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I have constructed a character table for $A_{4}$ and need to use induced representations to get a character table for $S_{4}$. I'm not very confident with the concept of induced representations, but I am familiar with the definition. In that sense, given a representation $V$ of $G$, and a representation $W$ of a subgroup $H$ of $G$, I understand how I would go about checking whether $V$ is induced by $W$ or not.

But starting with $W$, I don't see how to go about constructing $V$.

Can anyone give me advice on how to approach this problem, or a reference that they think might be helpful?

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The wikipedia article en.wikipedia.org/wiki/Induced_representation gives construction of induced representation. Moreover, the Frobenius formula tells you how to compute the character of an induced representation. As for reference, Serre's "Linear representations of finite groups" is a classic. –  user27126 Nov 16 '12 at 0:24
    
OK. I found that formula in chapter 7 of Serre. Thanks for the tip. I will try it. –  Kyle Schlitt Nov 16 '12 at 1:26
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