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We consider the bit-complexity of the problem stated in the title. Exact computations in algebraic number fields are performed symbolically. We present a polynomial-time algorithm to find a complete set of nonequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table. In particular, it follows that some representative of each equivalence class of irreducible representations admits a polynomial-size description. We also considerdoi:10.1090/s0025-5718-1990-1035925-1 fatcat:theuji7o7bd77fribcpi34apqe