The intermediate-coupling shell model for nuclei is considered in terms of the classification of states in a harmonic oscillator according to the irreducible representations of the unimodular group in three dimensions, SU/sub 3/ . The properties of this group are used to produce the approximate spectrum of a quadrupole force, acting within an oscillator shell. When specialized to the 1p shell, a more general interaction, including exchange forces, is shown to be approximately diagonal in the chosen representation, and its approximate spectrum is computed. A method is developed for calcu1ating the matrix elements of interactions not diagonal in the representation, in particular the singleparticle spin-orbit potential, using the generating functions of the group, SU/sub 3/. The intermediate-coupling energy spectra of the nuclei of the 1p shell are then calculated to the first or second order in perturbation theory. The results are compared with experimental spectra, and with calculations of Kurath (D. Kurath, Phys. Rev. 101: 216(1956). (auth)