Elementary abelian group:E81

This group is the elementary abelian group of order $$81$$. In other words, it is the additive group of a four-dimensional vector space over the field of three elements. Equivalently, it is the direct product of four copies of the cyclic group of order three.

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

ElementaryAbelianGroup(81)