We estimate the fraction of star-forming galaxies in a catalogue of groups, constructed from the 2dF Galaxy Redshift Survey by Merchan & Zandivarez. We use the η spectral type parameter of galaxies and subdivide the sample of galaxies in groups into four types depending on the values of the η parameter following Madgwick et al. We obtain a strong correlation between the relative fraction of galaxies with high star formation and the parent group virial mass. We find that even in the environment of groups with low virial mass M∼1013 M⊙ the star formation of their member galaxies is significantly suppressed. The relation between the fraction of early-type galaxies and the group virial mass obeys a simple power law spanning over three orders of magnitude in virial mass. Our results show quantitatively the way that the presence of galaxies with high star formation rates is inhibited in massive galaxy systems.