Direct product of prime-cube order group:U(3,3) and Z3

Definition
This group is defined as follows: It is the direct product of prime-cube order group:U(3,3) (the unique non-abelian group of order $$27$$ and exponent $$3$$) and the cyclic group of order three.

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

DirectProduct(SmallGroup(27,3),CyclicGroup(3))