Direct product of UT(3,p) and Zp

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 as the external direct product of unitriangular matrix group:UT(3,p) (order $p^{3}$) and the group of prime order $\mathbb {Z} _{p}$. The whole group has order $p^{4}$.

GAP implementation

For $p\neq 2$, the group has GAP ID $(p^{4},12)$. For $p=2$, the group is direct product of D8 and Z2 and has GAP ID $(16,11)$.