(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the kernel of all irreducible characters of G, when given the character table.

Find the centralizer of each irreducible character of G, when given the character table.

Find Z(G) (the centralizer of G) for the same character table.

2. Relevant equations

I know that ker([itex]\chi[/itex])={g [itex]\in[/itex]G| [itex]\chi[/itex](g)=[itex]\chi[/itex](1)} where [itex]\chi \in [/itex] Irr(G).

I also know that Z([itex]\chi[/itex])={g [itex]\in[/itex] G | |[itex]\chi[/itex](g)|=[itex]\chi[/itex](1)}

and I think Z(G) is the intersection of all Z([itex]\chi[/itex])

I hope you can the gist of the question.

3. The attempt at a solution

The question I have to answer pertains to a given character table of S4.

I do not want an answer to this particular table.

If someone could please give me an example using another character table so I can follow.

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# Homework Help: Kernel and centralizer of irreducible characters

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