We present N-body simulations of groups of galaxies with a number of very different initial conditions. These include spherical isotropic, nonspherical anisotropic collapses and virialised spherical systems. In all cases but one the merging instability leads to the formation of a giant central galaxy in the center of the group. The initial conditions of the exception are such that no galaxies are present in the central part of the group. Thus some central seed of material is necessary to trigger the formation of a giant central galaxy. We concentrate on the properties of these giant central galaxies. Spherical virialised systems give rise to relatively round and isotropic systems, while aspherical initial conditions give rise to triaxial objects with anisotropic velocity dispersion tensors. In the latter cases the orientation of the resulting central galaxy is well correlated with that of the initial cluster. We compare the projected properties of the objects formed with the properties of real brightest cluster member galaxies. The surface density profiles are in good agreement with the observed surface brightness profiles. In the case of extended virialised groups the projected properties of the giant central galaxy are the same as the properties of cD galaxies. These include a halo of luminous material and a nearly flat velocity dispersion profile.
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