# Classifying representation through extensions

Let $G$ be a group (you preferred type: finite, compact, ...):

Mackey has a machinery to classify all irreducible representations of a locally compact group $G$ in terms surjective group homomorphism: $$\sigma : G \rightarrow N$$ by some irreducible representations of subgroups of $N$ and some projective representations $G/ kern(\sigma)$, where $kern(\sigma)$ is a so called type-1 subgroup (i.e. the von Neumann group algebra is a direct integral type $1$ factors), e.g. take a finite, abelian, compact or amenable group.

Q1: Is there a nice reference for a condensed treatment of these results?

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