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This group can be defined in the following equivalent ways:
- It is the cyclic group, and specifically finite cyclic group, of order 36.
- It is the external direct product of cyclic group:Z4 and cyclic group:Z9.
This finite group has order 36 and has ID 2 among the groups of order 36 in GAP's SmallGroup library. For context, there are 14 groups of order 36. 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(36,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [36,2]
or just do:
to have GAP output the group ID, that we can then compare to what we want.