Let G be a finite group and let V be a finite and faithful G-module such that V is completely reducible, possibly of mixed characteristic. Suppose that M is the largest orbit size in the action of G on V. It is known  that the index of the commutator subgroup G' in G is bounded by M, that is, |G : G'|≤ M.

In this talk, we will provide the classification of all linear group actions in which |G:G'|=M. It turns out that our classification is a vast generalization of a classic 1967 result by D. Passman.