The SymmetricGroup: properties of permutations, cycle decompositions, operations on permutations. Also more GroupTheory: subgroups, homomorphisms, isomorphims, and embeddings. Readings: §10.6, 20.7, 20.5. Note that BiggsBook doesn't talk about group homomorphisms that aren't isomorphisms, so you may also want to read through the appropriate sections of GroupTheory.