(* 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)(b). *)
Lemma pgroup_cyclic_faithful (p : nat) :
p.-group G -> cyclic 'Z(G) -> exists i, cfaithful 'chi[G]_i.