  Context. The radio galaxy IC310 in the Perseus cluster has recently been
detected in the gamma-ray regime at GeV and TeV energies. The TeV emission
shows time variability and an extraordinarily hard spectrum, even harder than
the spectrum of the similar nearby gamma-ray emitting radio galaxy M87.
  Aims. High-resolution studies of the radio morphology help to constrain the
geometry of the jet on sub-pc scales and to find out where the high-energy
emission might come from.
  Methods. We analyzed May 2011 VLBA data of IC310 at a wavelength of 3.6 cm,
revealing the parsec-scale radio structure of this source. We compared our
findings with more information available from contemporary single-dish flux
density measurements with the 100-m Effelsberg radio telescope.
  Results. We have detected a one-sided core-jet structure with blazar-like,
beamed radio emission oriented along the same position angle as the kiloparsec
scale radio structure observed in the past by connected interferometers.
Doppler-boosting favoritism is consistent with an angle of theta < 38 degrees
between the jet axis and the line-of-sight, i.e., very likely within the
boundary dividing low-luminosity radio galaxies and BL Lac objects in unified
schemes.
  Conclusions. The stability of the jet orientation from parsec to kiloparsec
scales in IC310 argues against its classification as a headtail radio galaxy;
i.e., there is no indication of an interaction with the intracluster medium
that would determine the direction of the tail. IC310 seems to represent a
low-luminosity FRI radio galaxy at a borderline angle to reveal its BL Lac-type
central engine.
