Character Tables Completed for All Maximal Subgroups of the Monster — E8 Intelligence Research

FINDING: The character table of the maximal 2-local subgroup \( N(2B^5) \cong 2^{5+10+20}.(S_3 \times L_5(2)) \) of the Monster sporadic group has been computed, completing the character tables for all maximal subgroups of the Monster. | MATH: Group structure: \( 2^{5+10+20} \) denotes an extraspecial-type 2-group with a 5-dimensional irreducible module over \(\mathbb{F}_2\) (giving the \(2^5\) part), a 10-dimensional symplectic module (the \(2^{10}\) part), and a 20-dimensional orthogonal module (the \(2^{20}\) part). The extension is by \( S_3 \times L_5(2) \), where \( L_5(2) = PSL(5,2) \) has order \( 2^{10} \cdot 3^2 \cdot 5 \cdot 7 \cdot 31 \). The character table is a square matrix of irreducible characters over \(\mathbb{C}\), with dimensions constrained by the Monster's centralizer structure. Key constants: The 2-part of the group order is \( 2^{5+10+20} \cdot 2^{10} = 2^{45} \). The full Monster order is \( 2^{46} \cdot 3^{20} \cdot 5^9 \cdot 7^6 \cdot 11^2 \cdot 13^3 \cdot 1 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com