equivalent ways:


 * 1) It is the direct product of the symmetric group of degree five and the defining ingredient::Klein four-group.
 * 2) it is the direct product of the symmetric group of degree five and two copies of the cyclic group of order two.
 * 3) It is the automorphism group of general linear group:GL(2,5).
 * 4) It is the direct product of the automorphism group of general linear group:GL(2,4) and the cyclic group of order two.

Group ID
This group has ID $$1186$$ among the groups of order $$480$$, so it can be defined using GAP's SmallGroup function as:

SmallGroup(480,1186)

Other definitions
The group can be defined using GAP's DirectProduct, SymmetricGroup, and CyclicGroup functions:

DirectProduct(SymmetricGroup(5),CyclicGroup(2),CyclicGroup(2))

It can also be defined using the AutomorphismGroup and GeneralLinearGroup functions:

AutomorphismGroup(GL(2,5))