Fusion Ring
\[ \begin{array}{llllll} \htmlTitle{1\otimes 1}{1} & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5} & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{6 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5} & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{3 \oplus 6} & \htmlTitle{5\otimes 4}{5 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 4} & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5} & \htmlTitle{6\otimes 3}{5 \oplus 4} & \htmlTitle{6\otimes 4}{3 \oplus 6} & \htmlTitle{6\otimes 5}{3 \oplus 6 \oplus 2} & \htmlTitle{6\otimes 6}{1 \oplus 5 \oplus 4} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.802\) | \( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{7} \right)} \) |
| \( 4\) | \(1.802\) | \( - 2 \cos{\left(\frac{3 \pi}{7} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{7} \right)} \) |
| \( 5\) | \(2.247\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{7} \right)} \) |
| \( 6\) | \(2.247\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{7} \right)} \) |
| \( D^2\) | 18.592 | \(- 4 \cos{\left(\frac{3 \pi}{7} \right)} + 12 \cos{\left(\frac{2 \pi}{7} \right)} + 12\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{1}{2}} & \htmlTitle{\theta_{3}}{\frac{3}{14}} & \htmlTitle{\theta_{4}}{\frac{12}{7}} & \htmlTitle{\theta_{5}}{\frac{4}{7}} & \htmlTitle{\theta_{6}}{\frac{15}{14}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllll} \htmlTitle{S_{1; 1}}{1} & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{-1} & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{3; 2}}{\zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - \zeta_{56}^{8} - 1} & \htmlTitle{S_{3; 3}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 1} & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{4; 2}}{-\zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{4; 3}}{\zeta_{56}^{20} - \zeta_{56}^{8} - 1} & \htmlTitle{S_{4; 4}}{\zeta_{56}^{20} - \zeta_{56}^{8} - 1} & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{5; 3}}{1} & \htmlTitle{S_{5; 4}}{1} & \htmlTitle{S_{5; 5}}{\zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - \zeta_{56}^{8} - 1} & \\ \htmlTitle{S_{6; 1}}{-\zeta_{56}^{20} + \zeta_{56}^{8} + 1} & \htmlTitle{S_{6; 2}}{\zeta_{56}^{20} - \zeta_{56}^{8} - 1} & \htmlTitle{S_{6; 3}}{-1} & \htmlTitle{S_{6; 4}}{1} & \htmlTitle{S_{6; 5}}{\zeta_{56}^{20} - \zeta_{56}^{16} + \zeta_{56}^{12} - \zeta_{56}^{8} - 1} & \htmlTitle{S_{6; 6}}{-\zeta_{56}^{20} + \zeta_{56}^{16} - \zeta_{56}^{12} + \zeta_{56}^{8} + 1}\end{array}\right) \]
Central Charge
\[c = \frac{15}{7} \]