GAP computations needed in the proof of [DNT, Theorem 6.1 (ii)]
  This is a collection of example computations that are cited in the Appendix of [DNT]. In each case, the aim is to show that the extension of a given finite simple group by an elementary abelian group of given rank has the property that not all complex irreducible characters of the same degree are Galois conjugate. 
Thomas Breuer and Klaus Lux
math.RT