Direct product of S3 and Z3

Definition
This group is defined in the following equivalent ways (equivalent up to isomorphism):


 * 1) It is the direct product of the symmetric group of degree three and the cyclic group of order three.
 * 2) It is the defining ingredient::wreath product of the cyclic group of order three and the cyclic group of order two. In other words, it is the semidirect product $$(\Z_3 \times \Z_3) \rtimes \Z_2$$ where $$\Z_2$$ acts by coordinate exchange.

Other descriptions
The group can be described using the DirectProduct, SymmetricGroup, and CyclicGroup functions:

DirectProduct(SymmetricGroup(3),CyclicGroup(3))

It can also be defined using the WreathProduct and CyclicGroup functions:

WreathProduct(CyclicGroup(3),CyclicGroup(2))