Fusion Ring
\[ \begin{array}{lllllllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1} & & & & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{2} & \htmlTitle{4\otimes 4}{1} & & & & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{9} & \htmlTitle{5\otimes 4}{9} & \htmlTitle{5\otimes 5}{1 \oplus 6 \oplus 2} & & & & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{8} & \htmlTitle{6\otimes 4}{8} & \htmlTitle{6\otimes 5}{5 \oplus 7} & \htmlTitle{6\otimes 6}{1 \oplus 8 \oplus 2} & & & & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{7} & \htmlTitle{7\otimes 3}{7} & \htmlTitle{7\otimes 4}{7} & \htmlTitle{7\otimes 5}{6 \oplus 8} & \htmlTitle{7\otimes 6}{5 \oplus 9} & \htmlTitle{7\otimes 7}{1 \oplus 3 \oplus 4 \oplus 2} & & & & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{8} & \htmlTitle{8\otimes 3}{6} & \htmlTitle{8\otimes 4}{6} & \htmlTitle{8\otimes 5}{7 \oplus 9} & \htmlTitle{8\otimes 6}{6 \oplus 3 \oplus 4} & \htmlTitle{8\otimes 7}{5 \oplus 9} & \htmlTitle{8\otimes 8}{1 \oplus 8 \oplus 2} & & & & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{9} & \htmlTitle{9\otimes 3}{5} & \htmlTitle{9\otimes 4}{5} & \htmlTitle{9\otimes 5}{8 \oplus 3 \oplus 4} & \htmlTitle{9\otimes 6}{7 \oplus 9} & \htmlTitle{9\otimes 7}{6 \oplus 8} & \htmlTitle{9\otimes 8}{5 \oplus 7} & \htmlTitle{9\otimes 9}{1 \oplus 6 \oplus 2} & & & & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{13} & \htmlTitle{10\otimes 3}{10} & \htmlTitle{10\otimes 4}{13} & \htmlTitle{10\otimes 5}{11 \oplus 12} & \htmlTitle{10\otimes 6}{10 \oplus 13} & \htmlTitle{10\otimes 7}{11 \oplus 12} & \htmlTitle{10\otimes 8}{10 \oplus 13} & \htmlTitle{10\otimes 9}{11 \oplus 12} & \htmlTitle{10\otimes 10}{1 \oplus 6 \oplus 8 \oplus 3} & & & \\ \htmlTitle{11\otimes 1}{11} & \htmlTitle{11\otimes 2}{12} & \htmlTitle{11\otimes 3}{12} & \htmlTitle{11\otimes 4}{11} & \htmlTitle{11\otimes 5}{10 \oplus 13} & \htmlTitle{11\otimes 6}{11 \oplus 12} & \htmlTitle{11\otimes 7}{10 \oplus 13} & \htmlTitle{11\otimes 8}{11 \oplus 12} & \htmlTitle{11\otimes 9}{10 \oplus 13} & \htmlTitle{11\otimes 10}{5 \oplus 7 \oplus 9} & \htmlTitle{11\otimes 11}{1 \oplus 6 \oplus 8 \oplus 4} & & \\ \htmlTitle{12\otimes 1}{12} & \htmlTitle{12\otimes 2}{11} & \htmlTitle{12\otimes 3}{11} & \htmlTitle{12\otimes 4}{12} & \htmlTitle{12\otimes 5}{10 \oplus 13} & \htmlTitle{12\otimes 6}{11 \oplus 12} & \htmlTitle{12\otimes 7}{10 \oplus 13} & \htmlTitle{12\otimes 8}{11 \oplus 12} & \htmlTitle{12\otimes 9}{10 \oplus 13} & \htmlTitle{12\otimes 10}{5 \oplus 7 \oplus 9} & \htmlTitle{12\otimes 11}{6 \oplus 8 \oplus 3 \oplus 2} & \htmlTitle{12\otimes 12}{1 \oplus 6 \oplus 8 \oplus 4} & \\ \htmlTitle{13\otimes 1}{13} & \htmlTitle{13\otimes 2}{10} & \htmlTitle{13\otimes 3}{13} & \htmlTitle{13\otimes 4}{10} & \htmlTitle{13\otimes 5}{11 \oplus 12} & \htmlTitle{13\otimes 6}{10 \oplus 13} & \htmlTitle{13\otimes 7}{11 \oplus 12} & \htmlTitle{13\otimes 8}{10 \oplus 13} & \htmlTitle{13\otimes 9}{11 \oplus 12} & \htmlTitle{13\otimes 10}{6 \oplus 8 \oplus 4 \oplus 2} & \htmlTitle{13\otimes 11}{5 \oplus 7 \oplus 9} & \htmlTitle{13\otimes 12}{5 \oplus 7 \oplus 9} & \htmlTitle{13\otimes 13}{1 \oplus 6 \oplus 8 \oplus 3} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.000\) | \( 1 \) |
| \( 4\) | \(1.000\) | \( 1 \) |
| \( 5\) | \(2.000\) | \( 2 \) |
| \( 6\) | \(2.000\) | \( 2 \) |
| \( 7\) | \(2.000\) | \( 2 \) |
| \( 8\) | \(2.000\) | \( 2 \) |
| \( 9\) | \(2.000\) | \( 2 \) |
| \( 10\) | \(2.449\) | \( \sqrt{6} \) |
| \( 11\) | \(2.449\) | \( \sqrt{6} \) |
| \( 12\) | \(2.449\) | \( \sqrt{6} \) |
| \( 13\) | \(2.449\) | \( \sqrt{6} \) |
| \( D^2\) | 48.000 | \(48\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{1} & \htmlTitle{\theta_{4}}{1} & \htmlTitle{\theta_{5}}{\frac{11}{12}} & \htmlTitle{\theta_{6}}{\frac{5}{3}} & \htmlTitle{\theta_{7}}{\frac{1}{4}} & \htmlTitle{\theta_{8}}{\frac{2}{3}} & \htmlTitle{\theta_{9}}{\frac{11}{12}} & \htmlTitle{\theta_{10}}{\frac{11}{8}} & \htmlTitle{\theta_{11}}{\frac{11}{8}} & \htmlTitle{\theta_{12}}{\frac{3}{8}} & \htmlTitle{\theta_{13}}{\frac{3}{8}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{1} & \htmlTitle{S_{3; 3}}{1} & & & & & & & & & & \\ \htmlTitle{S_{4; 1}}{1} & \htmlTitle{S_{4; 2}}{1} & \htmlTitle{S_{4; 3}}{1} & \htmlTitle{S_{4; 4}}{1} & & & & & & & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{-2} & \htmlTitle{S_{5; 4}}{-2} & \htmlTitle{S_{5; 5}}{-2 \zeta_{96}^{24} + 4 \zeta_{96}^{8}} & & & & & & & & \\ \htmlTitle{S_{6; 1}}{2} & \htmlTitle{S_{6; 2}}{2} & \htmlTitle{S_{6; 3}}{2} & \htmlTitle{S_{6; 4}}{2} & \htmlTitle{S_{6; 5}}{2} & \htmlTitle{S_{6; 6}}{-2} & & & & & & & \\ \htmlTitle{S_{7; 1}}{2} & \htmlTitle{S_{7; 2}}{2} & \htmlTitle{S_{7; 3}}{-2} & \htmlTitle{S_{7; 4}}{-2} & \htmlTitle{S_{7; 5}}{0} & \htmlTitle{S_{7; 6}}{-4} & \htmlTitle{S_{7; 7}}{0} & & & & & & \\ \htmlTitle{S_{8; 1}}{2} & \htmlTitle{S_{8; 2}}{2} & \htmlTitle{S_{8; 3}}{2} & \htmlTitle{S_{8; 4}}{2} & \htmlTitle{S_{8; 5}}{-2} & \htmlTitle{S_{8; 6}}{-2} & \htmlTitle{S_{8; 7}}{4} & \htmlTitle{S_{8; 8}}{-2} & & & & & \\ \htmlTitle{S_{9; 1}}{2} & \htmlTitle{S_{9; 2}}{2} & \htmlTitle{S_{9; 3}}{-2} & \htmlTitle{S_{9; 4}}{-2} & \htmlTitle{S_{9; 5}}{2 \zeta_{96}^{24} - 4 \zeta_{96}^{8}} & \htmlTitle{S_{9; 6}}{2} & \htmlTitle{S_{9; 7}}{0} & \htmlTitle{S_{9; 8}}{-2} & \htmlTitle{S_{9; 9}}{-2 \zeta_{96}^{24} + 4 \zeta_{96}^{8}} & & & & \\ \htmlTitle{S_{10; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{10; 2}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{10; 3}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{10; 4}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{10; 5}}{0} & \htmlTitle{S_{10; 6}}{0} & \htmlTitle{S_{10; 7}}{0} & \htmlTitle{S_{10; 8}}{0} & \htmlTitle{S_{10; 9}}{0} & \htmlTitle{S_{10; 10}}{0} & & & \\ \htmlTitle{S_{11; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{11; 2}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{11; 3}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{11; 4}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{11; 5}}{0} & \htmlTitle{S_{11; 6}}{0} & \htmlTitle{S_{11; 7}}{0} & \htmlTitle{S_{11; 8}}{0} & \htmlTitle{S_{11; 9}}{0} & \htmlTitle{S_{11; 10}}{-2 \zeta_{96}^{24} + 4 \zeta_{96}^{8}} & \htmlTitle{S_{11; 11}}{0} & & \\ \htmlTitle{S_{12; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{12; 2}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{12; 3}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{12; 4}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{12; 5}}{0} & \htmlTitle{S_{12; 6}}{0} & \htmlTitle{S_{12; 7}}{0} & \htmlTitle{S_{12; 8}}{0} & \htmlTitle{S_{12; 9}}{0} & \htmlTitle{S_{12; 10}}{2 \zeta_{96}^{24} - 4 \zeta_{96}^{8}} & \htmlTitle{S_{12; 11}}{0} & \htmlTitle{S_{12; 12}}{0} & \\ \htmlTitle{S_{13; 1}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{13; 2}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{13; 3}}{2 \zeta_{96}^{28} - \zeta_{96}^{20} - \zeta_{96}^{12} - \zeta_{96}^{4}} & \htmlTitle{S_{13; 4}}{-2 \zeta_{96}^{28} + \zeta_{96}^{20} + \zeta_{96}^{12} + \zeta_{96}^{4}} & \htmlTitle{S_{13; 5}}{0} & \htmlTitle{S_{13; 6}}{0} & \htmlTitle{S_{13; 7}}{0} & \htmlTitle{S_{13; 8}}{0} & \htmlTitle{S_{13; 9}}{0} & \htmlTitle{S_{13; 10}}{0} & \htmlTitle{S_{13; 11}}{2 \zeta_{96}^{24} - 4 \zeta_{96}^{8}} & \htmlTitle{S_{13; 12}}{-2 \zeta_{96}^{24} + 4 \zeta_{96}^{8}} & \htmlTitle{S_{13; 13}}{0}\end{array}\right) \]
Central Charge
\[c = 11 \]