We compute the homology of limn->∞(Gn ≀ X), where (Gn) is a system of subgroups of Σpn containing a p-Sylow subgroup (Σpn p) and satisfying certain properties. We show that H*(limn->∞(Gn, ≀ X);Z/pZ) is built naturally over homology operations related to (Gn). We describe this family of operations using modular coinvariants.