What is the cardinality of finite order elements in Mapping class group of a surface $S_{g,n}$ of genus g and n boundary components.
1) If it is infinite then how can I generate a collection of finite order elements?
2)I know that any finite subgroup is of cardinality at most $84(g-1)$ and I also know that there are finitely many conjugacy classes of finite subgroup. But what about the number of subgroups in each conjugacy class?