For wild-by-tame split metacyclic groups, the stringy Euler number of the quotient depends on the representation and is not always equal to the number of conjugacy classes, unlike the classical McKay case.
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The McKay correspondence and local heights for wild-by-tame split metacyclic groups
For wild-by-tame split metacyclic groups, the stringy Euler number of the quotient depends on the representation and is not always equal to the number of conjugacy classes, unlike the classical McKay case.