Finite subgroups of the extended modular group
Finite subgroups of the extended modular group
We show that in the extended modular group $\overline \Gamma = \rm {PGL}(2, \mathbb {Z})$ there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.