SmallGroup(p^4,3)

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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)).