One of the most remarkable features in Nature is the existence of three generations of chiral quarks and leptons and these mass hierarchy. To understand the particle properties, I have been studying the supersymmetric vectorlike model with a noncompact group horizontal symmetry. The model has two aspects: (1) Three chiral generations emerge as a result of spontaneous breaking of the horizontal symmetry in the vectorlike model. (2) The structure of Yukawa couplings is constrained by the horizontal symmetry and become hierarchical naturally. In this talk, I will mainly discuss the above two characters. I will also introduce some other aspects of the model.