Wreath product of groups of order p

Definition
Let $$p$$ be a prime number. The wreath product of groups of order $$p$$ is any of the following equivalent things:


 * 1) It is the wreath product of the cyclic group of order $$p$$ with the cyclic group of order $$p$$, where the latter is given the regular action on a set of size $$p$$.
 * 2) It is the semidirect product of the elementary abelian group of order $$p^p$$ and a cyclic group of order $$p$$ acting on it by cyclic permutation of coordinates.
 * 3) It is the $$p$$-Sylow subgroup of the symmetric group of order $$p^2$$.

GAP implementation
Assign to $$p$$ any numerical value of a prime number. Then, the group can be defined as  WreathProduct(CyclicGroup(p),CyclicGroup(p)) using the GAP functions WreathProduct and CyclicGroup.