The differences between cold dark matter (CDM) and warm dark matter (WDM) in the formation of a group of galaxies are examined by running two identical simulations, where in the WDM case the initial power spectrum has been altered to mimic a 1-keV dark matter particle. The CDM initial conditions were constrained to reproduce at z = 0 the correct local environment within which a ‘Local Group’ (LG) of galaxies may form. Two significant differences between the two simulations are found. While in the CDM case a group of galaxies that resembles the real LG forms, the WDM run fails to reproduce a viable LG, instead forming a diffuse group which is still expanding at z = 0. This is surprising since, due to the suppression of small-scale power in its power spectrum, WDM is naively expected to only affect the collapse of small haloes and not necessarily the dynamics on a scale of a group of galaxies. Furthermore, the concentration of baryons in halo centre is greater in CDM than in WDM and the properties of the discs differ.