I want to know what can we get from (Brauer) character tables of a finite group. such as block distribution, the liftablity of a character and so on. For example, we can get both character table and Brauer character of $A_5$ from 'Atlas of fintie groups' and 'An atlas of Brauer charcters' respectively. How can I know the information of the blocks of $A_5$ or any properties of the characters of $A_5$?
2026-04-22 09:48:21.1776851301
What can we get from (Brauer) character tables of a finite group?
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There is now a paper by Navarro with the title "What do the modular characters know?" (published). He asked if the $p$-Brauer character table of a finite group $G$ determines the $p'$-part $|G|_{p'}$ (it is impossible to determine $|G|$). This has been answered affirmatively by Sambale (arxiv, published). Navarro proved that the Brauer character table determines if $G$ is solvable. In general, it seems there is not much information to get from the Brauer character table.