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.

Lemma Aut_extraspecial_full : Aut_in (Aut S) 'Z(S) \isog Aut 'Z(S).