Thanks HW. I have modified it according to your suggestion. Sorry for my ignorance of correct vocabulary.

Thanks Nick. The rephrasing of my question by Nick sounds more correct and appropriate. I will look forward to some answer or hint in this direction.

Misha and HW, generally the hyperbolic groups of these kind are infinite. However there exist some finite subgroups of them in certain cases. G(2,3,7) with an additional defining relation $(ST^{-1}ST)^{4}=E$ is such an example which is same as the group $PSL_2(7)$. My question is: Is there exist a generalization of the above example so we can find finite subgroups of other $G(l,m,n)$.

Since, I am talking about the hyperbolic group, I have edited the question.