Field generated by character values

Definition
Suppose $$G$$ is a finite group. Pick a characteristic that is either zero or a prime not dividing the order of $$G$$. The field generated by character values for $$G$$ in that characteristic is the smallest field in that characteristic containing the values of all the characters of irreducible representations of $$G$$ over a splitting field in that characteristic.

Relationship with cyclotomic extensions

 * In characteristic zero, field generated by character values is contained in a cyclotomic extension of rationals, because characters are cyclotomic integers.
 * Field generated by character values need not be cyclotomic

Uniqueness and relationship with splitting fields

 * The field generated by character values is unique up to isomorphism of fields.
 * The field generated by character values is contained in every splitting field, and hence also in every minimal splitting field.
 * Field generated by character values is splitting field implies it is the unique minimal splitting field
 * Field generated by character values need not be a splitting field