We present a complete set of generators for the rank 5 special unitary group, SU(6), to unify strong, weak and electromagnetic interactions. The unification is realized through the breaking pattern of $\mathrm{SU}(6)\to \mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_H\otimes \mathrm{U}(1{)}_C$ followed by $\mathrm{SU}(3{)}_H\to \mathrm{SU}(2{)}_L\otimes \mathrm{U}(1{)}_B$. All known elementary particles and its quantum numbers are well accommodated in its $\{6\}$ and $\{15\}$ multiplets. These multiplets require a new neutral fermion which should be assigned as the heavy Majorana neutrino to realize the seesaw mechanism naturally.

• Received 20 February 2005

DOI:https://doi.org/10.1103/PhysRevD.71.095013