Fusion Ring
\[ \begin{array}{lllll} \htmlTitle{1\otimes 1}{1} & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5} & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{5 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5} & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{3 \oplus 4} & \htmlTitle{5\otimes 4}{3 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 2} \\ \end{array} \]
Frobenius-Perron Dimensions
| Simple | Numeric | Symbolic |
|---|---|---|
| \( 1\) | \(1.000\) | \( 1 \) |
| \( 2\) | \(1.000\) | \( 1 \) |
| \( 3\) | \(1.732\) | \( \sqrt{3} \) |
| \( 4\) | \(1.732\) | \( \sqrt{3} \) |
| \( 5\) | \(2.000\) | \( 2 \) |
| \( D^2\) | 12.000 | \(12\) |
Modular Data
Twist Factors
\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{1}{4}} & \htmlTitle{\theta_{4}}{\frac{5}{4}} & \htmlTitle{\theta_{5}}{\frac{2}{3}} \end{pmatrix} \]
S Matrix
\[ \left(\begin{array}{lllll} \htmlTitle{S_{1; 1}}{1} & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \htmlTitle{S_{3; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{3; 3}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 3}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 4}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{0} & \htmlTitle{S_{5; 4}}{0} & \htmlTitle{S_{5; 5}}{-2}\end{array}\right) \]
Central Charge
\[c = 2 \]