  Using a large galaxy group catalogue constructed from the Sloan Digital Sky
Survey Data Release 4 (SDSS DR4) with an adaptive halo-based group finder, we
investigate the luminosity and stellar mass functions for different populations
of galaxies (central versus satellite; red versus blue; and galaxies in groups
of different masses) and for groups themselves. The conditional stellar mass
function (CSMF), which describes the stellar distribution of galaxies in halos
of a given mass for central and satellite galaxies can be well modeled with a
log-normal distribution and a modified Schechter form, respectively. On
average, there are about 3 times as many central galaxies as satellites. Among
the satellite population, there are in general more red galaxies than blue
ones. For the central population, the luminosity function is dominated by red
galaxies at the massive end, and by blue galaxies at the low mass end. At the
very low-mass end ($M_\ast \la 10^9 h^{-2}\Msun$), however, there is a marked
increase in the number of red centrals. We speculate that these galaxies are
located close to large halos so that their star formation is truncated by the
large-scale environments. The stellar-mass function of galaxy groups is well
described by a double power law, with a characteristic stellar mass at $\sim
4\times 10^{10}h^{-2}\Msun$. Finally, we use the observed stellar mass function
of central galaxies to constrain the stellar mass - halo mass relation for low
mass halos, and obtain $M_{\ast, c}\propto M_h^{4.9}$ for $M_h \ll 10^{11}
\msunh$.
