Fusion Ring
\[ \begin{array}{lllllll} \htmlTitle{1\otimes 1}{1} & & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5} & & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{6 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5} & & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{6} & \htmlTitle{5\otimes 3}{3 \oplus 7} & \htmlTitle{5\otimes 4}{7 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 6} & & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5} & \htmlTitle{6\otimes 3}{7 \oplus 4} & \htmlTitle{6\otimes 4}{3 \oplus 7} & \htmlTitle{6\otimes 5}{5 \oplus 6 \oplus 2} & \htmlTitle{6\otimes 6}{1 \oplus 5 \oplus 6} & \\ \htmlTitle{7\otimes 1}{7} & \htmlTitle{7\otimes 2}{7} & \htmlTitle{7\otimes 3}{5 \oplus 6} & \htmlTitle{7\otimes 4}{5 \oplus 6} & \htmlTitle{7\otimes 5}{3 \oplus 7 \oplus 4} & \htmlTitle{7\otimes 6}{3 \oplus 7 \oplus 4} & \htmlTitle{7\otimes 7}{1 \oplus 5 \oplus 6 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.848\) | \( \sqrt{\sqrt{2} + 2} \) |
| \( 4\) | \(1.848\) | \( \sqrt{\sqrt{2} + 2} \) |
| \( 5\) | \(2.414\) | \( 1 + \sqrt{2} \) |
| \( 6\) | \(2.414\) | \( 1 + \sqrt{2} \) |
| \( 7\) | \(2.613\) | \( \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2} \) |
| \( D^2\) | 27.314 | \(8 \sqrt{2} + 16\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{1} & \htmlTitle{\theta_{3}}{\frac{3}{16}} & \htmlTitle{\theta_{4}}{\frac{3}{16}} & \htmlTitle{\theta_{5}}{\frac{1}{2}} & \htmlTitle{\theta_{6}}{\frac{3}{2}} & \htmlTitle{\theta_{7}}{\frac{15}{16}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllllll} \htmlTitle{S_{1; 1}}{1} & & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{64}^{28} + \zeta_{64}^{4}} & \htmlTitle{S_{3; 2}}{\zeta_{64}^{28} - \zeta_{64}^{4}} & \htmlTitle{S_{3; 3}}{-\zeta_{64}^{28} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{4}} & & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{64}^{28} + \zeta_{64}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{64}^{28} - \zeta_{64}^{4}} & \htmlTitle{S_{4; 3}}{\zeta_{64}^{28} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{4}} & \htmlTitle{S_{4; 4}}{-\zeta_{64}^{28} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{4}} & & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{64}^{24} + \zeta_{64}^{8} + 1} & \htmlTitle{S_{5; 2}}{-\zeta_{64}^{24} + \zeta_{64}^{8} + 1} & \htmlTitle{S_{5; 3}}{-\zeta_{64}^{28} + \zeta_{64}^{4}} & \htmlTitle{S_{5; 4}}{-\zeta_{64}^{28} + \zeta_{64}^{4}} & \htmlTitle{S_{5; 5}}{-1} & & \\ \htmlTitle{S_{6; 1}}{-\zeta_{64}^{24} + \zeta_{64}^{8} + 1} & \htmlTitle{S_{6; 2}}{-\zeta_{64}^{24} + \zeta_{64}^{8} + 1} & \htmlTitle{S_{6; 3}}{\zeta_{64}^{28} - \zeta_{64}^{4}} & \htmlTitle{S_{6; 4}}{\zeta_{64}^{28} - \zeta_{64}^{4}} & \htmlTitle{S_{6; 5}}{-1} & \htmlTitle{S_{6; 6}}{-1} & \\ \htmlTitle{S_{7; 1}}{-\zeta_{64}^{28} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{4}} & \htmlTitle{S_{7; 2}}{\zeta_{64}^{28} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{4}} & \htmlTitle{S_{7; 3}}{0} & \htmlTitle{S_{7; 4}}{0} & \htmlTitle{S_{7; 5}}{\zeta_{64}^{28} + \zeta_{64}^{20} - \zeta_{64}^{12} - \zeta_{64}^{4}} & \htmlTitle{S_{7; 6}}{-\zeta_{64}^{28} - \zeta_{64}^{20} + \zeta_{64}^{12} + \zeta_{64}^{4}} & \htmlTitle{S_{7; 7}}{0}\end{array}\right) \]
Central Charge
\[c = \frac{9}{4} \]