It is well-known that multiple transmit and receiving antennas can significantly improve the performance of wireless networks. The design of good modulation schemes for the model of multiple antenna wireless transmission in a fast fading environment (e.g., mobile communication) leads to an interesting packing problem for unitary matrices. Surprisingly, the latter problem is related to certain aspects of finite (and infinite) group theory. In this paper we will give a brief survey of some of these connections.