Direct product of E8 and Z3
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This group is defined in the following equivalent ways:
- It is the direct product of the elementary abelian group of order eight and the cyclic group of order three.
- It is the direct product of the cyclic group of order six and the Klein four-group.
This finite group has order 24 and has ID 15 among the groups of order 24 in GAP's SmallGroup library. For context, there are 15 groups of order 24. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(24,15);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [24,15]
or just do:
to have GAP output the group ID, that we can then compare to what we want.