Section ExponentPextraspecialTheory.
Variable p : nat.
Hypothesis p_pr : prime p.
Let p_gt1 := prime_gt1 p_pr.
Let p_gt0 := ltnW p_gt1.
Local Notation gtype := Pextraspecial.gtype.
Local Notation actp := (Pextraspecial.groupAction p).

(* This is the uniqueness half of Aschbacher ex. (8.7)(1) *)
Lemma isog_pX1p2 (gT : finGroupType) (G : {group gT}) :
extraspecial G -> exponent G %| p -> #|G| = (p ^ 3)%N -> G \isog p^{1+2}.