decompositions of a representation I am reading J.P Serre's book on Linear representations of finite groups. In chapter 2.6 it states:

Let $\rho: G \rightarrow GL(V)$ be a linear representation of $G$. We are going to define a direct sum decomposition of $V$ which is "coarser" than the decomposition into irreducible representations, but which has the advantage of being $unique$.

Now what does it mean by "coarser" in this context? I believe it means the former is less powerful than the latter, correct?

It means that each piece of the former decomposition (that is, the decomposition into irreducible representations) will be part of some piece of the new decomposition.
