Direct product of Z16 and V4

Definition
This group is defined as the uses as intermediate construct::external direct product of the cyclic group of order 16 and defining ingredient::Klein four-group (i.e., the elementary abelian group of order four). In other words, it is given by the presentation:

$$G := \langle a,b,c \mid a^{16} = b^2 = c^2 = e, ab = ba, bc = cb, ac = ca \rangle$$.

It is the abelian group of prime power order corresponding to the prime $$2$$ and the partition $$6 = 4 + 1 + 1$$.

As an abelian group of prime power order
This group is the abelian group of prime power order corresponding to the partition:

$$\! 6 = 4 + 1 + 1$$

In other words, it is the group $$\mathbb{Z}_{p^2} \times \mathbb{Z}_{p^2}$$.

Other descriptions
The group can be defined using GAP's DirectProduct, CyclicGroup, and ElementaryAbelianGroup as:

DirectProduct(CyclicGroup(16),CyclicGroup(2),CyclicGroup(2))

or

DirectProduct(CyclicGroup(16),ElementaryAbelianGroup(4))