Definition cfConjC_vchar :=  cfAut_vchar conjC.
Section MoreVchar.
Variables (gT : finGroupType) (G H : {group gT}).

(* Specifications: *)
Lemma cfRes_vchar phi : phi \in 'Z[irr G] -> 'Res[H] phi \in 'Z[irr H].
Lemma cfRes_vchar_on A phi :
H \subset G -> phi \in 'Z[irr G, A] -> 'Res[H] phi \in 'Z[irr H, A].
Lemma cfInd_vchar phi : phi \in 'Z[irr H] -> 'Ind[G] phi \in 'Z[irr G].
Lemma sub_conjC_vchar A phi :
phi \in 'Z[irr G, A] -> phi - (phi^*)%CF \in 'Z[irr G, A^#].
Lemma Frobenius_kernel_exists :
[Frobenius G with complement H] -> {K : {group gT} | [Frobenius G = K ><| H]}.