This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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This group, denoted , , , is defined in the following equivalent ways:
- It is the direct product of cyclic group of order nine and cyclic group of order two.
- It is the cyclic group of order .
This finite group has order 18 and has ID 2 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(18,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [18,2]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
The group can be defined using GAP's CyclicGroup function: