In this work a comprehensive analysis is made of the galaxy composition and dynamics of galaxy groups. An extensive investigation into the changing nature of the Schechter luminosity function (LF) as a function of group size (calculated in multiple ways) is carried out, with the finding that the least massive, numerically poorest and least luminous systems possess a markedly repressed faint end. The projected 2D shape of groups is analysed carefully, taking into account the distortions created by a range of effects, and there is strong evidence that the smallest groups possess an underlying oblate (frisbee) 3D shape, in contrast to more massive systems that display significantly prolate (rugby ball) distributions. The radial profiles of groups are used to identify the key regions in which the group environment strongly influences galaxy morphology, with convincing evidence that the central scale-radius determines the LF of the full range of group scales.