Direct product of Z9 and E9
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This group is defined as the direct product of the cyclic group of order 9 and elementary abelian group of order 9. Equivalently, it is the direct product of the cyclic group of order and two copies of the cyclic group of order 3.
|minimum size of generating set||3|
|group of prime power order||Yes|
This finite group has order 81 and has ID 11 among the groups of order 81 in GAP's SmallGroup library. For context, there are 15 groups of order 81. 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(81,11);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [81,11]
or just do:
to have GAP output the group ID, that we can then compare to what we want.