Section Basic.
Variable S : {group gT}.
Hypotheses (pS : p.-group S) (esS : extraspecial S).
Let pZ : p.-group 'Z(S) := pgroupS (center_sub S) pS.
End Basic.

Lemma card_p3group_extraspecial E :
prime p -> #|E| = (p ^ 3)%N -> #|'Z(E)| = p -> extraspecial E.