Induced character

In mathematics, an induced character is the character of the representation "V" of a finite group "G" induced from a representation "W" of a subgroup "H" ≤ "G". More generally, there is also a notion of induction formula_1 of a class function "f" on "H" given by the formula
If "f" is a character of the representation "W" of "H", then this formula for formula_1 calculates the character of the induced representation "V" of "G".
The basic result on induced characters is Brauer's theorem on induced characters. It states that every irreducible character on "G" is a linear combination with integer coefficients of characters induced from elementary subgroups.