Reference request for value of characters of the symmetric group on various conjugacy classes

Question

Let $\chi^{\lambda}$ and $C_{\mu}$ denote the character of the conjugacy class of the symmetric group $S_n$ induced by partitions $\lambda,\mu \vdash n$

I'm interested in where I can find a table that has values for $|C_{\mu}|$ (the magnitude of these conjugacy class), as well as $\chi^{\lambda}(C_\mu)$ (the value of the character corresponding to the partion $\lambda$ on the conjugacy class corresponding to the partition $\mu$).

Thank you very much!

edit: Could someone give me some tips in calculating $\chi^{\lambda}(C_\mu)$? A bit of insight of what's going on would be nice!!

Answer 1

You can calculate $\chi^{\lambda}(C_{\mu})$ via the Frobenius formula:

https://en.wikipedia.org/wiki/Frobenius_formula