The Millennium N-body simulation and the Sloan Digital Sky Survey seventh data release (SDSS DR7) galaxy and galaxy group catalogues are compared to study the properties of galaxy groups and the distribution of galaxies in groups. We construct mock galaxy group catalogues for a Millennium semi-analytical galaxy catalogue by using the same friends-of-friends method, which was used by Tago et al to analyse the SDSS data. We analyse in detail the group luminosities, group richnesses, virial radii, sizes of groups and their rms velocities for four volume-limited samples from observations and simulations. Our results show that the spatial densities of groups agree within one order of magnitude in all samples with a rather good agreement between the mock catalogues and observations. All group property distributions have similar shapes and amplitudes for richer groups. For galaxy pairs and small groups, the group properties for observations and simulations are clearly different. In addition, the spatial distribution of galaxies in small groups is different: at the outskirts of the groups the galaxy number distributions do not agree, although the agreement is relatively good in the inner regions. Differences in the distributions are mainly due to the observational limitations in the SDSS sample and to the problems in the semi-analytical methods that produce too compact and luminous groups.
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