  We study the 6d $\mathcal{N}=(1,0)$ superconformal field theory with smallest
non-Higgsable gauge symmetry $SU(3)$. In particular, we propose new 2d gauge
theory descriptions of its self-dual strings in the tensor branch. We use our
gauge theories to compute the elliptic genera of the self-dual strings, which
completely agree with the partial data known from topological strings. We
further study the strings of the $(E_6,E_6)$ conformal matter by generalizing
our 2d gauge theories. We also show that anomalies of all our gauge theories
agree with the self-dual string anomalies computed by inflows from 6d.
