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 part of the existence half of Aschbacher ex. (8.7)(1) *)
Lemma exponent_pX1p2 : odd p -> exponent p^{1+2} %| p.