  We present the results of a deep photometric study of the outer halo of NGC
1275, the highly active cD galaxy at the center of the Perseus cluster. We find
a modest excess of faint ($R > 22.5$) starlike objects in its halo, indicating
a population of old-halo globular clusters. However, the total estimated
cluster population corresponds to a specific frequency of $S_N = 4.4 \pm 1.2$,
no larger than that of normal giant ellipticals and three times lower than that
of other central cD galaxies such as M87. We discuss several ideas for the
origin of this galaxy. Our results reinforce the view that high $S_N$ (ie:
highly efficient globular cluster formation) is not associated with cooling
flows, or with recent starburst or merger phenomena.
