Direct product of UT(3,p) and Zp

Definition
Let $$p$$ be a prime number. This group is defined as the defining ingredient::external direct product of defining ingredient::unitriangular matrix group:UT(3,p) (order $$p^3$$) and the defining ingredient::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 $$(16,11)$$.