2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171163We describe all finite orbits of an action of the extended modular group $\barΛ$ on conjugacy classes of SL(2,C)-triples. The result is used to classify all algebraic solutions of the general Painleve VI equation up to parameter equivalence.53 pages, many figuresClassical Analysis and ODEsHigh Energy Physics - TheoryMathematical PhysicsExactly Solvable and Integrable Systemstext