Fusion Ring
\[ \begin{array}{llllll} \htmlTitle{1\otimes 1}{1} & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 2} & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5} & \htmlTitle{4\otimes 3}{6} & \htmlTitle{4\otimes 4}{1 \oplus 5} & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{6} & \htmlTitle{5\otimes 4}{2 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5} & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{5 \oplus 4} & \htmlTitle{6\otimes 4}{3 \oplus 6} & \htmlTitle{6\otimes 5}{3 \oplus 6} & \htmlTitle{6\otimes 6}{1 \oplus 5 \oplus 2 \oplus 4} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.414\) | \( \sqrt{2} \) |
| \( 4\) | \(1.618\) | \( \frac{1}{2} + \frac{\sqrt{5}}{2} \) |
| \( 5\) | \(1.618\) | \( \frac{1}{2} + \frac{\sqrt{5}}{2} \) |
| \( 6\) | \(2.288\) | \( - \sqrt{2} \left(\frac{1}{4} - \frac{\sqrt{5}}{4}\right) + \frac{\sqrt{2}}{2} + \sqrt{2} \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right) \) |
| \( D^2\) | 14.472 | \(2 \sqrt{5} + 10\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{5}{8}} & \htmlTitle{\theta_{4}}{\frac{9}{5}} & \htmlTitle{\theta_{5}}{\frac{4}{5}} & \htmlTitle{\theta_{6}}{\frac{57}{40}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllll} \htmlTitle{S_{1; 1}}{1} & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{160}^{60} + \zeta_{160}^{20}} & \htmlTitle{S_{3; 2}}{\zeta_{160}^{60} - \zeta_{160}^{20}} & \htmlTitle{S_{3; 3}}{0} & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{160}^{48} + \zeta_{160}^{32} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{160}^{48} + \zeta_{160}^{32} + 1} & \htmlTitle{S_{4; 3}}{\zeta_{160}^{60} - \zeta_{160}^{36} + \zeta_{160}^{28} - \zeta_{160}^{12} - \zeta_{160}^{4}} & \htmlTitle{S_{4; 4}}{-1} & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{160}^{48} + \zeta_{160}^{32} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{160}^{48} + \zeta_{160}^{32} + 1} & \htmlTitle{S_{5; 3}}{-\zeta_{160}^{60} + \zeta_{160}^{36} - \zeta_{160}^{28} + \zeta_{160}^{12} + \zeta_{160}^{4}} & \htmlTitle{S_{5; 4}}{-1} & \htmlTitle{S_{5; 5}}{-1} & \\ \htmlTitle{S_{6; 1}}{-\zeta_{160}^{60} + \zeta_{160}^{36} - \zeta_{160}^{28} + \zeta_{160}^{12} + \zeta_{160}^{4}} & \htmlTitle{S_{6; 2}}{\zeta_{160}^{60} - \zeta_{160}^{36} + \zeta_{160}^{28} - \zeta_{160}^{12} - \zeta_{160}^{4}} & \htmlTitle{S_{6; 3}}{0} & \htmlTitle{S_{6; 4}}{-\zeta_{160}^{60} + \zeta_{160}^{20}} & \htmlTitle{S_{6; 5}}{\zeta_{160}^{60} - \zeta_{160}^{20}} & \htmlTitle{S_{6; 6}}{0}\end{array}\right) \]
Central Charge
\[c = \frac{133}{10} \]