Direct product of S5 and V4

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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 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.

GAP implementation

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))