field, which is always faithful/injective (since no two terms differ only by only a sign). Over the field with two elements, the projective line has only 3 points, and this is thus the exceptional isomorphism In characteristic 3, this embedding stabilizes the point since (in characteristic greater than 3 these points are distinct and permuted, and are the orbit of the harmonic cross-ratio). Over the field with three elements, the projective line has 4 elements, and since is isomorphic to the symmetric group on 4 elements, S4, the resulting embedding equals the stabilizer of the point . See also Dihedral group of order 8 References External links http://mathworld.wolfram.com/DihedralGroupD3.html Finite groups