  Combining recent results by A. Macinic, S. Papadima and R. Popescu with a
spectral sequence and computer aided computations, we determine the monodromy
action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the
hyperplane arrangement associated to the exceptional irreducible complex
reflection group $G_{31}$. This completes the description given by the first
author of such monodromy operators for all the other irreducible complex
reflection groups.
