Semidirect product of cyclic group of prime-cube order and cyclic group of prime order
This article is about a family of groups with a parameter that is prime. For any fixed value of the prime, we get a particular group.
View other such prime-parametrized groups
This finite group has order the fourth power of the prime, i.e., , and has ID 6 among the groups of order in GAP's SmallGroup library. For context, there are 15 groups of order for odd and 14 groups of order for . It can thus be defined using GAP's SmallGroup function as follows, assuming is specified beforehand:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^4,6);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^4,6]
or just do:
to have GAP output the group ID, that we can then compare to what we want.