  In this paper, we study distributional chaos for weighted translations on
locally compact groups. We give a sufficient condition for such operators to be
distributionally chaotic and construct an example of distributionally chaotic
weighted translations by way of the sufficient condition. In particular, we
prove the existence of distributional chaos and Li-Yorke chaos for weighted
translations operators with aperiodic elements.
  Furthermore, we also investigate the set of distributionally irregular
vectors ($DIV$) of weighted translations through the cone and equivalence
classes. When the field is that of complex numbers, we uncover several
properties on certain subsets of $DIV$, including their connectedness and
correspondences with some measurable subsets in locally compact groups.
