  We show that the braid group representations associated with the
$(3,6)$-quotients of the Hecke algebras factor over a finite group. This was
known to experts going back to the 1980s, but a proof has never appeared in
print. Our proof uses an unpublished quaternionic representation of the braid
group due to Goldschmidt and Jones. Possible topological and categorical
generalizations are discussed.
