Automorphism group of plane curve computed by Galois points, II

Abstract

Recently, the first author~[3] classified finite groups obtained as automorphism groups of smooth plane curves of degree $d \ge 4$ into five types. He gave an upper bound of the order of the automorphism group for each types. For one of them, the type (a-ii), that is given by $\max \{2d (d - 2), 60 d\}$. In this article, we shall construct typical examples of smooth plane curve $C$ by applying the method of Galois points, whose automorphism group has order $60d$. In fact, we determine the structure of the automorphism group of those curves.