Direct product of S5 and V4

From Groupprops
Jump to: navigation, search
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 group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

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))