Section StructureCorollaries.
Variable S : {group gT}.
Hypotheses (pS : p.-group S) (esS : extraspecial S).
Let p_pr := extraspecial_prime pS esS.
Let oZ := card_center_extraspecial pS esS.

(* This is Aschbacher (23.10)(2). *)
Lemma card_extraspecial : {n | n > 0 & #|S| = (p ^ n.*2.+1)%N}.