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 is defined as the cyclic group of order , and is denoted , or .
|prime-base logarithm of order||5|
|prime-base logarithm of exponent||5|
|minimum size of generating set||1|
|rank as p-group||1|
This finite group has order 243 and has ID 1 among the groups of order 243 in GAP's SmallGroup library. For context, there are groups of order 243. 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(243,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [243,1]
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 as: