Extraspecial 2-groups and images of braid group representations

We investigate a family of (reducible) representations of the braid groups B(n) corresponding to a specific solution to the Yang-Baxter equation. The images of B(n) under these representations are finite groups, and we identify them precisely as extensions of extra,special 2-groups. The decompositions of the representations into their irreducible constituents are determined, which allows us to relate them to the well-known Jones representations of B(n) factoring over Temperley-Lieb algebras and the corresponding link invariants.