(* This is part of Isaacs (2.27)(b). *)
Fact cfcenter_group_set phi : group_set ('Z(phi))%CF.
Canonical cfcenter_group f := Group (cfcenter_group_set f).

(* This is Isaacs (2.32)(a). *)
Lemma irr_faithful_center i : cfaithful 'chi[G]_i -> cyclic 'Z(G).