Let $E(3)$ be the Euclidean group of $\mathbb{R}^3$ defined, e.g., by $$E(3)=SO(3)\ltimes T(3)$$ where $T(3)$ is the translation group.

I am looking for a reference classifying all the finite-dimensional irreducible unitary representations of $E(3)$. Several sources (such as "Unitary Representations and Harmonic Analysis: An Introduction", Chapter IV or "Noncommutative Harmonic Analysis" Chapter 5 §4) give an analog classification for $E(2)$ but do not treat the three-dimensional case.

**Any help or comment is greatly appreciated!**