We present our analysis of HD~35502 based on high- and medium-resolution spectropolarimetric observations. Our results indicate that the magnetic B5IVsnp star is the primary component of a spectroscopic triple system and that it has an effective temperature of $18.4pm0.6,{rm kK}$, a mass of $5.7pm0.6,M_odot$, and a polar radius of $3.0^{+1.1}_{-0.5},R_odot$. The two secondary components are found to be essentially identical A-type stars for which we derive effective temperatures ($8.9pm0.3,{rm kK}$), masses ($2.1pm0.2,M_odot$), and radii ($2.1pm0.4,R_odot$). We infer a hierarchical orbital configuration for the system in which the secondary components form a tight binary with an orbital period of $5.66866(6),{rm d}$ that orbits the primary component with a period of over $40,{rm yrs}$. Least-Squares Deconvolution (LSD) profiles reveal Zeeman signatures in Stokes $V$ indicative of a longitudinal magnetic field produced by the B star ranging from approximately $-4$ to $0,{rm kG}$ with a median uncertainty of $0.4,{rm kG}$. These measurements, along with the line variability produced by strong emission in H$alpha$, are used to derive a rotational period of $0.853807(3),{rm d}$. We find that the measured $vsin{i}=75pm5,{rm km,s}^{-1}$ of the B star then implies an inclination angle of the stars rotation axis to the line of sight of $24^{+6}_{-10}degree$. Assuming the Oblique Rotator Model, we derive the magnetic field strength of the B stars dipolar component ($14^{+9}_{-3},{rm kG}$) and its obliquity ($63pm13degree$). Furthermore, we demonstrate that the calculated Alfv{e}n radius ($41^{+17}_{-6},R_ast$) and Kepler radius ($2.1^{+0.4}_{-0.7},R_ast$) place HD~35502s central B star well within the regime of centrifugal magnetosphere-hosting stars.
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