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

On the Milnor monodromy of the exceptional reflection arrangement of type $G_{31}$