Section GringIrrMode.
Variable i : Iirr G.
Let n := irr_degree (socle_of_Iirr i).
Let mxZn_inj: injective (@scalar_mx algCfield n).
End GringIrrMode.

(* This is Isaacs, Theorem (3.9). *)
Theorem primes_class_simple_gt1 C :
simple G -> ~~ abelian G -> C \in (classes G)^# -> (size (primes #|C|) > 1)%N.