The NGC 5846 group:: Dynamics and the luminosity function to MR = -12

We conduct a photometric and spectroscopic survey of a 10 deg(2) 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 of 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(-1), its virial mass is 8.4 x 10(13) M-circle dot, and M/L-R 320 M-circle dot L-circle dot(-1). 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.