List of Small Multiplicity-Free Fusion Rings

The list below contains all multiplicity free fusion rings up to 9 particles. Clicking on a name will redirect you to the page of the respective fusion ring. For more information on the formal names \(\text{FR}_m^{r,n}\) see the page on formal fusion ring names. Here the categorifiability is considered over the complex field. For the last 5 columns a value of T indicates that there exists at least 1 way to categorify the fusion ring to a category with the respective structure. There can be multiple categories stemming from the same fusion ring with multiple (possibly disjunct) properties. The abreviations FC, PFC, UFC, BFC, MFC respectively stand for Fusion Category, Pivotal Fusion Category, Unitary Fusion Category, Braided Fusion Category, Modular Fusion Category.

Name Rank \(\mathcal{D}_{FP}^2\) FC PFC UFC BFC MFC
\(\text{FR}^{1,0}_{1} :\ \text{Trivial}\) 1 1. T T T T T
\(\text{FR}^{2,0}_{1} :\ \bbz_2\) 2 2. T T T T T
\(\text{FR}^{2,0}_{2} :\ \text{Fib}\) 2 3.61803 T T T T T
\(\text{FR}^{3,0}_{1} :\ \text{Ising}\) 3 4. T T T T T
\(\text{FR}^{3,0}_{2} :\ \left.\text{Rep(}D_3\right)\) 3 6. T T T T F
\(\text{FR}^{3,0}_{3} :\ \text{PSU}(2)_5\) 3 9.2959 T T T T T
\(\text{FR}^{3,2}_{1} :\ \bbz_3\) 3 3. T T T T T
\(\text{FR}^{4,0}_{1} :\ \bbz_2\times \bbz_2\) 4 4. T T T T T
\(\text{FR}^{4,0}_{2} :\ \text{SU(2})_3\) 4 7.23607 T T T T T
\(\text{FR}^{4,0}_{3} :\ \left.\text{Rep(}D_5\right)\) 4 10. T T T T F
\(\text{FR}^{4,0}_{4} :\ \text{PSU(2})_6\) 4 13.6569 T T T T F
\(\text{FR}^{4,0}_{5} :\ \text{Fib}\times \text{Fib}\) 4 13.0902 T T T T T
\(\text{FR}^{4,0}_{6} :\ \text{PSU(2})_7\) 4 19.2344 T T T T T
\(\text{FR}^{4,2}_{1} :\ \bbz_4\) 4 4. T T T T T
\(\text{FR}^{4,2}_{2} :\ \text{TY}(\bbz_3)\) 4 6. T T T F F
\(\text{FR}^{4,2}_{3} :\ \left.\text{Fib(}\bbz_3\right)\) 4 8.30278 F F F F F
\(\text{FR}^{4,2}_{4} :\ \text{Pseudo PSU(2})_6\) 4 13.6569 T T T F F
\(\text{FR}^{5,0}_{1} :\ \left.\text{Rep(}D_4\right)\) 5 8. T T T T F
\(\text{FR}^{5,0}_{2} :\ \text{Fib}\left(\bbz_2\times \bbz_2\right)\) 5 10.5616 F F F F F
\(\text{FR}^{5,0}_{3} :\ \text{SU(2})_4\) 5 12. T T T T T
\(\text{FR}^{5,0}_{4} :\ \left.\text{Rep(}D_7\right)\) 5 14. T T T T F
\(\text{FR}^{5,0}_{5}\) 5 16.6056 F F F F F
\(\text{FR}^{5,0}_{6} :\ \left.\text{Rep(}S_4\right)\) 5 24. T T T T F
\(\text{FR}^{5,0}_{7} :\ \text{PSU(2})_8\) 5 26.1803 T T T T F
\(\text{FR}^{5,0}_{8}\) 5 31.0923 F F F F F
\(\text{FR}^{5,0}_{9}\) 5 30.1421 F F F F F
\(\text{FR}^{5,0}_{10} :\ \text{PSU(2})_9\) 5 34.6464 T T T T T
\(\text{FR}^{5,2}_{1} :\ \left.\text{TY(}\bbz_4\right)\) 5 8. T T T F F
\(\text{FR}^{5,2}_{2} :\ \text{Fib}(\bbz_4)\) 5 10.5616 F F F F F
\(\text{FR}^{5,2}_{3} :\ \text{Pseudo SU}(2)_4\) 5 12. T T T F F
\(\text{FR}^{5,2}_{4} :\ \text{Pseudo Rep}(S_4)\) 5 24. T T T F F
\(\text{FR}^{5,2}_{5}\) 5 31.0923 F F F F F
\(\text{FR}^{5,4}_{1} :\ \bbz_5\) 5 5. T T T T T
\(\text{FR}^{6,0}_{1} :\ \bbz_2 \times \text{Ising}\) 6 8. T T T T T
\(\text{FR}^{6,0}_{2} :\ \bbz_2 \times \text{Rep}(D_3)\) 6 12. T T T T F
\(\text{FR}^{6,0}_{3}\) 6 18.9282 F F F F F
\(\text{FR}^{6,0}_{4} :\ \text{TriCritIsing}\) 6 14.4721 T T T T T
\(\text{FR}^{6,0}_{5} :\ \text{Fib}\times \text{Rep}(D_3)\) 6 21.7082 T T T T F
\(\text{FR}^{6,0}_{6} :\ \text{SU(2})_5\) 6 18.5918 T T T T T
\(\text{FR}^{6,0}_{7}:\ \text{Rep}(\mathbb{Z}_3\rtimes D_3)\) 6 18. T T T T F
\(\text{FR}^{6,0}_{8}:\ \text{Rep}(D_9)\) 6 18. T T T T F
\(\text{FR}^{6,0}_{9}:\ \text{SO}(5)_2\) 6 20. T T T T T
\(\text{FR}^{6,0}_{10}\) 6 25.5826 F F F F F
\(\text{FR}^{6,0}_{11}\) 6 28.3923 F F F F F
\(\text{FR}^{6,0}_{12}\) 6 28.3923 F F F F F
\(\text{FR}^{6,0}_{13}\) 6 33.798 F F F F F
\(\text{FR}^{6,0}_{14} :\ \text{Fib}\times \text{ExtRep}(D_3)\) 6 33.6329 T T T T T
\(\text{FR}^{6,0}_{15}\) 6 36.7792 F F F F F
\(\text{FR}^{6,0}_{16} :\ \text{PSU}(2)_{10}\) 6 44.7846 T T T T F
\(\text{FR}^{6,0}_{17}\) 6 55.1442 F F F F F
\(\text{FR}^{6,0}_{18} :\ \text{PSU}(2)_{11}\) 6 56.7468 T T T T T
\(\text{FR}^{6,0}_{19}\) 6 63.1472 F F F F F
\(\text{FR}^{6,0}_{20}\) 6 63.1472 F F F F F
\(\text{FR}^{6,2}_{1} :\ D_3\) 6 6. T T T F F
\(\text{FR}^{6,2}_{2}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_4]_{\mathbf{1}|0}^{\text{Id}}\) 6 8. T T T F F
\(\text{FR}^{6,2}_{3}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_2\times \mathbb{Z}_2]_{\mathbf{3}|0}^{\text{Id}}\) 6 8. T T T T F
\(\text{FR}^{6,2}_{4} :\ \left.\text{Rep(}\text{Dic}_{12}\right)\) 6 12. T T T T F
\(\text{FR}^{6,2}_{5}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_4]_{\mathbf{1}|1}^{\text{Id}}\) 6 18.9282 F F F F F
\(\text{FR}^{6,2}_{6}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_2 \times \mathbb{Z}_2]_{\mathbf{3}|1}^{\text{Id}}\) 6 18.9282 F F F F F
\(\text{FR}^{6,2}_{7} :\ \text{Pseudo SO(5})_2\) 6 20. T T T F F
\(\text{FR}^{6,2}_{8} :\ \left.\text{HI(}\bbz_3\right)\) 6 35.725 T T T F F
\(\text{FR}^{6,2}_{9}\) 6 33.798 F F F F F
\(\text{FR}^{6,2}_{10}\) 6 36.7792 F F F F F
\(\text{FR}^{6,2}_{11}\) 6 55.1442 F F F F F
\(\text{FR}^{6,4}_{1} :\ \bbz_6\) 6 6. T T T T T
\(\text{FR}^{6,4}_{2} :\ \text{MR}_6\) 6 8. T T T F F
\(\text{FR}^{6,4}_{3} :\ \left.\text{TY(}\bbz_5\right)\) 6 10. T T T F F
\(\text{FR}^{6,4}_{4}: [\mathbb{Z}_5 \trianglelefteq \mathbb{Z}_5]_{\mathbf{1}|1}^{\text{Id}}\) 6 12.7913 F F F F F
\(\text{FR}^{6,4}_{5} :\ \text{Fib}\times \bbz_3\) 6 10.8541 T T T T T
\(\text{FR}^{6,4}_{6}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_4]_{\mathbf{3}|1}^{\text{Id}}\) 6 18.9282 F F F F F
\(\text{FR}^{6,4}_{7}\) 6 20.4853 F F F F F
\(\text{FR}^{6,4}_{8}: [I \trianglelefteq \mathbb{Z}_3]_{\mathbf{1}|1}^{\text{Id}}\) 6 35.725 F F F F F
\(\text{FR}^{7,0}_{1}: \mathrm{Adj}(\mathrm{SO}(16)_2)\) 7 16. T       F
\(\text{FR}^{7,0}_{2}\) 7 21.1231 F F F F F
\(\text{FR}^{7,0}_{3}\) 7 27.1537 F F F F F
\(\text{FR}^{7,0}_{4}\) 7 28.9443 F F F F F
\(\text{FR}^{7,0}_{5}\) 7 29.46 F F F F F
\(\text{FR}^{7,0}_{6}: \mathrm{Adj}(\mathrm{SO}(11)_2)\) 7 22. T       F
\(\text{FR}^{7,0}_{7} :\ \text{SU}(2)_6\) 7 27.3137 T T T T T
\(\text{FR}^{7,0}_{8}: \text{SO}(7)_2\) 7 28. T T T T T
\(\text{FR}^{7,0}_{9}\) 7 34.3852 F F F F F
\(\text{FR}^{7,0}_{10}\) 7 43.3137 F F F F F
\(\text{FR}^{7,0}_{11}\) 7 36.9706 F F F F F
\(\text{FR}^{7,0}_{12}\) 7 42. F F F F F
\(\text{FR}^{7,0}_{13}\) 7 52.93 F F F F F
\(\text{FR}^{7,0}_{14} :\ \text{PSU}(2)_{12}\) 7 70.6848 T T T T F
\(\text{FR}^{7,0}_{15}\) 7 81.6695 F F F F F
\(\text{FR}^{7,0}_{16}\) 7 87.0937 F F F F F
\(\text{FR}^{7,0}_{17} :\ \text{PSU}(2)_{13}\) 7 86.7508 T T T T T
\(\text{FR}^{7,0}_{18}\) 7 118.138 F F F F F
\(\text{FR}^{7,2}_{1} :\ \left.\text{TY(}D_3\right)\) 7 12. F F F F F
\(\text{FR}^{7,2}_{2}: [D_3 \trianglelefteq D_3]_{\mathbf{1}|1}^{\text{Id}}\) 7 15. F F F F F
\(\text{FR}^{7,2}_{3}\) 7 16. T       F
\(\text{FR}^{7,2}_{4}: \text{Rep}(SD_{16})\) 7 16. T T T T F
\(\text{FR}^{7,2}_{5}\) 7 21.1231 F F F F F
\(\text{FR}^{7,2}_{6}\) 7 27.1537 F F F F F
\(\text{FR}^{7,2}_{7}\) 7 27.1537 F F F F F
\(\text{FR}^{7,2}_{8}\) 7 28.9443 F F F F F
\(\text{FR}^{7,2}_{9}\) 7 28.9443 F F F F F
\(\text{FR}^{7,2}_{10}\) 7 29.46 F F F F F
\(\text{FR}^{7,2}_{11}\) 7 27.3137 F F F F F
\(\text{FR}^{7,2}_{12}\) 7 28. T       F
\(\text{FR}^{7,2}_{13}\) 7 43.3137 F F F F F
\(\text{FR}^{7,2}_{14}\) 7 52.93 F F F F F
\(\text{FR}^{7,2}_{15}\) 7 71.0118 F F F F F
\(\text{FR}^{7,2}_{16}\) 7 81.6695 F F F F F
\(\text{FR}^{7,2}_{17}\) 7 87.0937 F F F F F
\(\text{FR}^{7,4}_{1} :\ \left.\text{TY(}\bbz_2\times \bbz_3\right)\) 7 12. T T T F F
\(\text{FR}^{7,4}_{2}: [\mathbb{Z}_6 \trianglelefteq \mathbb{Z}_6]_{\mathbf{1}|1}^{\text{Id}}\) 7 15. F F F F F
\(\text{FR}^{7,4}_{3}\) 7 16. T       F
\(\text{FR}^{7,4}_{4}\) 7 27.1537 F F F F F
\(\text{FR}^{7,4}_{5}\) 7 28.9443 F F F F F
\(\text{FR}^{7,4}_{6}\) 7 57.2354 F F F F F
\(\text{FR}^{7,4}_{7}\) 7 71.0118 F F F F F
\(\text{FR}^{7,6}_{1} :\ \bbz_7\) 7 7. T T T T T
\(\text{FR}^{8,0}_{1} :\ \bbz_2\times \bbz_2\times \bbz_2\) 8 8. T T T T T
\(\text{FR}^{8,0}_{2} :\ \text{Fib} \times \bbz_2\times \bbz_2\) 8 14.4721 T T T T T
\(\text{FR}^{8,0}_{3} :\ \text{Rep}(D_5)\times \bbz_2\) 8 20. T T T T F
\(\text{FR}^{8,0}_{4} :\text{One-half SO}(12)_2\) 8 24. T T T T F
\(\text{FR}^{8,0}_{5} :\ \text{PSU}(2)_6\times \bbz_2\) 8 27.3137 T T T T F
\(\text{FR}^{8,0}_{6}\) 8 30. F F F F F
\(\text{FR}^{8,0}_{7} :\ \text{Fib} \times \text{Fib} \times \bbz_2\) 8 26.1803 T T T T T
\(\text{FR}^{8,0}_{8}\) 8 38.583 F F F F F
\(\text{FR}^{8,0}_{9}: \mathrm{Adj}(\mathrm{SO}(13)_2)\) 8 26.         F
\(\text{FR}^{8,0}_{10}\) 8 42.4585 F F F F F
\(\text{FR}^{8,0}_{11} :\ \text{Fib} \times \text{Rep}(D_5)\) 8 36.1803 T T T T F
\(\text{FR}^{8,0}_{12}\) 8 47.6333 F F F F F
\(\text{FR}^{8,0}_{13}: \text{SO}(9)_2\) 8 36. T T T T T
\(\text{FR}^{8,0}_{14}:\ \text{Rep}(D(D_3))\) 8 36. T T T T T
\(\text{FR}^{8,0}_{15} :\ \text{SU}(2)_7\) 8 38.4688 T T T T T
\(\text{FR}^{8,0}_{16} :\ \text{Fib} \times \text{PSU}(2)_6\) 8 49.411 T T T T F
\(\text{FR}^{8,0}_{17}\) 8 43.0828 F F F F F
\(\text{FR}^{8,0}_{18}\) 8 43.0828 F F F F F
\(\text{FR}^{8,0}_{19}\) 8 68.6639 F F F F F
\(\text{FR}^{8,0}_{20}\) 8 52.6491 F F F F F
\(\text{FR}^{8,0}_{21}\) 8 52.6491 F F F F F
\(\text{FR}^{8,0}_{22} :\ \text{Fib} \times \text{Fib} \times \text{Fib}\) 8 47.3607 T T T T T
\(\text{FR}^{8,0}_{23} :\ \left.\text{HI}(\bbz_2\times \bbz_2\right)\) 8 75.7771         F
\(\text{FR}^{8,0}_{24}\) 8 48.0685 F F F F F
\(\text{FR}^{8,0}_{25}\) 8 58.1168 F F F F F
\(\text{FR}^{8,0}_{26}\) 8 58.1168 F F F F F
\(\text{FR}^{8,0}_{27} :\ \text{Fib} \times \text{PSU}(2)_7\) 8 69.5908 T T T T T
\(\text{FR}^{8,0}_{28}\) 8 72.         F
\(\text{FR}^{8,0}_{29}\) 8 72.         F
\(\text{FR}^{8,0}_{30}\) 8 78.1637 F F F F F
\(\text{FR}^{8,0}_{31} :\ \text{PSU}(2)_{14}\) 8 105.097 T T T T F
\(\text{FR}^{8,0}_{32}\) 8 126.522 F F F F F
\(\text{FR}^{8,0}_{33}\) 8 126.522 F F F F F
\(\text{FR}^{8,0}_{34}\) 8 128.169 F F F F F
\(\text{FR}^{8,0}_{35}\) 8 122.573 F F F F F
\(\text{FR}^{8,0}_{36} :\ \text{PSU}(2)_{15}\) 8 125.874 T T T T T
\(\text{FR}^{8,0}_{37}\) 8 140.586 F F F F F
\(\text{FR}^{8,0}_{38}\) 8 201.126 F F F F F
\(\text{FR}^{8,2}_{1} :\ D_4\) 8 8. T T T F F
\(\text{FR}^{8,2}_{2}: [\mathbb{Z}_3 \trianglelefteq D_3]_{\mathbf{1}|0}^{\text{Id}}\) 8 12. T       F
\(\text{FR}^{8,2}_{3}\) 8 16.6056         F
\(\text{FR}^{8,2}_{4}: [\mathbb{Z}_3 \trianglelefteq D_3]_{\mathbf{1}|1}^{\text{Id}}\) 8 24. F F F F F
\(\text{FR}^{8,2}_{5}: \text{Rep}(Dic_5)\) 8 20. T T T T F
\(\text{FR}^{8,2}_{6}\) 8 20.         F
\(\text{FR}^{8,2}_{7}\) 8 24.         F
\(\text{FR}^{8,2}_{8}\) 8 27.3137         F
\(\text{FR}^{8,2}_{9}:\) 8 27.3137         F
\(\text{FR}^{8,2}_{10}\) 8 27.3137         F
\(\text{FR}^{8,2}_{11}\) 8 26.1803         F
\(\text{FR}^{8,2}_{12}\) 8 38.583 F F F F F
\(\text{FR}^{8,2}_{13}\) 8 42.4585 F F F F F
\(\text{FR}^{8,2}_{14}\) 8 36.         F
\(\text{FR}^{8,2}_{15}\) 8 36.         F
\(\text{FR}^{8,2}_{16}\) 8 68.6639 F F F F F
\(\text{FR}^{8,2}_{17}\) 8 52.6491 F F F F F
\(\text{FR}^{8,2}_{18}\) 8 52.6491 F F F F F
\(\text{FR}^{8,2}_{19} :\ \left.\text{HI}(\bbz_4\right)\) 8 75.7771         F
\(\text{FR}^{8,2}_{20}: [I \trianglelefteq \mathbb{Z}_2\times \mathbb{Z}_2]_{\mathbf{1}|1}^{( \mathbf{3} \ \mathbf{4} )}\) 8 75.7771         F
\(\text{FR}^{8,2}_{21}\) 8 48.0685 F F F F F
\(\text{FR}^{8,2}_{22}\) 8 58.1168 F F F F F
\(\text{FR}^{8,2}_{23}\) 8 58.1168 F F F F F
\(\text{FR}^{8,2}_{24}\) 8 72.         F
\(\text{FR}^{8,2}_{25}\) 8 72.         F
\(\text{FR}^{8,2}_{26}\) 8 126.522 F F F F F
\(\text{FR}^{8,2}_{27}\) 8 126.522 F F F F F
\(\text{FR}^{8,2}_{28}\) 8 128.169 F F F F F
\(\text{FR}^{8,2}_{29}\) 8 122.573         F
\(\text{FR}^{8,2}_{30}\) 8 140.586         F
\(\text{FR}^{8,4}_{1} :\ \bbz_2\times \bbz_4\) 8 8. T T T T T
\(\text{FR}^{8,4}_{2}: [\mathbb{Z}_3 \trianglelefteq D_3]_{\mathbf{2}|0}^{\text{Id}}\) 8 12. F F F F F
\(\text{FR}^{8,4}_{3} :\ \bbz_2 \times \text{TY}(\bbz_3)\) 8 12. T T T F F
\(\text{FR}^{8,4}_{4} :\ \left.\bbz_2 \times \text{Fib}(\bbz_3\right)\) 8 16.6056 F F F F F
\(\text{FR}^{8,4}_{5}: [\mathbb{Z}_3 \trianglelefteq D_3]_{\mathbf{2}|1}^{\text{Id}}\) 8 24. F F F F F
\(\text{FR}^{8,4}_{6}: [\mathbb{Z}_3 \trianglelefteq \mathbb{Z}_6]_{\mathbf{1}|1}^{\text{Id}}\) 8 24.         F
\(\text{FR}^{8,4}_{7} :\ \text{Fib} \times \bbz_4\) 8 14.4721 T T T T T
\(\text{FR}^{8,4}_{8}\) 8 20.         F
\(\text{FR}^{8,4}_{9} :\ \text{Fib} \times \text{TY}(\bbz_3)\) 8 21.7082 T T T F F
\(\text{FR}^{8,4}_{10} :\ \left.\text{Fib} \times \text{Fib}(\bbz_3\right)\) 8 30.0397 F F F F F
\(\text{FR}^{8,4}_{11}\) 8 27.3137         F
\(\text{FR}^{8,4}_{12}\) 8 27.3137         F
\(\text{FR}^{8,4}_{13} :\ \left.\bbz_2 \times (\text{Pseudo PSU}(2)_6\right)\) 8 27.3137 T T T F F
\(\text{FR}^{8,4}_{14}\) 8 47.6333 F F F F F
\(\text{FR}^{8,4}_{15} :\ \left.\text{Fib} \times (\text{Pseudo PSU}(2)_6\right)\) 8 49.411 T T T F F
\(\text{FR}^{8,4}_{16}: [I \trianglelefteq \mathbb{Z}_4]_{\mathbf{1}|1}^{\text{Id}}\) 8 75.7771         F
\(\text{FR}^{8,4}_{17}: [I \trianglelefteq \mathbb{Z}_2\times \mathbb{Z}_2]_{\mathbf{2}|1}^{\text{Id}}\) 8 75.7771         F
\(\text{FR}^{8,4}_{18}\) 8 78.1637 F F F F F
\(\text{FR}^{8,6}_{1} :\ \text{Q}\) 8 8. T T T F F
\(\text{FR}^{8,6}_{2} :\ \bbz_8\) 8 8. T T T T T
\(\text{FR}^{8,6}_{3} :\ \left.\text{TY(}\bbz_7\right)\) 8 14. T T T F F
\(\text{FR}^{8,6}_{4}: [\mathbb{Z}_7 \trianglelefteq \mathbb{Z}_7]_{\mathbf{1}|1}^{\text{Id}}\) 8 17.1926 F F F F F
\(\text{FR}^{8,6}_{5}: [\mathbb{Z}_3 \trianglelefteq \mathbb{Z}_6]_{\mathbf{2}|0}^{\text{Id}}\) 8 12.         F
\(\text{FR}^{8,6}_{6}:[\mathbb{Z}_3 \trianglelefteq \mathbb{Z}_6]_{\mathbf{2}|1}^{\text{Id}}\) 8 24.         F
\(\text{FR}^{8,6}_{7}\) 8 27.3137         F
\(\text{FR}^{8,6}_{8}\) 8 27.3137 F F F F F
\(\text{FR}^{8,6}_{9}: [I \trianglelefteq \mathbb{Z}_4]_{\mathbf{2}|1}^{( \mathbf{3} \ \mathbf{4} )}\) 8 75.7771         F
\(\text{FR}^{8,6}_{10}: [I \trianglelefteq \mathbb{Z}_4]_{\mathbf{3}|1}^{\text{Id}}\) 8 75.7771         F
\(\text{FR}^{9,0}_{1} :\ \left.\text{TY(}\bbz_2\times \bbz_2\times \bbz_2\right)\) 9 16. T T T T F
\(\text{FR}^{9,0}_{2}: [(\mathbb{Z}_2)^{\times 3} \trianglelefteq (\mathbb{Z}_2)^{\times 3}]_{\mathbf{1}|1}^{\text{Id}}\) 9 19.3723 F F F F F
\(\text{FR}^{9,0}_{3} :\ \text{Ising}\times \text{Ising}\) 9 16. T T T T T
\(\text{FR}^{9,0}_{4} :\ \left.\text{Ising} \times \text{Rep}(D_3\right)\) 9 24. T T T T F
\(\text{FR}^{9,0}_{5}: \mathrm{Adj}(\mathrm{SO}(24)_2)\) 9 24.         F
\(\text{FR}^{9,0}_{6} :\ \text{Rep}(D_3)\times \text{Rep}(D_3)\) 9 36. T T T T F
\(\text{FR}^{9,0}_{7}:\text{One-half SO}(16)_2\) 9 32. T T T T F
\(\text{FR}^{9,0}_{8}\) 9 38.7446 F F F F F
\(\text{FR}^{9,0}_{9}\) 9 37.8564         F
\(\text{FR}^{9,0}_{10}\) 9 48.         F
\(\text{FR}^{9,0}_{11}\) 9 37.8564 F F F F F
\(\text{FR}^{9,0}_{12}: \mathrm{Adj}(\mathrm{SO}(15)_2)\) 9 30.         F
\(\text{FR}^{9,0}_{13}\) 9 49.551 F F F F F
\(\text{FR}^{9,0}_{14} :\ \text{Ising} \times \text{PSU}(2)_5\) 9 37.1836 T T T T T
\(\text{FR}^{9,0}_{15}\) 9 60.         F
\(\text{FR}^{9,0}_{16}\) 9 58.7386 F F F F F
\(\text{FR}^{9,0}_{17}\) 9 58.2213 F F F F F
\(\text{FR}^{9,0}_{18}\) 9 58.2213 F F F F F
\(\text{FR}^{9,0}_{19}: \text{SO}(11)_2\) 9 44. T T T T T
\(\text{FR}^{9,0}_{20} :\ \text{Rep(}D_3 \times \text{PSU}(2)_5\) 9 55.7754 T T T T F
\(\text{FR}^{9,0}_{21}\) 9 51.7082 F F F F F
\(\text{FR}^{9,0}_{22}: \text{Rep}(S_3 \wr S_2)\) 9 72. T T T T F
\(\text{FR}^{9,0}_{23}\) 9 74.3672         F
\(\text{FR}^{9,0}_{24}\) 9 61.8564 F F F F F
\(\text{FR}^{9,0}_{25}\) 9 48. F F F F F
\(\text{FR}^{9,0}_{26}\) 9 87.1918         F
\(\text{FR}^{9,0}_{27} :\ \text{SU}(2)_8\) 9 52.3607 T T T T T
\(\text{FR}^{9,0}_{28}\) 9 60. F F F F F
\(\text{FR}^{9,0}_{29}\) 9 108.321 F F F F F
\(\text{FR}^{9,0}_{30}\) 9 70.2101 F F F F F
\(\text{FR}^{9,0}_{31}\) 9 88.108 F F F F F
\(\text{FR}^{9,0}_{32}\) 9 77.166 F F F F F
\(\text{FR}^{9,0}_{33}\) 9 77.166 F F F F F
\(\text{FR}^{9,0}_{34} :\ \text{PSU}(2)_5\times \text{PSU}(2)_5\) 9 86.4137 T T T T T
\(\text{FR}^{9,0}_{35}\) 9 134.976 F F F F F
\(\text{FR}^{9,0}_{36}\) 9 97.9329 F F F F F
\(\text{FR}^{9,0}_{37}\) 9 100.467 F F F F F
\(\text{FR}^{9,0}_{38}\) 9 108.99   F     F
\(\text{FR}^{9,0}_{39}\) 9 110.912 F F F F F
\(\text{FR}^{9,0}_{40}\) 9 130.596 F F F F F
\(\text{FR}^{9,0}_{41} :\ \text{PSU}(2)_{16}\) 9 149.235 T T T T F
\(\text{FR}^{9,0}_{42}\) 9 137.082 F F F F F
\(\text{FR}^{9,0}_{43}\) 9 179.586 F F F F F
\(\text{FR}^{9,0}_{44} :\ \text{PSU}(2)_{17}\) 9 175.333 T T T T T
\(\text{FR}^{9,0}_{45}\) 9 227.519 F F F F F
\(\text{FR}^{9,0}_{46}\) 9 318.114 F F F F F
\(\text{FR}^{9,2}_{1} :\ \left.\text{TY(}D_4\right)\) 9 16. F F F F F
\(\text{FR}^{9,2}_{2}: [D_4 \trianglelefteq D_4]_{\mathbf{1}|1}^{\text{Id}}\) 9 19.3723 F F F F F
\(\text{FR}^{9,2}_{3}\) 9 16.         F
\(\text{FR}^{9,2}_{4}\) 9 29.67         F
\(\text{FR}^{9,2}_{5}\) 9 24.         F
\(\text{FR}^{9,2}_{6}\) 9 24.         F
\(\text{FR}^{9,2}_{7}\) 9 24.         F
\(\text{FR}^{9,2}_{8}: \text{Rep}(Dic_3 \rtimes \mathbb{Z}_2)\) 9 24. T T T T F
\(\text{FR}^{9,2}_{9}\) 9 32.         F
\(\text{FR}^{9,2}_{10}\) 9 32.         F
\(\text{FR}^{9,2}_{11}\) 9 38.7446 F F F F F
\(\text{FR}^{9,2}_{12}\) 9 37.8564         F
\(\text{FR}^{9,2}_{13}\) 9 37.8564         F
\(\text{FR}^{9,2}_{14}\) 9 48.         F
\(\text{FR}^{9,2}_{15}\) 9 48.         F
\(\text{FR}^{9,2}_{16}\) 9 37.8564 F F F F F
\(\text{FR}^{9,2}_{17}\) 9 49.551 F F F F F
\(\text{FR}^{9,2}_{18}\) 9 49.551 F F F F F
\(\text{FR}^{9,2}_{19}\) 9 60.         F
\(\text{FR}^{9,2}_{20}\) 9 60.         F
\(\text{FR}^{9,2}_{21}\) 9 58.7386 F F F F F
\(\text{FR}^{9,2}_{22}\) 9 58.7386         F
\(\text{FR}^{9,2}_{23}\) 9 58.7386 F F F F F
\(\text{FR}^{9,2}_{24}\) 9 58.2213 F F F F F
\(\text{FR}^{9,2}_{25}\) 9 58.2213 F F F F F
\(\text{FR}^{9,2}_{26}\) 9 44.         F
\(\text{FR}^{9,2}_{27}\) 9 74.3672         F
\(\text{FR}^{9,2}_{28}\) 9 74.3672         F
\(\text{FR}^{9,2}_{29}\) 9 61.8564 F F F F F
\(\text{FR}^{9,2}_{30}\) 9 48. F F F F F
\(\text{FR}^{9,2}_{31}\) 9 87.1918         F
\(\text{FR}^{9,2}_{32}\) 9 60.         F
\(\text{FR}^{9,2}_{33}\) 9 60. F F F F F
\(\text{FR}^{9,2}_{34}\) 9 77.166 F F F F F
\(\text{FR}^{9,2}_{35}\) 9 77.166 F F F F F
\(\text{FR}^{9,2}_{36}\) 9 134.976         F
\(\text{FR}^{9,2}_{37}\) 9 134.976         F
\(\text{FR}^{9,2}_{38}\) 9 100.467         F
\(\text{FR}^{9,2}_{39}\) 9 100.467 F F F F F
\(\text{FR}^{9,2}_{40}\) 9 130.596 F F F F F
\(\text{FR}^{9,2}_{41}\) 9 137.082         F
\(\text{FR}^{9,2}_{42}\) 9 137.082 F F F F F
\(\text{FR}^{9,2}_{43}\) 9 179.586 F F F F F
\(\text{FR}^{9,2}_{44}\) 9 227.519         F
\(\text{FR}^{9,2}_{45}\) 9 227.519 F F F F F
\(\text{FR}^{9,4}_{1} :\ \left.\text{TY}(\bbz_2\times \bbz_4\right)\) 9 16. T T T F F
\(\text{FR}^{9,4}_{2}: [\mathbb{Z}_2\times \mathbb{Z}_4 \trianglelefteq \mathbb{Z}_2\times \mathbb{Z}_4]_{\mathbf{1}|1}^{\text{Id}}\) 9 19.3723 F F F F F
\(\text{FR}^{9,4}_{3}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_6]_{\mathbf{1}|0}^{( \mathbf{2} \ \mathbf{3} )}\) 9 12. T       F
\(\text{FR}^{9,4}_{4}\) 9 16.         F
\(\text{FR}^{9,4}_{5}\) 9 16.         F
\(\text{FR}^{9,4}_{6}\) 9 29.67         F
\(\text{FR}^{9,4}_{7}\) 9 29.67 F F F F F
\(\text{FR}^{9,4}_{8}\) 9 24.         F
\(\text{FR}^{9,4}_{9}\) 9 24.         F
\(\text{FR}^{9,4}_{10}\) 9 24.         F
\(\text{FR}^{9,4}_{11}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_6]_{\mathbf{1}|1}^{( \mathbf{2} \ \mathbf{3} )}\) 9 44.054         F
\(\text{FR}^{9,4}_{12}\) 9 32.         F
\(\text{FR}^{9,4}_{13}\) 9 37.8564         F
\(\text{FR}^{9,4}_{14}\) 9 48.         F
\(\text{FR}^{9,4}_{15}\) 9 49.551 F F F F F
\(\text{FR}^{9,4}_{16}\) 9 60.         F
\(\text{FR}^{9,4}_{17}\) 9 58.7386         F
\(\text{FR}^{9,4}_{18}\) 9 58.7386 F F F F F
\(\text{FR}^{9,4}_{19}\) 9 74.3672         F
\(\text{FR}^{9,4}_{20}\) 9 48.         F
\(\text{FR}^{9,4}_{21}\) 9 48. F F F F F
\(\text{FR}^{9,4}_{22}\) 9 87.1918         F
\(\text{FR}^{9,4}_{23}\) 9 87.1918         F
\(\text{FR}^{9,4}_{24}\) 9 52.3607         F
\(\text{FR}^{9,4}_{25}\) 9 108.321 F F F F F
\(\text{FR}^{9,4}_{26}\) 9 77.166 F F F F F
\(\text{FR}^{9,4}_{27}\) 9 94.2873         F
\(\text{FR}^{9,4}_{28}\) 9 134.976 F F F F F
\(\text{FR}^{9,4}_{29}\) 9 134.976 F F F F F
\(\text{FR}^{9,4}_{30}\) 9 97.9329 F F F F F
\(\text{FR}^{9,4}_{31}\) 9 130.596         F
\(\text{FR}^{9,4}_{32}\) 9 130.596 F F F F F
\(\text{FR}^{9,4}_{33}\) 9 227.519         F
\(\text{FR}^{9,6}_{1} :\ \text{TY(Q)}\) 9 16. F F F F F
\(\text{FR}^{9,6}_{2} :\ \left.\text{TY(}\bbz_8\right)\) 9 16. T T T F F
\(\text{FR}^{9,6}_{3}:[\text{Q} \trianglelefteq \text{Q}]_{\mathbf{1}|1}^{\text{Id}}\) 9 19.3723 F F F F F
\(\text{FR}^{9,6}_{4}:[\mathbb{Z}_8 \trianglelefteq \mathbb{Z}_8]_{\mathbf{1}|1}^{\text{Id}}\) 9 19.3723 F F F F F
\(\text{FR}^{9,6}_{5} :\ \text{Ising}\times \bbz_3\) 9 12. T T T T T
\(\text{FR}^{9,6}_{6} :\ \text{Rep}(D_3)\times \bbz_3\) 9 18. T T T T F
\(\text{FR}^{9,6}_{7}\) 9 29.67 F F F F F
\(\text{FR}^{9,6}_{8}\) 9 28.3923 F F F F F
\(\text{FR}^{9,6}_{9}: [\mathbb{Z}_2 \trianglelefteq \mathbb{Z}_6]_{\mathbf{1}|1}^{\text{Id}}\) 9 44.054 F F F F F
\(\text{FR}^{9,6}_{10} :\ \text{PSU}(2)_5\times \bbz_3\) 9 27.8877 T T T T T
\(\text{FR}^{9,6}_{11}\) 9 55.1689 F F F F F
\(\text{FR}^{9,6}_{12}\) 9 94.2873 F F F F F
\(\text{FR}^{9,6}_{13}\) 9 134.976         F
\(\text{FR}^{9,6}_{14}\) 9 134.976 F F F F F
\(\text{FR}^{9,6}_{15}\) 9 127.95 F F F F F
\(\text{FR}^{9,6}_{16}\) 9 163.373 F F F F F
\(\text{FR}^{9,8}_{1} :\ \bbz_9\) 9 9. T T T T T
\(\text{FR}^{9,8}_{2} :\ \bbz_3\times \bbz_3\) 9 9. T T T T T

References