Character formula for an induced representation

For

H \leq G

and an

H

-character

χ

,

(Ind_{H}^{G} χ) (g) = \frac{1}{∣ H ∣} \sum_{x \in G x^{- 1} gx \in H} χ (x^{- 1} gx) .

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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 160 / 2 / c / Solution

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