Elementary abelian group:E27

Definition
This group, sometimes denoted $$E_{27}$$, is the elementary abelian group of order $$27$$. In other words, it is the additive group of a three-dimensional vector space over the field of three elements. Equivalently, it is the additive group of the field of 27 elements. Equivalently, it is the direct product of three copies of the cyclic group of order three.

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

ElementaryAbelianGroup(27)