The group of automorphisms of the Fermat curve

In his paper, "The group of automorphisms of the Fermat curve" (see [7]), Tzermias proved that the automorphism group of the projective Fermat curves in characteristic 0 is the semidirect product of the direct sum of 2 copies of the cyclic group of order n and the symmetric group on 3 letters. In this paper we present an alternative proof of this fact accessible to someone with basic knowledge of Riemann surfaces and group theory. Also we include the geometric correspondence of the action.