Cayley graph with permutations of a triangleCycle graph with permutation matrices of 3 elements (The generators a and b are the same as in the Cayley graph shown above.)Cayley table as multiplication table of the permutation matricesPositions of the six elements in the Cayley table Only the neutral elements are symmetric to the main diagonal, so this group is not abelian.Cayley table as general (and special) linear group GL(2, 2)
This page illustrates many group concepts using this group as example.
^Kubo, Jisuke (2008), "The dihedral group as a family group", Quantum field theory and beyond, World Sci. Publ., Hackensack, NJ, pp. 46–63, doi:10.1142/9789812833556_0004, MR2588575. For the identification of D3 with S3, and the observation that this group is the smallest possible non-abelian group, see p. 49.