| Label |
Wt |
Deg |
$\mathrm{dim}_{\mathbb{R}}$ |
$\mathrm{G}^0$ |
Name |
$\mathrm{G}/\mathrm{G}^0$ |
$\mathrm{Pr}[t\!=\!0]$ |
$\mathrm{E}[a_1^2]$ |
$\mathrm{E}[a_1^4]$ |
$\mathrm{E}[a_1^6]$ |
$\mathrm{E}[a_1^8]$ |
$\mathrm{E}[a_1^{10}]$ |
$\mathrm{E}[a_1^{12}]$ |
$\mathrm{E}[a_2]$ |
$\mathrm{E}[a_2^2]$ |
$\mathrm{E}[a_2^3]$ |
$\mathrm{E}[a_2^4]$ |
$\mathrm{E}[a_2^5]$ |
$\mathrm{E}[a_2^6]$ |
$\mathrm{E}[a_3^2]$ |
$\mathrm{E}[a_3^4]$ |
$\mathrm{E}[a_3^6]$ |
Maximal |
Rational |
Diagonal |
| 1.4.F.4.1a |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$C_{4,1}$ |
$4$ |
$3/4$ |
$2$ |
$24$ |
$320$ |
$4480$ |
$64512$ |
$64512$ |
$1$ |
$5$ |
$22$ |
$115$ |
$606$ |
$3314$ |
|
|
|
|
✓ |
$[1, 2, 4, 9, 20, 16, 26, 77, 92, 52]$ |
| 1.4.F.4.2a |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$D_2$ |
$4$ |
$3/4$ |
$2$ |
$24$ |
$320$ |
$4480$ |
$64512$ |
$64512$ |
$1$ |
$6$ |
$22$ |
$118$ |
$606$ |
$3324$ |
|
|
|
|
✓ |
$[1, 2, 5, 10, 20, 20, 26, 79, 92, 60]$ |
| 1.4.F.4.2b |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$J(C_2)$ |
$4$ |
$3/4$ |
$2$ |
$24$ |
$320$ |
$4480$ |
$64512$ |
$64512$ |
$1$ |
$7$ |
$22$ |
$123$ |
$606$ |
$3346$ |
|
|
|
|
✓ |
$[1, 2, 6, 11, 20, 26, 26, 83, 92, 78]$ |
| 1.4.F.4.2c |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$D_{2,1}$ |
$4$ |
$3/4$ |
$2$ |
$24$ |
$320$ |
$4480$ |
$64512$ |
$64512$ |
$2$ |
$7$ |
$26$ |
$123$ |
$622$ |
$3346$ |
|
|
|
|
✓ |
$[1, 2, 4, 11, 20, 18, 26, 77, 92, 54]$ |
| 1.6.E.1.1a |
$1$ |
$6$ |
$9$ |
$\mathrm{SU}(2)^3$ |
$E$ |
$1$ |
$0$ |
$3$ |
$24$ |
$285$ |
$4242$ |
$73206$ |
$73206$ |
$3$ |
$12$ |
$60$ |
$363$ |
$2553$ |
$20109$ |
$13$ |
$728$ |
$73565$ |
|
✓ |
$[1, 3, 7, 4, 6, 22, 19, 27, 30, 10, 10, 45, 45, 88, 140, 57, 77, 118, 78, 20]$ |
| 1.6.H.4.1a |
$1$ |
$6$ |
$3$ |
$\mathrm{U}(1)^3$ |
$H_{act}$ |
$4$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11200$ |
$293202$ |
$293202$ |
$2$ |
$8$ |
$53$ |
$482$ |
$5117$ |
$58715$ |
$10$ |
$1254$ |
$277600$ |
|
✓ |
$[1, 2, 5, 4, 8, 38, 39, 54, 86, 35, 24, 188, 214, 474, 900, 424, 431, 990, 807, 218]$ |
| 1.6.J.6.1b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(J(E_3))$ |
$6$ |
$0$ |
$3$ |
$24$ |
$345$ |
$6832$ |
$159264$ |
$159264$ |
$2$ |
$8$ |
$45$ |
$348$ |
$3267$ |
$34220$ |
$10$ |
$846$ |
$154620$ |
|
✓ |
$[1, 3, 5, 5, 8, 26, 29, 36, 55, 25, 19, 102, 121, 248, 466, 224, 220, 489, 394, 110]$ |
| 1.6.J.8.3c |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(J(E_4))$ |
$8$ |
$0$ |
$3$ |
$24$ |
$340$ |
$6454$ |
$142674$ |
$142674$ |
$2$ |
$8$ |
$44$ |
$329$ |
$2962$ |
$29790$ |
$10$ |
$780$ |
$129960$ |
|
✓ |
$[1, 3, 5, 5, 8, 25, 27, 33, 47, 26, 18, 93, 108, 205, 368, 187, 174, 396, 315, 109]$ |
| 1.6.J.12.4d |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(J(E_6))$ |
$12$ |
$0$ |
$3$ |
$24$ |
$340$ |
$6440$ |
$140994$ |
$140994$ |
$2$ |
$8$ |
$44$ |
$328$ |
$2932$ |
$29110$ |
$10$ |
$774$ |
$124700$ |
|
✓ |
$[1, 3, 5, 5, 8, 25, 27, 32, 45, 23, 18, 92, 106, 195, 340, 161, 154, 336, 256, 85]$ |
| 1.6.L.12.4a |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_3),J(C_3))$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$56$ |
$507$ |
$5562$ |
$67046$ |
$9$ |
$1311$ |
$330040$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 71, 102, 56, 27, 213, 264, 583, 1150, 586, 607, 1422, 1209, 383]$ |
| 1.6.L.12.4b |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_3),D_3)$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$56$ |
$507$ |
$5562$ |
$67046$ |
$9$ |
$1311$ |
$330030$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 69, 100, 52, 27, 213, 260, 583, 1150, 580, 601, 1401, 1196, 355]$ |
| 1.6.L.12.4c |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{6,1},D_3)$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$57$ |
$511$ |
$5577$ |
$67096$ |
$9$ |
$1311$ |
$330030$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 71, 100, 52, 27, 213, 260, 583, 1150, 580, 607, 1401, 1196, 355]$ |
| 1.6.L.12.4d |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{6,1},C_{6,1})$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$57$ |
$511$ |
$5577$ |
$67096$ |
$9$ |
$1311$ |
$330040$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 69, 98, 48, 27, 213, 256, 583, 1150, 574, 601, 1382, 1185, 331]$ |
| 1.6.L.12.4e |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_3),D_{3,2})$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$56$ |
$507$ |
$5562$ |
$67046$ |
$10$ |
$1326$ |
$330250$ |
|
✓ |
$[1, 2, 6, 4, 9, 39, 42, 62, 98, 44, 26, 213, 250, 583, 1150, 569, 586, 1381, 1182, 331]$ |
| 1.6.L.12.4f |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{6,1},D_{3,2})$ |
$12$ |
$1/2$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$57$ |
$511$ |
$5577$ |
$67096$ |
$10$ |
$1326$ |
$330250$ |
|
✓ |
$[1, 2, 6, 4, 9, 39, 42, 64, 98, 44, 26, 213, 250, 583, 1150, 569, 592, 1381, 1182, 331]$ |
| 1.6.L.16.11d |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_4),D_4)$ |
$16$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11235$ |
$297612$ |
$297612$ |
$2$ |
$9$ |
$56$ |
$492$ |
$5172$ |
$59691$ |
$9$ |
$1242$ |
$284820$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 66, 89, 48, 25, 191, 227, 490, 942, 469, 490, 1113, 940, 285]$ |
| 1.6.L.16.11e |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_4),J(C_4))$ |
$16$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11235$ |
$297612$ |
$297612$ |
$2$ |
$9$ |
$56$ |
$492$ |
$5172$ |
$59691$ |
$9$ |
$1245$ |
$284880$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 66, 90, 49, 25, 191, 228, 490, 942, 471, 491, 1124, 947, 300]$ |
| 1.6.L.16.11f |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_4),D_{4,2})$ |
$16$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11235$ |
$297612$ |
$297612$ |
$2$ |
$9$ |
$56$ |
$492$ |
$5172$ |
$59691$ |
$10$ |
$1257$ |
$285040$ |
|
✓ |
$[1, 2, 6, 4, 9, 38, 40, 59, 87, 40, 24, 191, 217, 490, 942, 458, 475, 1093, 926, 261]$ |
| 1.6.L.24.12b |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(O_1)$ |
$24$ |
$0$ |
$3$ |
$24$ |
$350$ |
$7280$ |
$184338$ |
$184338$ |
$2$ |
$8$ |
$45$ |
$349$ |
$3372$ |
$37405$ |
$10$ |
$852$ |
$176980$ |
|
✓ |
$[1, 3, 5, 5, 8, 26, 29, 37, 57, 28, 20, 117, 140, 303, 588, 301, 303, 710, 606, 185]$ |
| 1.6.L.24.13b |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(J(T))$ |
$24$ |
$0$ |
$3$ |
$24$ |
$350$ |
$7280$ |
$184338$ |
$184338$ |
$2$ |
$8$ |
$44$ |
$344$ |
$3352$ |
$37335$ |
$10$ |
$846$ |
$176880$ |
|
✓ |
$[1, 3, 5, 5, 8, 26, 29, 38, 59, 33, 20, 116, 146, 303, 588, 309, 303, 730, 615, 211]$ |
| 1.6.L.24.14e |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_6),J(C_6))$ |
$24$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11200$ |
$293202$ |
$293202$ |
$2$ |
$9$ |
$56$ |
$491$ |
$5142$ |
$58786$ |
$9$ |
$1239$ |
$277400$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 65, 88, 46, 25, 189, 224, 474, 900, 435, 453, 1012, 829, 246]$ |
| 1.6.L.24.14f |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_6),D_6)$ |
$24$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11200$ |
$293202$ |
$293202$ |
$2$ |
$9$ |
$56$ |
$491$ |
$5142$ |
$58786$ |
$9$ |
$1239$ |
$277390$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 65, 88, 46, 25, 189, 224, 474, 900, 435, 453, 1011, 828, 244]$ |
| 1.6.L.24.14g |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(J(D_6),D_{6,2})$ |
$24$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11200$ |
$293202$ |
$293202$ |
$2$ |
$9$ |
$56$ |
$491$ |
$5142$ |
$58786$ |
$10$ |
$1254$ |
$277610$ |
|
✓ |
$[1, 2, 6, 4, 9, 38, 40, 58, 86, 38, 24, 189, 214, 474, 900, 424, 438, 991, 814, 220]$ |
| 1.6.L.48.48e |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(J(O))$ |
$48$ |
$0$ |
$3$ |
$24$ |
$340$ |
$6475$ |
$145278$ |
$145278$ |
$2$ |
$8$ |
$44$ |
$329$ |
$2962$ |
$29980$ |
$10$ |
$780$ |
$131720$ |
|
✓ |
$[1, 3, 5, 5, 8, 25, 27, 33, 47, 26, 18, 94, 110, 210, 380, 194, 187, 432, 353, 128]$ |
| 1.6.N.24.12b |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$D(2,2)$ |
$24$ |
$1/3$ |
$2$ |
$24$ |
$620$ |
$19180$ |
$620172$ |
$620172$ |
$1$ |
$6$ |
$55$ |
$670$ |
$8871$ |
$121254$ |
$10$ |
$1994$ |
$644320$ |
|
✓ |
$[1, 2, 5, 8, 10, 54, 71, 104, 182, 103, 42, 378, 516, 1200, 2466, 1338, 1332, 3354, 2954, 984]$ |
| 1.6.N.32.43a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(1,8)_1)$ |
$32$ |
$1/2$ |
$2$ |
$24$ |
$530$ |
$15085$ |
$472752$ |
$472752$ |
$2$ |
$9$ |
$59$ |
$583$ |
$7057$ |
$93132$ |
$9$ |
$1600$ |
$488910$ |
|
✓ |
$[1, 2, 6, 5, 11, 44, 54, 88, 137, 74, 31, 290, 375, 898, 1852, 987, 1019, 2487, 2216, 693]$ |
| 1.6.N.36.10b |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(3,3))$ |
$36$ |
$5/9$ |
$2$ |
$24$ |
$500$ |
$13720$ |
$423612$ |
$423612$ |
$2$ |
$9$ |
$58$ |
$547$ |
$6432$ |
$83697$ |
$9$ |
$1455$ |
$436020$ |
|
✓ |
$[1, 2, 6, 5, 11, 41, 49, 81, 124, 64, 31, 261, 332, 801, 1653, 874, 916, 2205, 1968, 603]$ |
| 1.6.N.48.15a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(3,4;4))$ |
$48$ |
$13/24$ |
$2$ |
$24$ |
$480$ |
$12250$ |
$354312$ |
$354312$ |
$2$ |
$9$ |
$57$ |
$514$ |
$5707$ |
$70552$ |
$9$ |
$1329$ |
$356580$ |
✓ |
✓ |
$[1, 2, 6, 5, 11, 39, 45, 72, 104, 53, 27, 220, 272, 635, 1287, 670, 707, 1681, 1498, 447]$ |
| 1.6.N.48.17a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J_s(B(3,4;4))$ |
$48$ |
$13/24$ |
$2$ |
$24$ |
$480$ |
$12250$ |
$354312$ |
$354312$ |
$2$ |
$9$ |
$56$ |
$510$ |
$5692$ |
$70502$ |
$9$ |
$1329$ |
$356580$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 70, 104, 53, 27, 220, 272, 635, 1287, 670, 701, 1681, 1498, 447]$ |
| 1.6.N.48.38a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(6,2))$ |
$48$ |
$13/24$ |
$2$ |
$24$ |
$470$ |
$11830$ |
$342342$ |
$342342$ |
$2$ |
$9$ |
$56$ |
$500$ |
$5517$ |
$68237$ |
$9$ |
$1301$ |
$347160$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 45, 70, 100, 59, 25, 210, 272, 616, 1257, 679, 692, 1685, 1499, 494]$ |
| 1.6.N.48.38b |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(3,4))$ |
$48$ |
$13/24$ |
$2$ |
$24$ |
$480$ |
$12250$ |
$354312$ |
$354312$ |
$2$ |
$9$ |
$57$ |
$514$ |
$5707$ |
$70552$ |
$9$ |
$1333$ |
$356670$ |
✓ |
✓ |
$[1, 2, 6, 5, 11, 39, 46, 73, 104, 58, 27, 220, 278, 637, 1287, 684, 709, 1699, 1508, 483]$ |
| 1.6.N.48.41a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J_s(B(3,4))$ |
$48$ |
$13/24$ |
$2$ |
$24$ |
$480$ |
$12250$ |
$354312$ |
$354312$ |
$2$ |
$9$ |
$56$ |
$510$ |
$5692$ |
$70502$ |
$9$ |
$1333$ |
$356670$ |
✓ |
✓ |
$[1, 2, 6, 5, 11, 39, 46, 71, 104, 58, 27, 220, 278, 637, 1287, 684, 703, 1699, 1508, 483]$ |
| 1.6.N.64.134a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(4,4))$ |
$64$ |
$1/2$ |
$2$ |
$24$ |
$470$ |
$11305$ |
$306432$ |
$306432$ |
$2$ |
$9$ |
$56$ |
$493$ |
$5227$ |
$61482$ |
$9$ |
$1248$ |
$299700$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 67, 91, 51, 25, 194, 233, 522, 1026, 537, 561, 1319, 1164, 371]$ |
| 1.6.N.72.21a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J_s(B(3,6;2))$ |
$72$ |
$19/36$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$56$ |
$507$ |
$5562$ |
$67057$ |
$9$ |
$1311$ |
$330280$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 69, 100, 52, 27, 213, 260, 583, 1151, 580, 604, 1409, 1210, 361]$ |
| 1.6.N.72.23a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J_s(B(3,6))$ |
$72$ |
$19/36$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$56$ |
$507$ |
$5562$ |
$67057$ |
$9$ |
$1311$ |
$330280$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 69, 100, 52, 27, 213, 260, 583, 1151, 582, 604, 1411, 1210, 369]$ |
| 1.6.N.72.23b |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(3,6;2))$ |
$72$ |
$19/36$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$57$ |
$511$ |
$5577$ |
$67107$ |
$9$ |
$1311$ |
$330280$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 71, 100, 52, 27, 213, 260, 583, 1151, 580, 610, 1409, 1210, 361]$ |
| 1.6.N.72.46a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(3,6))$ |
$72$ |
$19/36$ |
$2$ |
$24$ |
$480$ |
$12040$ |
$336672$ |
$336672$ |
$2$ |
$9$ |
$57$ |
$511$ |
$5577$ |
$67107$ |
$9$ |
$1311$ |
$330280$ |
|
✓ |
$[1, 2, 6, 5, 11, 39, 45, 71, 100, 52, 27, 213, 260, 583, 1151, 582, 610, 1411, 1210, 369]$ |
| 1.6.N.144.154a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(B(6,6))$ |
$144$ |
$37/72$ |
$2$ |
$24$ |
$470$ |
$11200$ |
$293202$ |
$293202$ |
$2$ |
$9$ |
$56$ |
$491$ |
$5142$ |
$58787$ |
$9$ |
$1239$ |
$277410$ |
|
✓ |
$[1, 2, 6, 5, 11, 38, 43, 65, 88, 46, 25, 189, 224, 474, 900, 435, 454, 1013, 831, 248]$ |
