The NGC 1407 Group stands out among nearby structures by its properties that
suggest it is massive and evolved. It shares properties with entities that have
been called fossil groups: the 1.4 magnitude differential between the dominant
elliptical galaxy and the second brightest galaxy comes close to satisfying the
definition that has been used to define the fossil class. There are few
intermediate luminosity galaxies, but a large number of dwarfs in the group. We
estimate there are 250 group members to the depth of our survey. The slope of
the faint end of the luminosity function (reaching M_R = -12) is alpha = -1.35.
Velocities for 35 galaxies demonstrate that this group with one dominant galaxy
has a mass of 7 X 10^13 M_sun and M/L_R = 340. Two galaxies in close proximity
to NGC 1407 have very large blueshifts. The most notable is the second
brightest galaxy, NGC 1400, with a velocity of -1072 km/s with respect to the
group mean. We report the detection of X-ray emission from this galaxy and from
the group.Comment: final version to appear in MNRAS, URL for data include