Deep HST/WFPC2 images in V and I are used to investigate the globular cluster system ( GCS ) in NGC 4874 , the central cD galaxy of the Coma cluster . Although the luminosity function of the clusters displays its normal Gaussian-like shape and turnover level , other features of the system are surprising . We find the GCS to be ( a ) spatially extended , with core radius r _ { c } \sim 22 kpc , ( b ) entirely metal-poor ( a narrow , unimodal metallicity distribution with \langle [ Fe/H ] \rangle \sim - 1.5 ) , and ( c ) modestly populated for a cD-type galaxy , with specific frequency S _ { N } = 3.7 \pm 0.5 . Model interpretations suggest to us that as much as half of this galaxy might have accreted from low-mass satellites , but no single one of the three classic modes of galaxy formation ( accretion , disk mergers , in situ formation ) can supply a fully satisfactory model for the formation of NGC 4874 . Even when they are used in combination , strong challenges to these models remain . We suggest that the principal anomaly in this GCS is essentially the complete lack of metal-rich clusters . If these were present in normal ( M87-like ) numbers in addition to the metal-poor ones that are already there , then the GCS in total would more closely resemble what we see in many other giant E galaxies . This supergiant galaxy appears to have avoided forming globular clusters during the main metal-rich stage of star formation which built the bulk of the galaxy .