Elementary abelian group of prime-square order
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(p^2,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [p^2,2]
or just do:
to have GAP output the group ID, that we can then compare to what we want.