Aims: The radio galaxy NGC 1275, recently identified as a very high energy (VHE, >100 GeV) γ-ray emitter by MAGIC, is one of the few non-blazar active galactic nuclei detected in the VHE regime. The purpose of this work is to better understand the origin of the γ-ray emission and locate it within the galaxy. Methods: We studied contemporaneous multifrequency observations of NGC 1275 and modeled the overall spectral energy distribution. We analyzed unpublished MAGIC observations carried out between October 2009 and February 2010, and the previously published observations taken between August 2010 and February 2011. We studied the multiband variability and correlations by analyzing data of Fermi-LAT in the 100 MeV-100 GeV energy band, as well as Chandra (X-ray), KVA (optical), and MOJAVE (radio) data taken during the same period. Results: Using customized Monte Carlo simulations corresponding to early MAGIC stereoscopic data, we detect NGC 1275 also in the earlier MAGIC campaign. The flux level and energy spectra are similar to the results of the second campaign. The monthly light curve above 100 GeV shows a hint of variability at the 3.6σ level. In the Fermi-LAT band, both flux and spectral shape variabilities are reported. The optical light curve is also variable and shows a clear correlation with the γ-ray flux above 100 MeV. In radio, three compact components are resolved in the innermost part of the jet. One of these components shows a similar trend as the Fermi-LAT and KVA light curves. The γ-ray spectra measured simultaneously with MAGIC and Fermi-LAT from 100 MeV to 650 GeV can be well fitted either by a log-parabola or by a power-law with a subexponential cutoff for the two observation campaigns. A single-zone synchrotron-self-Compton model, with an electron spectrum following a power-law with an exponential cutoff, can explain the broadband spectral energy distribution and the multifrequency behavior of the source. However, this model suggests an untypical low bulk-Lorentz factor or a velocity alignment closer to the line of sight than the parsec-scale radio jet.