Geodesic
Some Results on the Schur Index of a Representation of a Finite Group
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 626-640

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Let C be a finite group with a representation as an irreducible group of linear transformations on a finite-dimensional complex vector space. Every choice of a basis for the space gives the representing transformations the form of a particular group of matrices. If for some choice of a basis the resulting group of matrices has entries which all lie in a subfield K of the complex field, we say that the representation can be realized in K. It is well known that every representation of C can be realized in some algebraic number field, a finitedimensional extension of the rational field Q. 
Ford, Charles. Some Results on the Schur Index of a Representation of a Finite Group. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 626-640. doi: 10.4153/CJM-1970-069-3
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