Certain classes of superconformal field theories in six dimensions (6D SCFTs) are in one-to-one correspondence with certain classes of group homomorphisms. In this talk, we will see that this correspondence allows us to classify homomorphisms that were previously unknown in the mathematics literature and understand aspects of 6DSCFTs that were previously unknown in the physics literature. We speculate on the implications for the future study of 6D SCFTs and these group homomorphisms.