Direct product of A5 and Z2

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Definition

This group is defined in the following equivalent ways:

1. It is the full icosahedral group: it is the group of all rigid symetries of the regular icosahedron, including both orientation-preserving symmetries and orientation-reversing symmetries.
2. It is the external direct product of the alternating group of degree five and the cyclic group of order two.

GAP implementation

Group ID

This group has ID $35$ among the groups of order $120$. Thus, it can be defined using GAP's SmallGroup function:

SmallGroup(120,35)

Other definitions

The group can also be defined using GAP's DirectProduct, AlternatingGroup and CyclicGroup functions:

DirectProduct(AlternatingGroup(5),CyclicGroup(2))