Direct product of Z8 and Z8

Definition
This group can be defined as the uses as intermediate construct::external direct product of two copies of the cyclic group of order eight. In other words, it has the presentation:

$$G := \langle x,y \mid x^8 = y^8 = e, xy = yx \rangle$$.

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

$$\! 6 = 3 + 3$$

In other words, it is the group $$\mathbb{Z}_{p^3} \times \mathbb{Z}_{p^3}$$.

Other descriptions
The group can be defined using the DirectProduct and CyclicGroup functions as:

DirectProduct(CyclicGroup(8),CyclicGroup(8))