I am reading the journel by Patrick l. Nash: mapping from tetrad to Dirac spinor. While reading this ,I came across the term concrete real 4*4 irreducible representation of SO(3,3). I know SO(3) is a special orthogonal group of rotations in R^3 and it is a 3*3 orthogonal matrix where determinant is +1. Now I am having a problem of understanding the extra 3 in SO(3,3) and How can real 4*4 irreducible representation be related with Dirac gamma matrix? Would be better if provided by matrix example.