GUTs with four families / generations, SU(8) : Assuming 4 generations of fermions instead of 3 makes a total of 64 types of particles. These can be put into 64 = 8 + 56 representations of SU(8). This can be divided into SU(5) × SU(3) F × U(1) which is the SU(5) theory together with some heavy bosons which act on the generation number.