# Direct product of S5 and V4

From Groupprops

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

This group is defined in the following equivalent ways:

- It is the direct product of the symmetric group of degree five and the Klein four-group.
- it is the direct product of the symmetric group of degree five and two copies of the cyclic group of order two.
- It is the automorphism group of general linear group:GL(2,5).
- 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 among the groups of order , 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))