Fusion Ring
\[ \begin{array}{lllll} \htmlTitle{1\otimes 1}{1} & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1 \oplus 3} & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{2 \oplus 4} & \htmlTitle{3\otimes 3}{1 \oplus 5 \oplus 3} & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{5 \oplus 3} & \htmlTitle{4\otimes 3}{5 \oplus 2 \oplus 4} & \htmlTitle{4\otimes 4}{1 \oplus 5 \oplus 4 \oplus 3} & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5 \oplus 4} & \htmlTitle{5\otimes 3}{5 \oplus 4 \oplus 3} & \htmlTitle{5\otimes 4}{5 \oplus 2 \oplus 4 \oplus 3} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 2 \oplus 4 \oplus 3} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.919\) | \( - 2 \cos{\left(\frac{3 \pi}{11} \right)} - 2 \cos{\left(\frac{5 \pi}{11} \right)} + 2 \cos{\left(\frac{4 \pi}{11} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{11} \right)} \) |
| \( 3\) | \(2.683\) | \( 1 + 2 \cos{\left(\frac{2 \pi}{11} \right)} \) |
| \( 4\) | \(3.229\) | \( - 2 \cos{\left(\frac{5 \pi}{11} \right)} + 2 \cos{\left(\frac{4 \pi}{11} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{11} \right)} \) |
| \( 5\) | \(3.513\) | \( 2 \cos{\left(\frac{4 \pi}{11} \right)} + 1 + 2 \cos{\left(\frac{2 \pi}{11} \right)} \) |
| \( D^2\) | 34.646 | \(- 2 \cos{\left(\frac{3 \pi}{11} \right)} - 6 \cos{\left(\frac{5 \pi}{11} \right)} + 12 \cos{\left(\frac{4 \pi}{11} \right)} + 15 + 20 \cos{\left(\frac{2 \pi}{11} \right)}\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{18}{11}} & \htmlTitle{\theta_{3}}{\frac{4}{11}} & \htmlTitle{\theta_{4}}{\frac{2}{11}} & \htmlTitle{\theta_{5}}{\frac{12}{11}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllll} \htmlTitle{S_{1; 1}}{1} & & & & \\ \htmlTitle{S_{2; 1}}{-\zeta_{88}^{36} + \zeta_{88}^{32} - \zeta_{88}^{28} + \zeta_{88}^{24} - \zeta_{88}^{20} + \zeta_{88}^{16} - \zeta_{88}^{12} + \zeta_{88}^{8} + 1} & \htmlTitle{S_{2; 2}}{\zeta_{88}^{36} + \zeta_{88}^{28} - \zeta_{88}^{24} + \zeta_{88}^{20} - \zeta_{88}^{16} - \zeta_{88}^{8} - 1} & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{88}^{36} + \zeta_{88}^{8} + 1} & \htmlTitle{S_{3; 2}}{-\zeta_{88}^{36} - \zeta_{88}^{28} + \zeta_{88}^{16} + \zeta_{88}^{8} + 1} & \htmlTitle{S_{3; 3}}{-\zeta_{88}^{36} + \zeta_{88}^{32} - \zeta_{88}^{28} + \zeta_{88}^{24} - \zeta_{88}^{20} + \zeta_{88}^{16} - \zeta_{88}^{12} + \zeta_{88}^{8} + 1} & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{88}^{36} - \zeta_{88}^{28} + \zeta_{88}^{24} - \zeta_{88}^{20} + \zeta_{88}^{16} + \zeta_{88}^{8} + 1} & \htmlTitle{S_{4; 2}}{\zeta_{88}^{36} - \zeta_{88}^{8} - 1} & \htmlTitle{S_{4; 3}}{-1} & \htmlTitle{S_{4; 4}}{-\zeta_{88}^{36} - \zeta_{88}^{28} + \zeta_{88}^{16} + \zeta_{88}^{8} + 1} & \\ \htmlTitle{S_{5; 1}}{-\zeta_{88}^{36} - \zeta_{88}^{28} + \zeta_{88}^{16} + \zeta_{88}^{8} + 1} & \htmlTitle{S_{5; 2}}{1} & \htmlTitle{S_{5; 3}}{\zeta_{88}^{36} + \zeta_{88}^{28} - \zeta_{88}^{24} + \zeta_{88}^{20} - \zeta_{88}^{16} - \zeta_{88}^{8} - 1} & \htmlTitle{S_{5; 4}}{\zeta_{88}^{36} - \zeta_{88}^{32} + \zeta_{88}^{28} - \zeta_{88}^{24} + \zeta_{88}^{20} - \zeta_{88}^{16} + \zeta_{88}^{12} - \zeta_{88}^{8} - 1} & \htmlTitle{S_{5; 5}}{-\zeta_{88}^{36} + \zeta_{88}^{8} + 1}\end{array}\right) \]
Central Charge
\[c = \frac{104}{11} \]