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 \pm 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 ^ { -1 } , its virial mass is 8.4 \times 10 ^ { 13 } M _ { \odot } , and M / L _ { R } = 320 M _ { \odot } / L _ { \odot } .
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 \pm 0.1 ( statistical ) \pm 0.1 ( systematic ) at our completeness limit of M _ { R } = -12 .