(* 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 (2.28). *)
Lemma cap_cfcenter_irr : \bigcap_i 'Z('chi[G]_i)%CF = 'Z(G).