For any smooth Hurwitz curve $\mathcal{ H}_n: \, XY^n+YZ^n+X^nZ=0$ over the finite field $\mathbb{ F}_{ p}$, an explict description of its Weierstrass points for the morphism of lines is presented. As a consequence, the full automorphism group ${ \rm Aut}(\mathcal{ H}_n)$, as well as the genera of all Galois subcovers of $\mathcal{ H}_n$, with $n\neq 3, p^r$, are computed. Finally, a question by F. Torres on plane non nonsingular maximal curves is answered.
Categories: math.AG