Representation theory is a branch of algebra that allows the study of groups through linear applications, i.e. matrices. Thus problems in abstract groups can be reduced to problems on matrices. Representation theory is the basis of character theory. In this paper we present a formalization of finite groups representation theory in the Coq system that includes a formalization of Maschke's theorem on reducible finite group algebra. This work is a part of the Mathematical Components project which aims to develop a formal proof of the Feit-Thompson theorem.