Context. According to radiative models, radio galaxies may produce gamma-ray emission from the first stages of their evolution. However, very few such galaxies have been detected by the Fermi Large Area Telescope (LAT) so far. Aims. NGC 3894 is a nearby (z = 0.0108) object that belongs to the class of compact symmetric objects (CSOs, i.e., the most compact and youngest radio galaxies), which is associated with a gamma-ray counterpart in the Fourth Fermi-LAT source catalog. Here we present a study of the source in the gamma-ray and radio bands aimed at investigating its high-energy emission and assess its young nature. Methods. We analyzed 10.8 years of Fermi-LAT data between 100 MeV and 300 GeV and determined the spectral and variability characteristics of the source. Multi-epoch very long baseline array (VLBA) observations between 5 and 15 GHz over a period of 35 years were used to study the radio morphology of NGC 3894 and its evolution. Results. NGC 3894 is detected in gamma-rays with a significance >9 sigma over the full period, and no significant variability has been observed in the gamma-ray flux on a yearly time-scale. The spectrum is modeled with a flat power law ($Gamma$ = 2.0$pm$0.1) and a flux on the order of 2.2 $times$ 10$^{-9}$ ph cm$^{-2}$ s$^{-1}$. For the first time, the VLBA data allow us to constrain with high precision the apparent velocity of the jet and counter-jet side to be $beta_{mathrm{app,NW}}$ = 0.132$pm$0.004 and $beta_{mathrm{app,SE}}$ = 0.065$pm$0.003, respectively. Conclusions. Fermi-LAT and VLBA results favor the youth scenario for the inner structure of this object, with an estimated dynamical age of 59$pm$5 years. The estimated range of viewing angle (10{deg} < $theta$ < 21{deg}) does not exclude a possible jet-like origin of the gamma-ray emission.
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