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).

Lemma Grp_pX1p2 :
p^{1+2} \isog Grp (x : y : (x ^+ p, y ^+ p, [~ x, y, x], [~ x, y, y])).