A generalization of Hurwitz group

Question

Ignoring its geometric origin, a Hurwitz group might be defined abstractly by a non-trivial finite group which can be generated by elements $x$ and $y$ such that $x^2=y^3=(xy)^7=1$. I am wondering if there is any study on finite groups replacing $(2,3,7)$ by a triple of prime integers $(p,q,r)$, i.e. finite groups generated by elements $x$ and $y$ satisfying $x^p=y^q=(xy)^r=1$ for primes $p,q,r$.