Fusion Ring
\[ \begin{array}{llllllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{7} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 8} & & & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5} & \htmlTitle{4\otimes 3}{3 \oplus 10} & \htmlTitle{4\otimes 4}{1 \oplus 8 \oplus 5} & & & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{10 \oplus 7} & \htmlTitle{5\otimes 4}{4 \oplus 9 \oplus 2} & \htmlTitle{5\otimes 5}{1 \oplus 8 \oplus 5} & & & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{8 \oplus 9} & \htmlTitle{6\otimes 4}{10 \oplus 6} & \htmlTitle{6\otimes 5}{10 \oplus 6} & \htmlTitle{6\otimes 6}{1 \oplus 4 \oplus 5 \oplus 2} & & & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{3} & \htmlTitle{7\otimes 3}{5 \oplus 9 \oplus 2} & \htmlTitle{7\otimes 4}{10 \oplus 7} & \htmlTitle{7\otimes 5}{3 \oplus 10} & \htmlTitle{7\otimes 6}{8 \oplus 9} & \htmlTitle{7\otimes 7}{1 \oplus 4 \oplus 8} & & & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{9} & \htmlTitle{8\otimes 3}{3 \oplus 10 \oplus 6} & \htmlTitle{8\otimes 4}{4 \oplus 8 \oplus 9} & \htmlTitle{8\otimes 5}{8 \oplus 5 \oplus 9} & \htmlTitle{8\otimes 6}{3 \oplus 10 \oplus 7} & \htmlTitle{8\otimes 7}{10 \oplus 6 \oplus 7} & \htmlTitle{8\otimes 8}{1 \oplus 4 \oplus 8 \oplus 5 \oplus 9} & & \\ \htmlTitle{9\otimes 1}{9} & \htmlTitle{9\otimes 2}{8} & \htmlTitle{9\otimes 3}{10 \oplus 6 \oplus 7} & \htmlTitle{9\otimes 4}{8 \oplus 5 \oplus 9} & \htmlTitle{9\otimes 5}{4 \oplus 8 \oplus 9} & \htmlTitle{9\otimes 6}{3 \oplus 10 \oplus 7} & \htmlTitle{9\otimes 7}{3 \oplus 10 \oplus 6} & \htmlTitle{9\otimes 8}{4 \oplus 8 \oplus 5 \oplus 9 \oplus 2} & \htmlTitle{9\otimes 9}{1 \oplus 4 \oplus 8 \oplus 5 \oplus 9} & \\ \htmlTitle{10\otimes 1}{10} & \htmlTitle{10\otimes 2}{10} & \htmlTitle{10\otimes 3}{4 \oplus 8 \oplus 5 \oplus 9} & \htmlTitle{10\otimes 4}{3 \oplus 10 \oplus 6 \oplus 7} & \htmlTitle{10\otimes 5}{3 \oplus 10 \oplus 6 \oplus 7} & \htmlTitle{10\otimes 6}{4 \oplus 8 \oplus 5 \oplus 9} & \htmlTitle{10\otimes 7}{4 \oplus 8 \oplus 5 \oplus 9} & \htmlTitle{10\otimes 8}{3 \oplus 2\cdot10 \oplus 6 \oplus 7} & \htmlTitle{10\otimes 9}{3 \oplus 2\cdot10 \oplus 6 \oplus 7} & \htmlTitle{10\otimes 10}{1 \oplus 4 \oplus 2\cdot8 \oplus 5 \oplus 2\cdot9 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(2.732\) | \( 1 + \sqrt{3} \) |
| \( 4\) | \(2.732\) | \( 1 + \sqrt{3} \) |
| \( 5\) | \(2.732\) | \( 1 + \sqrt{3} \) |
| \( 6\) | \(2.732\) | \( 1 + \sqrt{3} \) |
| \( 7\) | \(2.732\) | \( 1 + \sqrt{3} \) |
| \( 8\) | \(3.732\) | \( \sqrt{3} + 2 \) |
| \( 9\) | \(3.732\) | \( \sqrt{3} + 2 \) |
| \( 10\) | \(4.732\) | \( \sqrt{3} + 3 \) |
| \( D^2\) | 89.569 | \(24 \sqrt{3} + 48\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{5}{12}} & \htmlTitle{\theta_{4}}{\frac{2}{3}} & \htmlTitle{\theta_{5}}{\frac{5}{3}} & \htmlTitle{\theta_{6}}{\frac{7}{4}} & \htmlTitle{\theta_{7}}{\frac{5}{12}} & \htmlTitle{\theta_{8}}{1} & \htmlTitle{\theta_{9}}{0} & \htmlTitle{\theta_{10}}{\frac{5}{4}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{3; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{3; 3}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 3} & & & & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{4; 3}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{4; 4}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & & & & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{5; 3}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{5; 4}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{5; 5}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & & & & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{6; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{2 \zeta_{48}^{12} - 4 \zeta_{48}^{4} - 2} & \htmlTitle{S_{6; 5}}{-2 \zeta_{48}^{12} + 4 \zeta_{48}^{4} + 2} & \htmlTitle{S_{6; 6}}{0} & & & & \\ \htmlTitle{S_{7; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{7; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{7; 3}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 3} & \htmlTitle{S_{7; 4}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{7; 5}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{7; 6}}{0} & \htmlTitle{S_{7; 7}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 3} & & & \\ \htmlTitle{S_{8; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 2} & \htmlTitle{S_{8; 2}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 2} & \htmlTitle{S_{8; 3}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{8; 4}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{8; 5}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{8; 6}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{8; 7}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 1} & \htmlTitle{S_{8; 8}}{1} & & \\ \htmlTitle{S_{9; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 2} & \htmlTitle{S_{9; 2}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 2} & \htmlTitle{S_{9; 3}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{9; 4}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{9; 5}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{9; 6}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{9; 7}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 1} & \htmlTitle{S_{9; 8}}{1} & \htmlTitle{S_{9; 9}}{1} & \\ \htmlTitle{S_{10; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 3} & \htmlTitle{S_{10; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 3} & \htmlTitle{S_{10; 3}}{0} & \htmlTitle{S_{10; 4}}{0} & \htmlTitle{S_{10; 5}}{0} & \htmlTitle{S_{10; 6}}{0} & \htmlTitle{S_{10; 7}}{0} & \htmlTitle{S_{10; 8}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4} - 3} & \htmlTitle{S_{10; 9}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4} + 3} & \htmlTitle{S_{10; 10}}{0}\end{array}\right) \]
Central Charge
\[c = 5 \]