(* 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).

Lemma char_cfcenterE chi x :
chi \is a character -> x \in G ->
(x \in ('Z(chi))%CF) = (`|chi x| == chi 1%g).