[rocqua]

The additive group of the integers is the set of isomorphisms of a line with evenly spaced points and a direction.

Alternatively, take a directed graph with:

V = The integers

E = {x, y | x - y = 1}

and that graph has the same isomorphism group.

Replace the nodes of that graph with asymmetric graphs, and the resultant undirected graph again has the same isomorphism group.

[Koshkin]

Again, this is only what is called 'a representation.' (The problem with trying to use one as a substitute for the abstract definition is that there usually are many different representations.)