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Sorry about asking so many questions, but I had an idea for my study of groups, and I wanted to know if it was already a thing people use. My idea is to make a multiplication table with all the conjugacy classes of a group. In each box, there would be a list of the possible conjugacy classes that you could get from multiplying the specified two conjugacy classes together.

Is this something new, and would it be useful in the study of some groups?

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  • $\begingroup$ This is a pretty standard idea. Have a look at an introductory textbook. Not entirely related, but you might get a kick out of character tables too. Voting to close. $\endgroup$
    – David White
    Commented Sep 19, 2013 at 17:53

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The numbers are called class multiplication coefficients. Definitely not something new! Knowing them and the size of the conjugacy classes, you have the structure constants for the center of the group algebra. There is some discussion of using them computationally in 2.3 of Lux-Pahlings book. There are actual tables of them for the symmetric group in the back of Kerber's book.

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  • $\begingroup$ Oh good, they actually have a use after all! Could you provide a link to those books? $\endgroup$
    – Thomas
    Commented Sep 19, 2013 at 13:54

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