Direct product of Z4 and Z4 and Z4

Definition
This group is defined in the following equivalent ways:


 * 1) It is the external direct product of three copies of defining ingredient::cyclic group:Z4.
 * 2) It is a homocyclic group of order $$2^6 = 64$$ and exponent $$4$$.
 * 3) It is the cube of the group cyclic group:Z4.

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

$$\! 6 = 2 + 2 + 2$$

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