Let $G$ be the planar group generated by rotations of $2\pi /3$ about the three vertexes of a equilateral triangle, so there's a surjective homomorphism from $\langle x,y,z\mid x^3,y^3,z^3,xyz\rangle$ to $G$, but then is there a efficient way to determine if it's an isomorphism?
Thank you very much.