SmallGroup(p^4,3)

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

Definition

Let $p$ be a prime number. This group is defined by the followin presentation:

$G:=\langle a,b,c\mid a^{p^{2}}=b^{p}=c^{p}=e,ab=ba,bc=cb,cac^{-1}=ab\rangle$

It is a group of order $p^{4}$. Particular cases are $p=2$ (we get SmallGroup(16,3)) and $p=3$ (we get SmallGroup(81,3)).