Dihedral group of order 6

Cayley graph with permutations of a triangle
Cycle 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 matrices
Positions 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)

In mathematics, D3 (sometimes alternatively denoted by D6) is the dihedral group of degree 3 and order 6. It equals the symmetric group S3. It is also the smallest non-abelian group.[1]

This page illustrates many group concepts using this group as example.

  1. ^ 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, MR 2588575. For the identification of D3 with S3, and the observation that this group is the smallest possible non-abelian group, see p. 49.