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, some of the following are provided: order profile; 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.

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