Goal:

For a given positive integer n, list the groups of order n, verifying that no two of the groups listed are isomorphic. For each group, we provide its order profile and some of the following: Cayley digraph; lattice (or list) of subgroups; conjugacy classes; automorphism group; inner automorphism group; and alternate representations. For some small values of n, we outline a proof that the list is complete.