  Massive stars are always the focus of astronomical research and a significant
part of them (10--20%) moves in space at a high (supersonic) velocity. This
paper presents the results of a study of the $\alpha$ Crucis system, located at
$\sim$114 pc distance from the Sun, with an observed bow shock around it. We
used data and images from the Gaia and WISE space telescopes. The coordinates,
distance, and proper motion of the $\alpha$ Crucis system were used to
determine its space velocity. We managed to find a stellar cluster to which the
$\alpha$ Crucis system belongs, that is, it has not been ejected from its
parent cluster, but is moving in space together with other members of the
cluster. The $\alpha$ Crucis system has a velocity of $\sim$1.3 km/s relative
to the star cluster. The geometric parameters of the bow shock are compatible
with other known bow shocks. The bow shock is unaligned, i.e., most likely
interstellar medium large-scale motions are responsible for the resulting bow
shock, which is further evidence that the $\alpha$ Crucis system is not runaway
in nature.
