Direct product of A5 and S3
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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.
This group has ID among the groups of order . It can thus be defined using GAP's SmallGroup function as:
The group can be defined using the DirectProduct function: