On the monodromy of the inflection points of plane curves

We prove that the monodromy group of the inflection points of plane curves of degree $d$ is the symmetric group ${\mathbb{S}}_{3d(d-2)}$ for $d\ge 4$ and in the case $d=3$ this group is the group of the projective transformations of ${\mathbb{P}}^2$ leaving invariant the nine inflection points of the Fermat curve of degree three.