This paper presents results from simulations of a massive, rich galaxy cluster in a flat, low-density universe. The simulations track the formation of galaxies and their dark matter haloes, with high resolution for galaxies brighter than the SMC. The simulations use a new parallel N-body code and substructure identification algorithm, SUBFIND, to trace dark matter substructure and galaxy populations. The results show good numerical convergence for galaxies brighter than the SMC, and demonstrate that galaxy merging quantitatively explains the observed population of bulges and ellipticals in clusters. The simulations include a detailed study of the formation history of the cluster and its galaxies, including star formation histories, the origin of the first stars in the cluster, and the evolution of galaxy merger rates. The results are compared with observational data, showing good agreement, especially for the cluster luminosity function. The simulations also reveal that subhaloes play a key role in the formation of galaxy populations, and that the inclusion of subhaloes improves the agreement with observational data. The paper discusses the techniques used to model galaxy formation, including the physical processes of gas cooling, star formation, feedback, and galaxy merging. The results show that the semi-analytic models used in the simulations are able to reproduce the observed properties of galaxies, including their luminosity functions, mass-to-light ratios, and morphology-radius relations. The simulations also show that the velocity dispersion profiles of galaxies depend on their luminosity and colour, and that these profiles are consistent with those of dark matter. The paper concludes that the simulations provide a detailed understanding of galaxy formation and clustering in a CDM universe.This paper presents results from simulations of a massive, rich galaxy cluster in a flat, low-density universe. The simulations track the formation of galaxies and their dark matter haloes, with high resolution for galaxies brighter than the SMC. The simulations use a new parallel N-body code and substructure identification algorithm, SUBFIND, to trace dark matter substructure and galaxy populations. The results show good numerical convergence for galaxies brighter than the SMC, and demonstrate that galaxy merging quantitatively explains the observed population of bulges and ellipticals in clusters. The simulations include a detailed study of the formation history of the cluster and its galaxies, including star formation histories, the origin of the first stars in the cluster, and the evolution of galaxy merger rates. The results are compared with observational data, showing good agreement, especially for the cluster luminosity function. The simulations also reveal that subhaloes play a key role in the formation of galaxy populations, and that the inclusion of subhaloes improves the agreement with observational data. The paper discusses the techniques used to model galaxy formation, including the physical processes of gas cooling, star formation, feedback, and galaxy merging. The results show that the semi-analytic models used in the simulations are able to reproduce the observed properties of galaxies, including their luminosity functions, mass-to-light ratios, and morphology-radius relations. The simulations also show that the velocity dispersion profiles of galaxies depend on their luminosity and colour, and that these profiles are consistent with those of dark matter. The paper concludes that the simulations provide a detailed understanding of galaxy formation and clustering in a CDM universe.