(* 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 (2.27)(d). *)
Lemma cfcenter_cyclic chi : cyclic ('Z(chi)%CF / cfker chi)%g.