# Presentation of finite subgroups of mapping class group of genus 2 surface by Dehn twists

## TL;DR

This paper provides explicit presentations of all finite subgroups of the genus 2 surface's mapping class group using Humphries generators, up to conjugacy.

## Contribution

It offers a complete classification and presentation of finite subgroups of the genus 2 mapping class group, a previously unlisted comprehensive result.

## Key findings

- Presentations of all finite subgroups by Humphries generators
- Classification of subgroups up to conjugacy
- Explicit descriptions for genus 2 surface

## Abstract

In this note we give presentations of all finite subgroups of the mapping class group of a closed surface of genus 2 by the Humphries generators up to conjugacy.