The involutions and the symmetric spaces associated to the family of modular groups of order are explored. We begin by analyzing the structure of the automorphism group and by establishing which automorphisms are involutions. We conclude by calculating the fixed-point group and symmetric spaces determined by each involution.
"The classification of involutions and symmetric spaces of modular groups." Involve 12 (4) 565 - 583, 2019. https://doi.org/10.2140/involve.2019.12.565