∀ {α : Type u_2} [inst : Fintype α] [inst_1 : DecidableEq α] {g c : Equiv.Perm α},
  c.IsCycle →
    (Commute g c ↔
      ∃ (hc' : ∀ (x : α), g x ∈ c.support ↔ x ∈ c.support),
        Equiv.Perm.ofSubtype (g.subtypePerm hc') ∈ Subgroup.zpowers c)