Wreath product of Z3 and Z3

Definition
This group is defined in the following equivalent ways:


 * It is the wreath product of the cyclic group of order three and the cyclic group of order three, acting regularly. In other words, if $$\Z_3$$ denotes the cyclic group of order three, this is $$(\Z_3 \times \Z_3 \times \Z_3) \rtimes \Z_3$$.
 * It is the $$3$$-Sylow subgroup of the symmetric group of degree nine.

Other descriptions
The group can be defined using GAP's WreathProduct and CyclicGroup functions:

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