Direct product of S5 and V4
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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))