Section Dihedral_extension.
Variable p : nat.
Hypotheses (p_gt1 : p > 1) (even_p : 2 %| p).
Local Notation ED := [set: gsort (Extremal.gtype q p q.-1)].
End Dihedral_extension.
End DihedralGroup.

Lemma card_2dihedral n : n > 1 -> #|'D_(2 ^ n)| = (2 ^ n)%N.