Fusion Ring
\[ \begin{array}{llllllll} \htmlTitle{1\otimes 1}{1} & & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{3} & \htmlTitle{3\otimes 3}{1 \oplus 4 \oplus 2} & & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{4} & \htmlTitle{4\otimes 3}{3 \oplus 5} & \htmlTitle{4\otimes 4}{1 \oplus 6 \oplus 2} & & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{4 \oplus 6} & \htmlTitle{5\otimes 4}{3 \oplus 6} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 2} & & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{6} & \htmlTitle{6\otimes 3}{5 \oplus 6} & \htmlTitle{6\otimes 4}{4 \oplus 5} & \htmlTitle{6\otimes 5}{3 \oplus 4} & \htmlTitle{6\otimes 6}{1 \oplus 3 \oplus 2} & & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{8} & \htmlTitle{7\otimes 3}{7 \oplus 8} & \htmlTitle{7\otimes 4}{7 \oplus 8} & \htmlTitle{7\otimes 5}{7 \oplus 8} & \htmlTitle{7\otimes 6}{7 \oplus 8} & \htmlTitle{7\otimes 7}{1 \oplus 3 \oplus 4 \oplus 5 \oplus 6} & \\ \htmlTitle{8\otimes 1}{8} & \htmlTitle{8\otimes 2}{7} & \htmlTitle{8\otimes 3}{7 \oplus 8} & \htmlTitle{8\otimes 4}{7 \oplus 8} & \htmlTitle{8\otimes 5}{7 \oplus 8} & \htmlTitle{8\otimes 6}{7 \oplus 8} & \htmlTitle{8\otimes 7}{3 \oplus 4 \oplus 5 \oplus 6 \oplus 2} & \htmlTitle{8\otimes 8}{1 \oplus 3 \oplus 4 \oplus 5 \oplus 6} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(2.000\) | \( 2 \) |
| \( 4\) | \(2.000\) | \( 2 \) |
| \( 5\) | \(2.000\) | \( 2 \) |
| \( 6\) | \(2.000\) | \( 2 \) |
| \( 7\) | \(3.000\) | \( 3 \) |
| \( 8\) | \(3.000\) | \( 3 \) |
| \( D^2\) | 36.000 | \(36\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{8}{9}} & \htmlTitle{\theta_{4}}{\frac{14}{9}} & \htmlTitle{\theta_{5}}{0} & \htmlTitle{\theta_{6}}{\frac{2}{9}} & \htmlTitle{\theta_{7}}{1} & \htmlTitle{\theta_{8}}{0} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{llllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & & \\ \htmlTitle{S_{3; 1}}{2} & \htmlTitle{S_{3; 2}}{2} & \htmlTitle{S_{3; 3}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4}} & & & & & \\ \htmlTitle{S_{4; 1}}{2} & \htmlTitle{S_{4; 2}}{2} & \htmlTitle{S_{4; 3}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{16}} & \htmlTitle{S_{4; 4}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & & & & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{-2} & \htmlTitle{S_{5; 4}}{-2} & \htmlTitle{S_{5; 5}}{4} & & & \\ \htmlTitle{S_{6; 1}}{2} & \htmlTitle{S_{6; 2}}{2} & \htmlTitle{S_{6; 3}}{2 \zeta_{72}^{20} - 2 \zeta_{72}^{8} - 2 \zeta_{72}^{4}} & \htmlTitle{S_{6; 4}}{-2 \zeta_{72}^{16} + 2 \zeta_{72}^{8} + 2 \zeta_{72}^{4}} & \htmlTitle{S_{6; 5}}{-2} & \htmlTitle{S_{6; 6}}{-2 \zeta_{72}^{20} + 2 \zeta_{72}^{16}} & & \\ \htmlTitle{S_{7; 1}}{3} & \htmlTitle{S_{7; 2}}{-3} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{0} & \htmlTitle{S_{7; 5}}{0} & \htmlTitle{S_{7; 6}}{0} & \htmlTitle{S_{7; 7}}{3} & \\ \htmlTitle{S_{8; 1}}{3} & \htmlTitle{S_{8; 2}}{-3} & \htmlTitle{S_{8; 3}}{0} & \htmlTitle{S_{8; 4}}{0} & \htmlTitle{S_{8; 5}}{0} & \htmlTitle{S_{8; 6}}{0} & \htmlTitle{S_{8; 7}}{-3} & \htmlTitle{S_{8; 8}}{3}\end{array}\right) \]
Central Charge
\[c = 8 \]