Degrees of irreducible representations are the same for all splitting fields
Suppose is a finite group. Then, given any splitting field for (so the characteristic of does not divide the order of ) it is possible to construct a bijection between the irreducible representations of over and the irreducible representations of over the field of complex numbers, such that the bijection preserves the degree of a representation.
In particular, this means that the Degrees of irreducible representations (?) for a finite group are the same for all splitting fields (characteristic not dividing the group order).