  We consider an orbifold Landau-Ginzburg model $(f,G)$, where $f$ is an
invertible polynomial in three variables and $G$ a finite group of symmetries
of $f$ containing the exponential grading operator, and its Berglund-H\"ubsch
transpose $(f^T, G^T)$. We show that this defines a mirror symmetry between
orbifold curves and cusp singularities with group action. We define Dolgachev
numbers for the orbifold curves and Gabrielov numbers for the cusp
singularities with group action. We show that these numbers are the same and
that the stringy Euler number of the orbifold curve coincides with the
$G^T$-equivariant Milnor number of the mirror cusp singularity.
