The quotient variety associated to a permutation representation of a finite group has only canonical singularities in arbitrary characteristic. Moreover, the log pair associated to such a representation is Kawamata log terminal except in characteristic two, and log canonical in arbitrary characteristic.

17 pages. v2: minor revision. v3: added section 2.2, added more detailed explanations about stringy motives, P-moduli spaces and so on. v4: the final version appearing in EPIGA