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 |
1.6.J.2.1a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(E_2,E_1)$ |
$2$ |
$1/2$ |
$3$ |
$43$ |
$830$ |
$18627$ |
$458010$ |
$458010$ |
$2$ |
$13$ |
$99$ |
$907$ |
$9188$ |
$99515$ |
$18$ |
$2338$ |
$456520$ |
|
✓ |
$[1, 3, 10, 7, 12, 70, 71, 94, 151, 58, 34, 287, 328, 725, 1376, 631, 636, 1440, 1149, 295]$ |
1.6.J.2.1b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(E_2)$ |
$2$ |
$0$ |
$4$ |
$46$ |
$840$ |
$18662$ |
$458136$ |
$458136$ |
$2$ |
$13$ |
$99$ |
$907$ |
$9188$ |
$99515$ |
$20$ |
$2356$ |
$456720$ |
|
✓ |
$[1, 4, 10, 12, 15, 70, 80, 102, 160, 82, 40, 287, 368, 732, 1376, 680, 649, 1520, 1188, 396]$ |
1.6.J.3.1a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(E_3)$ |
$3$ |
$0$ |
$4$ |
$42$ |
$670$ |
$13594$ |
$318276$ |
$318276$ |
$2$ |
$11$ |
$77$ |
$661$ |
$6438$ |
$68173$ |
$16$ |
$1656$ |
$308840$ |
|
✓ |
$[1, 4, 8, 8, 13, 52, 54, 66, 108, 44, 34, 201, 234, 490, 932, 438, 431, 970, 780, 210]$ |
1.6.J.4.1a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(E_4,E_2)$ |
$4$ |
$0$ |
$3$ |
$27$ |
$440$ |
$9443$ |
$229740$ |
$229740$ |
$2$ |
$9$ |
$57$ |
$479$ |
$4688$ |
$50123$ |
$14$ |
$1242$ |
$229640$ |
|
✓ |
$[1, 3, 6, 7, 8, 36, 41, 52, 81, 44, 20, 145, 184, 371, 688, 345, 326, 760, 599, 203]$ |
1.6.J.4.1b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(E_4)$ |
$4$ |
$0$ |
$4$ |
$42$ |
$660$ |
$12838$ |
$285096$ |
$285096$ |
$2$ |
$11$ |
$75$ |
$623$ |
$5828$ |
$59313$ |
$16$ |
$1524$ |
$259520$ |
|
✓ |
$[1, 4, 8, 8, 13, 50, 50, 60, 92, 46, 32, 183, 208, 404, 736, 364, 339, 784, 622, 208]$ |
1.6.J.4.2a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_2),E_2)$ |
$4$ |
$1/2$ |
$2$ |
$23$ |
$420$ |
$9331$ |
$229068$ |
$229068$ |
$2$ |
$9$ |
$56$ |
$471$ |
$4642$ |
$49891$ |
$10$ |
$1178$ |
$228360$ |
|
✓ |
$[1, 2, 6, 6, 10, 35, 41, 58, 80, 44, 20, 145, 184, 366, 688, 340, 336, 760, 599, 198]$ |
1.6.J.4.2b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_2),J(E_1))$ |
$4$ |
$1/2$ |
$2$ |
$23$ |
$420$ |
$9331$ |
$229068$ |
$229068$ |
$2$ |
$9$ |
$56$ |
$471$ |
$4642$ |
$49891$ |
$10$ |
$1178$ |
$228360$ |
|
✓ |
$[1, 2, 6, 4, 8, 35, 37, 52, 76, 32, 18, 145, 166, 364, 688, 318, 326, 722, 579, 150]$ |
1.6.J.4.2c |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(J(E_2))$ |
$4$ |
$0$ |
$3$ |
$26$ |
$430$ |
$9366$ |
$229194$ |
$229194$ |
$2$ |
$9$ |
$56$ |
$471$ |
$4642$ |
$49891$ |
$12$ |
$1196$ |
$228560$ |
|
✓ |
$[1, 3, 6, 7, 9, 35, 42, 54, 81, 44, 22, 145, 188, 369, 688, 345, 329, 764, 598, 203]$ |
1.6.J.4.2d |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(E_2)$ |
$4$ |
$1/4$ |
$3$ |
$31$ |
$500$ |
$10227$ |
$239820$ |
$239820$ |
$2$ |
$11$ |
$69$ |
$547$ |
$5068$ |
$52285$ |
$14$ |
$1306$ |
$233480$ |
|
✓ |
$[1, 3, 8, 7, 10, 40, 43, 58, 81, 44, 24, 153, 188, 371, 688, 345, 340, 764, 609, 203]$ |
1.6.J.6.1a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_3),E_3)$ |
$6$ |
$1/2$ |
$2$ |
$21$ |
$335$ |
$6797$ |
$159138$ |
$159138$ |
$2$ |
$8$ |
$45$ |
$348$ |
$3267$ |
$34220$ |
$8$ |
$828$ |
$154420$ |
|
✓ |
$[1, 2, 5, 4, 9, 26, 28, 40, 54, 25, 17, 102, 117, 245, 466, 219, 227, 485, 395, 105]$ |
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.6.2a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(E_6,E_3)$ |
$6$ |
$1/6$ |
$3$ |
$27$ |
$380$ |
$7175$ |
$162540$ |
$162540$ |
$2$ |
$9$ |
$51$ |
$381$ |
$3438$ |
$35093$ |
$12$ |
$924$ |
$157300$ |
|
✓ |
$[1, 3, 6, 5, 8, 28, 29, 34, 55, 24, 18, 103, 118, 247, 466, 221, 218, 486, 395, 107]$ |
1.6.J.6.2b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(E_3)$ |
$6$ |
$0$ |
$3$ |
$27$ |
$390$ |
$7399$ |
$166320$ |
$166320$ |
$2$ |
$9$ |
$53$ |
$397$ |
$3548$ |
$35813$ |
$12$ |
$924$ |
$157940$ |
|
✓ |
$[1, 3, 6, 5, 8, 30, 29, 38, 55, 24, 20, 107, 120, 249, 466, 223, 226, 488, 399, 109]$ |
1.6.J.6.2c |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_1(E_6)$ |
$6$ |
$0$ |
$4$ |
$42$ |
$660$ |
$12810$ |
$281736$ |
$281736$ |
$2$ |
$11$ |
$75$ |
$621$ |
$5768$ |
$57953$ |
$16$ |
$1512$ |
$249000$ |
|
✓ |
$[1, 4, 8, 8, 13, 50, 50, 58, 88, 40, 32, 181, 204, 384, 680, 312, 299, 664, 504, 160]$ |
1.6.J.8.2a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(E_4)$ |
$8$ |
$1/8$ |
$3$ |
$27$ |
$380$ |
$6923$ |
$148260$ |
$148260$ |
$2$ |
$9$ |
$51$ |
$371$ |
$3198$ |
$31103$ |
$12$ |
$858$ |
$132960$ |
|
✓ |
$[1, 3, 6, 5, 8, 28, 27, 34, 47, 26, 18, 97, 106, 207, 368, 187, 178, 394, 321, 109]$ |
1.6.J.8.3a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_4),J(E_2))$ |
$8$ |
$1/4$ |
$2$ |
$15$ |
$225$ |
$4739$ |
$114933$ |
$114933$ |
$2$ |
$7$ |
$35$ |
$257$ |
$2392$ |
$25195$ |
$8$ |
$630$ |
$114920$ |
|
✓ |
$[1, 2, 4, 4, 6, 18, 22, 31, 41, 25, 11, 74, 94, 187, 344, 175, 171, 382, 304, 104]$ |
1.6.J.8.3b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_4),E_4)$ |
$8$ |
$1/2$ |
$2$ |
$21$ |
$330$ |
$6419$ |
$142548$ |
$142548$ |
$2$ |
$8$ |
$44$ |
$329$ |
$2962$ |
$29790$ |
$8$ |
$762$ |
$129760$ |
|
✓ |
$[1, 2, 5, 4, 9, 25, 26, 37, 46, 26, 16, 93, 104, 202, 368, 182, 181, 392, 316, 104]$ |
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.8.5a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(J(E_2))$ |
$8$ |
$3/8$ |
$2$ |
$17$ |
$255$ |
$5131$ |
$119973$ |
$119973$ |
$2$ |
$8$ |
$41$ |
$291$ |
$2582$ |
$26276$ |
$8$ |
$662$ |
$116840$ |
|
✓ |
$[1, 2, 5, 4, 7, 20, 23, 34, 41, 25, 13, 78, 96, 187, 344, 175, 178, 384, 309, 104]$ |
1.6.J.12.4a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_6),J(E_3))$ |
$12$ |
$1/3$ |
$2$ |
$15$ |
$195$ |
$3605$ |
$81333$ |
$81333$ |
$2$ |
$7$ |
$32$ |
$208$ |
$1767$ |
$17680$ |
$7$ |
$471$ |
$78750$ |
|
✓ |
$[1, 2, 4, 3, 6, 14, 16, 22, 28, 15, 10, 53, 61, 125, 233, 113, 117, 245, 202, 56]$ |
1.6.J.12.4b |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(J(E_3))$ |
$12$ |
$1/4$ |
$2$ |
$15$ |
$200$ |
$3717$ |
$83223$ |
$83223$ |
$2$ |
$7$ |
$33$ |
$216$ |
$1822$ |
$18040$ |
$7$ |
$471$ |
$79070$ |
|
✓ |
$[1, 2, 4, 3, 6, 15, 16, 24, 28, 15, 11, 55, 62, 126, 233, 114, 121, 246, 204, 57]$ |
1.6.J.12.4c |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J(J(E_6),E_6)$ |
$12$ |
$1/2$ |
$2$ |
$21$ |
$330$ |
$6405$ |
$140868$ |
$140868$ |
$2$ |
$8$ |
$44$ |
$328$ |
$2932$ |
$29110$ |
$8$ |
$756$ |
$124500$ |
|
✓ |
$[1, 2, 5, 4, 9, 25, 26, 36, 44, 23, 16, 92, 102, 192, 340, 156, 161, 332, 257, 80]$ |
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.J.12.5a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(E_6)$ |
$12$ |
$1/12$ |
$3$ |
$27$ |
$380$ |
$6895$ |
$146160$ |
$146160$ |
$2$ |
$9$ |
$51$ |
$369$ |
$3158$ |
$30343$ |
$12$ |
$852$ |
$127700$ |
|
✓ |
$[1, 3, 6, 5, 8, 28, 27, 32, 45, 22, 18, 95, 104, 195, 340, 159, 156, 334, 259, 83]$ |
1.6.J.16.11a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(J(E_4))$ |
$16$ |
$5/16$ |
$2$ |
$15$ |
$195$ |
$3479$ |
$74193$ |
$74193$ |
$2$ |
$7$ |
$32$ |
$203$ |
$1647$ |
$15685$ |
$7$ |
$438$ |
$66580$ |
✓ |
✓ |
$[1, 2, 4, 3, 6, 14, 15, 22, 24, 16, 10, 50, 55, 105, 184, 96, 97, 199, 165, 57]$ |
1.6.J.24.14a |
$1$ |
$6$ |
$4$ |
$\mathrm{U}(1)\times\mathrm{SU}(2)_2$ |
$J_2(J(E_6))$ |
$24$ |
$7/24$ |
$2$ |
$15$ |
$195$ |
$3465$ |
$73143$ |
$73143$ |
$2$ |
$7$ |
$32$ |
$202$ |
$1627$ |
$15305$ |
$7$ |
$435$ |
$63950$ |
✓ |
✓ |
$[1, 2, 4, 3, 6, 14, 15, 21, 23, 14, 10, 49, 54, 99, 170, 82, 86, 169, 134, 44]$ |