Elementary abelian group:E64

Definition
This group is defined as the elementary abelian group of order $$64$$, i.e., the direct product of six copies of the cyclic group of order two. It can also be viewed as the additive group of a six-dimensional vector space over the field of two elements.

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

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

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

Other descriptions
The group can be defined using GAP's ElementaryAbelianGroup function as:

ElementaryAbelianGroup(64)