Section IrrClassDef.
Variables (gT : finGroupType) (G : {group gT}).
Let sG := DecSocleType (regular_repr algCF G).
Let sG := DecSocleType (regular_repr algCF G).
Let C'G := algC'G G.
Let closG := @groupC _ G.
Local Notation W i := (@socle_of_Iirr _ G i).
Local Notation "''n_' i" := 'n_(W i).
Local Notation "''R_' i" := 'R_(W i).
Local Notation "''e_' i" := 'e_(W i).

(* This is Isaacs, Lemma (2.11). *)
Lemma cfReg_sum : cfReg G = \sum_i 'chi_i 1%g *: 'chi_i.