Direct product of UT(3,p) and Zp

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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 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 \ne 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).