Direct product of A5 and S3

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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
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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 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.

GAP implementation

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))