Direct product of Z6 and Z2
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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 cyclic group of order two.
- It is the direct product of the Klein four-group and the cyclic group of order three.
- It is the direct product of the cyclic group of order three and two copies of the cyclic group of order two.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 12#Arithmetic functions
This finite group has order 12 and has ID 5 among the groups of order 12 in GAP's SmallGroup library. For context, there are 5 groups of order 12. 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(12,5);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [12,5]
or just do:
to have GAP output the group ID, that we can then compare to what we want.