Based on recessional velocity of 12735 km/sec, about 570 million light years away. Given that and apparent size of 0.9 by 0.8 arcmin (for the outer ring), about 150 thousand light years across. The apparent size of the core is 0.3 by 0.3 arcmin, implying a size of about 50 thousand light years. First noticed in 1950 by astronomer Art Hoag, the physical nature of Hoag's Object was uncertain until fairly recently. It is now known to be a peculiar type of galaxy, in which a bright central nucleus consisting of ancient lower Main Sequence stars is surrounded by a ring of hot young stars, similar to those found in the arms of spiral nebulae, but of less certain origin. If not for the bluish ring, the galaxy would probably be thought to be an elliptical galaxy, or perhaps a spiral galaxy of type S0 (one in which the disk is almost too faint to notice, in comparison to the nucleus). The mechanisms which led to such a strange distribution of young stars are unknown, but probably unusual (see the next paragraph), so such galaxies are probably uncommon; but ironically, another one is visible to the upper right of the nucleus. (Given its small size, the second ring galaxy is probably five to ten times the distance of Hoag's Object, so there is no connection between the two, save for coincidence.) Given its size, the galaxy probably contains several hundred billion solar masses, in a similar number of objects. Of that, half is probably in the densely packed core, and the rest in the ring and presumably disk-shaped region between the core and the ring. One thing to keep in mind with galaxies is that apparently empty regions such as the space between the core and the ring may be full of faint stars, similar to those in the core, too thinly spread out to notice; and the ring may not contain any more stars than the apparently empty region, but simply be the site of recent star formation, which is lit up by the hot bright young stars resulting from that.
The origin of objects such as Hoag's would normally be attributed to gravitational encounters with other galaxies, as in the case of the probable interaction of M31
and M110. But there are no other galaxies visible in the vicinity of Hoag's Object. Study of other ring galaxies suggest that if Hoag's Object is the result of such a collision, it probably occurred two to three billion years ago, and the ring may be a gradually spreading "shock wave" of star formation triggered by the gravitational encounter, similar to ripples spreading outwards in a pond.
Above, ~ 1 arcmin closeup (Credit: R. Lucas (STScI/AURA), Hubble Heritage Team, NASA, apod040815)
Below, a 12 arcmin wide region centered on the galaxy