(* Lemmas bundling Aschbacher (23.10) with (19.1), (19.2), (19.12) and (20.8) *)
Section ExtraspecialFormspace.
Variable G : {group gT}.
Hypotheses (pG : p.-group G) (esG : extraspecial G).
Let p_pr := extraspecial_prime pG esG.
Let oZ := card_center_extraspecial pG esG.
Let p_gt1 := prime_gt1 p_pr.
Let p_gt0 := prime_gt0 p_pr.

(* This is the tranposition of the orthogonal subspace dimension theorem      *)
(* (Aschbacher (19.2)) to subgroups of an extraspecial group.                 *)
Lemma card_subcent_extraspecial U :
U \subset G -> #|'C_G(U)| = (#|'Z(G) :&: U| * #|G : U|)%N.