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For each finite quasi-Frobenius ring E McCulloh has constructed an order T (E) in a Galois algebra over Q with Galois group E * . For E=Z/nZ the order T (E) is the cyclotomic ring Z[ζ n ]. This note addresses the conductor discriminant formula that McCulloh has proposed for these orders. For commutative E we show that one inequality holds and that we have equality if and only if E is a principal ideal ring.doi:10.1215/ijm/1255986109 fatcat:ghhp6hgeavgybgwvbezkj5rtaa