  We use a sample of galaxy groups selected from the SDSS DR 4 with an adaptive halo-based group finder to probe how the clustering strength of groups depends on their masses and colors. In particular, we determine the relative biases of groups of different masses, as well as that of groups with the same mass but with different colors. In agreement with previous studies, we find that more massive groups are more strongly clustered, and the inferred mass dependence of the halo bias is in good agreement with predictions for the $\Lambda$CDM cosmology. Regarding the color dependence, we find that groups with red centrals are more strongly clustered than groups of the same mass but with blue centrals. Similar results are obtained when the color of a group is defined to be the total color of its member galaxies. The color dependence is more prominent in less massive groups and becomes insignificant in groups with masses $\gta 10^{14}\msunh$. We construct a mock galaxy redshift survey constructed from the large Millenium simulation that is populated with galaxies according to the semi-analytical model of Croton et al. Applying our group finder to this mock survey, and analyzing the mock data in exactly the same way as the true data, we are able to accurately recover the intrinsic mass and color dependencies of the halo bias in the model. This suggests that our group finding algorithm and our method of assigning group masses do not induce spurious mass and/or color dependencies in the group-galaxy correlation function. The semi-analytical model reveals the same color dependence of the halo bias as we find in our group catalogue. In halos with $M\sim 10^{12}\msunh$, though, the strength of the color dependence is much stronger in the model than in the data. 
The clustering of SDSS galaxy groups: mass and color dependence