Classification of gauge groups for unified weak and electromagnetic interactions. UR-654

General structure of the gauge group C underlying the unified weak and electromagnetic interactions, assuming that G is compact and that all quarks have only electric charges 2/3 and -1/3. Then, it is proven that G cannot contain any exceptional Lie groups G2, F4, E6, E7, and E8 as its factor. Moreover, the underlying representations for quark multiplets to be used must be one of fundamental representations for each component simple Lie group contained as a factor of G. For example, only spinor representation is allowed for SO(2l + 1) groups. If G is semi-simple in addition, then G must be a product of SU(3l) groups. This latter fact is likely in conflict with the present experimental data