We explicitly compute the McKay quivers of small finite subgroups of $GL(2,\mathbb{C})$ relative to the natural representation, using character theory and the McKay quivers of finite subgroups of $SU(2)$. We present examples that shows the rich symmetry and combinatorial structure of these quivers. We compare our results with the MacKay quivers computed by Auslander and Reiten.
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