Context. The radio galaxy IC 310 has recently been identified as a gamma-ray emitter based on observations at GeV energies with Fermi-LAT and at very high energies (VHE, E>100GeV) with the MAGIC telescopes. Originally classified as a head-tail radio galaxy, the nature of this object is subject of controversy since its nucleus shows blazar-like behavior. Aims. In order to understand the nature of IC 310 and the origin of the VHE emission we studied the spectral and flux variability of IC 310 from the X-ray band to the VHE gamma-ray regime. Methods. The light curve of IC 310 above 300GeV has been measured with the MAGIC telescopes from Oct. 2009 to Feb. 2010. Fermi-LAT data (2008-2011) in the 10-500GeV energy range were also analyzed. In X-ray, archival observations from 2003 to 2007 with XMM, Chandra, and Swift-XRT in the 0.5-10keV band were studied. Results. The VHE light curve reveals several high-amplitude and short-duration flares. Day-to-day flux variability is clearly present. The photon index between 120GeV and 8TeV remains at the value $Gammasim2.0$ during both low and high flux states. The VHE spectral shape does not show significant variability, whereas the flux at 1TeV changes by a factor of $sim7$. Fermi-LAT detected only eight gamma-ray events in the energy range 10GeV-500GeV in three years of observation. The measured photon index of $Gamma=1.3pm0.5$ in the Fermi-LAT range is very hard. The X-ray measurements show strong variability in flux and photon index. The latter varied from $1.76pm0.07$ to $2.55pm0.07$. Conclusion. The rapid variability measured confirms the blazar-like behavior of IC 310. The TeV emission seems to originate from scales of less than 80 Schwarzschild radii within the compact core of its FRI radio jet with orientation angle 10deg-38deg. The SED resembles that of an extreme blazar, albeit the luminosity is more than two orders of magnitude lower.
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