Group $\Gamma$ minimizing $\mu(X(\Gamma))$ (Shimura section 2.5)

Question

At the end of section 2.5 of Shimura's Introduction to Arithmetic Theory of Automorphic Functions, it is argued that the group $\Gamma$ whose modular curve has minimum measure $\mu(X(\Gamma))$ satisfies $g=0$, has no cusps, and has three inequivalent elliptic points of orders 2, 3, and 7. Is this the (2,3,7) triangle group? Regardless, how would one construct $\Gamma$ just based on knowledge of its genus, cusp count, and elliptic point orders?