Definition cfDet phi := \prod_i detRepr 'Chi_i ^+ truncC '[phi, 'chi[G]_i].

(* Specifications: *)
Lemma cfDet_lin_char phi : cfDet phi \is a linear_char.
Lemma cfDet0 : cfDet 0 = 1.
Lemma cfDetRepr n rG : cfDet (cfRepr rG) = @detRepr n rG.
Lemma cfDet_id xi : xi \is a linear_char -> cfDet xi = xi.
Definition cfDet_order phi := #[cfDet phi]%CF.