Direct product of Z6 and Z3
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This group is defined in the following equivalent ways:
- It is the direct product of the cyclic group of order six and the cyclic group of order three.
- It is the direct product of the elementary abelian group of order nine and cyclic group of order two.
- It is the direct product of the cyclic group of order two and two copies of the cyclic group of order three.
This finite group has order 18 and has ID 5 among the groups of order 18 in GAP's SmallGroup library. For context, there are groups of order 18. 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(18,5);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [18,5]
or just do:
to have GAP output the group ID, that we can then compare to what we want.