  D3 branes in the vicinity of an E6, E7, or E8 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 C2/Zn, 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.
