Lauricella's $F_C$ with finite irreducible monodromy group

We study the conditions under which the monodromy group for Lauricella’s hypergeometric function $F_C(a,b,c;x)$ is finite irreducible. We give the conditions in terms of the parameters $a,b,c$. In addition, we discuss the structure of the finite irreducible monodromy group.