Probing 7-branes on orbifolds

D3 branes in the vicinity of an E 6 , E 7 , or E 8 stack of 7-branes in flat space are known to host at low energy a famous class of strongly-coupled 𝒩 = 2 superconformal field theories featuring exceptional global symmetry. What if, instead, the 7-branes wrap an orbifold? We give a systematic characterization of such theories in the case of ℂ 2 / ℤ n , and determine their main properties, like global symmetries, spectra of Coulomb-branch operators, and patterns of Higgs-branch flows. We put forward a set of rules to construct their magnetic quivers, which directly generalize what happens in the perturbative case, and later derive them using the duality with M5 branes probing M9 walls.