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We present an optical to near-infrared transmission spectrum of the inflated hot Jupiter WASP-52b using three transit observations from the Space Telescope Imaging Spectrograph mounted on the Hubble Space Telescope, combined with Spitzer/Infrared Array Camera photometry at 3.6 and 4.5 μm. Since WASP-52 is a moderately active (log(Lx/Lbol) = −4.7) star, we correct the transit light curves for the effect of stellar activity using ground-based photometric monitoring data from the All-sky Automated Survey for Supernovae (ASAS-SN) and Tennessee State University's Automatic Imaging Telescope. We bin the data in 38 spectrophotometric light curves from 0.29 to 4.5 μm and measure the transit depths to a median precision of 90 ppm. We compare the transmission spectrum to a grid of forward atmospheric models and find that our results are consistent with a cloudy spectrum and evidence of sodium at 2.3σ confidence, but we find no observable evidence of potassium absorption even in the narrowest spectroscopic channel. We find that the optical transmission spectrum of WASP-52b is similar to that of the well-studied inflated hot Jupiter HAT-P-1b, which has comparable surface gravity, equilibrium temperature, mass, radius, and stellar irradiation levels. At longer wavelengths, however, the best-fitting models for WASP-52b and HAT-P-1b predict quite dissimilar properties, which could be confirmed with observations at wavelengths longer than ∼1 μm. The identification of planets with common atmospheric properties and similar system parameters will be insightful for comparative atmospheric studies with the James Webb Space Telescope.