The groups Gm,n,p

We determine (except for two outstanding cases) for which values of m, n and p the group Gm,n,p defined by the presentation 〈a,b,c|a2,b2,2(ab),c2,m(ac),n(bc),p(abc)〉 is finite. These groups formed one of three families of groups first studied systematically by Coxeter in 1939.