  It has been shown that ultra-diffuse galaxies (UDGs) have higher specific
frequencies of globular clusters on average than other dwarf galaxies with
similar luminosities. The UDG NGC5846-UDG1 is among the most extreme examples
of globular cluster-rich galaxies found so far. Here we present new Hubble
Space Telescope (HST) observations and analysis of this galaxy and its globular
cluster system. We find that NGC5846-UDG1 hosts $54 \pm 9$ globular clusters,
three to four times more than any previously known galaxy with a similar
luminosity, and higher than reported in previous studies. With a galaxy
luminosity of $L_{V,\mathrm{gal}} \approx 6 \times 10^7\,{\rm L}_{\odot}$
($M_\star \approx 1.2 \times 10^8\,{\rm M}_\odot$) and a total globular cluster
luminosity of $L_{V,\mathrm{GCs}} \approx 7.6 \times 10^6\,{\rm L}_{\odot}$, we
find that the clusters currently comprise $\sim 13 \%$ of the total light.
Taking into account the effects of mass loss from clusters during their
formation and throughout their lifetime, we infer that most of the stars in the
galaxy likely formed in globular clusters, and very little to no "normal"
low-density star formation occurred. This result implies that the most extreme
conditions during early galaxy formation promoted star formation in massive and
dense clumps, in contrast to the dispersed star formation observed in galaxies
today.
