  We investigate a family of (reducible) representations of Artin's braid
groups corresponding to a specific solution to the Yang-Baxter equation. The
images of the braid groups 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 the braid groups factoring over Temperley-Lieb algebras and
the corresponding link invariants.
