Direct product of A5 and S3
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Definition
This group can be defined in a number of equivalent ways:
- It is the direct product of the alternating group of degree five and the symmetric group of degree three. In other words, it is
.
- It is the outer linear group
, 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 among the groups of order
. 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))