proposition: Lemma dihedral_classP : extremal_class G = Dihedral <-> (exists2 n, n > 1 & G \isog 'D_(2 ^ n)).
proof: Proof. rewrite /extremal_class; split=> [ | [n n_gt1 isoG]]. by move: (logn _ _) => n; do 4?case: ifP => //; case/andP; exists n. rewrite (card_isog isoG) card_2dihedral // -(ltn_predK n_gt1) pdiv_pfactor //. by rewrite pfactorK // (ltn_predK n_gt1) n_gt1 isoG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism presentation) mathcomp(quotient action commutator gproduct gfunctor) mathcomp(ssralg countalg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule matrix maximal)