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We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ isa finite subgroup of $SU(3)$. M-theory on this orbifold singularity gives riseto a 5d SCFT, which is investigated with two methods. The first approach is via3d McKay correspondence which relates the group theoretic data of $\Gamma$ tothe physical properties of the 5d SCFT. In particular, the 1-form symmetry ofthe 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 theCoulomb branch information of the 5d SCFT, which is applied to toric, non-torichypersurface and complete intersection cases. Many new theories areconstructed, either with or without an IR quiver gauge theory description. Wefind that many resolved Calabi-Yau threefolds, $\widetilde{X}$, contain compactexceptional divisors that are singular by themselves. Moreover, for certaincases of $\Gamma$, the orbifold singularity $\mathbb{C}^3/\Gamma$ can beembedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theoryconstruction. Such 6d theory is naturally related to the 5d SCFT defined on thesame singularity. We find examples of rank-1 6d SCFTs without a gauge group,which are potentially different from the rank-1 E-string theory.

5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds