The maximal finite subgroup in the mapping class group of genus 5 (Q676749)

The highest order of the group of automorphisms of compact Riemann surfaces of genus five is 192. The Riemann surface which realizes the maximum is unique and is realized as the modular curve \(X(8)\) of level 8 [see \textit{A. Kuribayashi} and \textit{H. Kimura}, J. Algebra 134, No. 1, 80-103 (1990; Zbl 0709.30037)]. The author of this note gives the action of the group of automorphisms of \(X(8)\) on a set of generators of its fundamental group and determines a set of canonical generators.