Large-scale multicast applications for the Internet require the availability of multicast protocols that enhance the basic connectionless IP multicast service. A critical requirement of such protocols in their ability to support a large group of simultaneous users. In this paper, we present a new approach for distributing control information within a multicast group. The goal of our approach is to scale to very large group sizes (in excess of 100,000 users). Multicast group members are organized as a logical n-dimensional hypercube, and all control information is transmitted along the edges of the hypercube. We analyze the scalability of the hypercube control topology and show that the hypercube balances the load per member for processing control information better than existing topologies.