Supercharacter theories for Sylow $p$-subgroups of the Ree groups

Abstract

We determine a supercharacter theory for Sylow $p$-subgroups ${}^2{G}_2^{syl}(3^{2m+1})$ of the Ree groups ${}^2{G}_2(3^{2m+1})$, calculate the conjugacy classes of ${}^2{G}_2^{syl}(3^{2m+1})$, and establish the character table of ${}^2{G}_2^{syl}(3)$.

20 pages, 6 tables. arXiv admin note: text overlap with arXiv:1808.03115