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
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
It is given by the presentation (with denoting the identity element):
It is part of the family of groups: semidirect product of cyclic group of prime-square order and cyclic group of prime order.
|group of prime power order||Yes|
This finite group has order 27 and has ID 4 among the groups of order 27 in GAP's SmallGroup library. For context, there are groups of order 27. 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(27,4);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [27,4]
or just do:
to have GAP output the group ID, that we can then compare to what we want.