  We conduct a photometric and spectroscopic survey of a 10 sq. deg. region
surrounding the nearby NGC 5846 group of galaxies, using the
Canada-France-Hawaii and Keck I telescopes to study the population of dwarf
galaxies as faint as M_R=-10. Candidates are identified on the basis of
quantitative surface brightness and qualitative morphological criteria.
Spectroscopic follow up and a spatial correlation analysis provide the basis
for affirming group memberships. Altogether, 324 candidates are identified and
83 have spectroscopic membership confirmation. We argue on statistical grounds
that a total 251 +/- 10 galaxies in our sample are group members. The
observations, together with archival Sloan Digital Sky Survey, ROSAT,
XMM-Newton, and ASCA data, suggest that the giant ellipticals NGC 5846 and NGC
5813 are the dominant components of subgroups separated by 600 kpc in
projection and embedded in a 1.6 Mpc diameter dynamically evolved halo. The
galaxy population is overwhelmingly early type. The group velocity dispersion
is 322 km/s, its virial mass is 8.4 x 10^13 M_sun, and M/L_R = 320 M_sun/L_sun.
The ratio of dwarfs to giants is large compared with other environments in the
Local Supercluster studied and, correspondingly, the luminosity function is
relatively steep, with a faint end Schechter function slope of \alpha_d = -1.3
+/- 0.1 (statistical) +/- 0.1 (systematic) at our completeness limit of M_R =
-12.
