In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2π/p with p > 2. We will mainly concentrate on the groups where some elements are elliptic of finite order. Then we will classify all such groups which are candidates for being discrete. There are only 4 types.
Parker, J. R., & Sun, L. (2017). Complex Hyperbolic Triangle Groups with 2-fold Symmetry. Proceedings of the International Geometry Center, 10(1), 1-21. https://doi.org/10.15673/tmgc.v1i10.547