  We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ is
a finite subgroup of $SU(3)$. M-theory on this orbifold singularity gives rise
to a 5d SCFT, which is investigated with two methods. The first approach is via
3d McKay correspondence which relates the group theoretic data of $\Gamma$ to
the physical properties of the 5d SCFT. In particular, the 1-form symmetry of
the 5d SCFT is read off from the McKay quiver of $\Gamma$ in an elegant way.
The second method is to explicitly resolve the singularity $X$ and study the
Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric
hypersurface and complete intersection cases. Many new theories are
constructed, either with or without an IR quiver gauge theory description. We
find that many resolved Calabi-Yau threefolds, $\widetilde{X}$, contain compact
exceptional divisors that are singular by themselves. Moreover, for certain
cases of $\Gamma$, the orbifold singularity $\mathbb{C}^3/\Gamma$ can be
embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory
construction. Such 6d theory is naturally related to the 5d SCFT defined on the
same singularity. We find examples of rank-1 6d SCFTs without a gauge group,
which are potentially different from the rank-1 E-string theory.
