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.E.8.3a |
$1$ |
$4$ |
$3$ |
$\mathrm{SU}(2)_{2}$ |
$J(E_4)$ |
$8$ |
$5/8$ |
$1$ |
$6$ |
$50$ |
$504$ |
$5712$ |
$5712$ |
$1$ |
$3$ |
$7$ |
$26$ |
$96$ |
$422$ |
|
|
|
✓ |
✓ |
$[1, 1, 2, 3, 3, 5, 3, 8, 8, 9]$ |
1.4.F.8.3a |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$D_{4,1}$ |
$8$ |
$7/8$ |
$1$ |
$12$ |
$160$ |
$2240$ |
$32256$ |
$32256$ |
$1$ |
$4$ |
$13$ |
$63$ |
$311$ |
$1678$ |
|
|
|
|
✓ |
$[1, 1, 3, 6, 10, 11, 13, 40, 46, 31]$ |
1.4.F.8.3b |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$D_4$ |
$8$ |
$5/8$ |
$2$ |
$18$ |
$200$ |
$2520$ |
$34272$ |
$34272$ |
$1$ |
$5$ |
$16$ |
$78$ |
$366$ |
$1898$ |
|
|
|
|
✓ |
$[1, 2, 4, 7, 12, 13, 14, 42, 48, 35]$ |
1.4.F.8.3c |
$1$ |
$4$ |
$1$ |
$\mathrm{U}(1)_{2}$ |
$D_{4,2}$ |
$8$ |
$5/8$ |
$2$ |
$18$ |
$200$ |
$2520$ |
$34272$ |
$34272$ |
$2$ |
$6$ |
$20$ |
$83$ |
$382$ |
$1920$ |
|
|
|
|
✓ |
$[1, 2, 3, 8, 12, 11, 14, 40, 48, 29]$ |
1.6.I.8.3a |
$1$ |
$6$ |
$6$ |
$\mathrm{SU}(2)\times\mathrm{SU}(2)_2$ |
$\mathrm{SU}(2)\times J(E_4)$ |
$8$ |
$0$ |
$2$ |
$14$ |
$175$ |
$2898$ |
$56364$ |
$56364$ |
$2$ |
$7$ |
$32$ |
$197$ |
$1502$ |
$13185$ |
$7$ |
$412$ |
$52590$ |
✓ |
✓ |
$[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 37, 39, 75, 125, 58, 67, 121, 91, 28]$ |
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.K.8.3a |
$1$ |
$6$ |
$4$ |
$\mathrm{SU}(2)\times\mathrm{U}(1)_2$ |
$\mathrm{SU}(2)\times D_{4,1}$ |
$8$ |
$0$ |
$2$ |
$20$ |
$375$ |
$8554$ |
$213528$ |
$213528$ |
$2$ |
$8$ |
$47$ |
$390$ |
$3892$ |
$42621$ |
$8$ |
$942$ |
$193110$ |
|
✓ |
$[1, 2, 5, 4, 8, 30, 31, 46, 63, 27, 21, 141, 154, 328, 596, 271, 292, 623, 489, 130]$ |
1.6.K.8.3b |
$1$ |
$6$ |
$4$ |
$\mathrm{SU}(2)\times\mathrm{U}(1)_2$ |
$\mathrm{SU}(2)\times D_4$ |
$8$ |
$0$ |
$3$ |
$32$ |
$535$ |
$10934$ |
$251874$ |
$251874$ |
$2$ |
$10$ |
$65$ |
$537$ |
$5072$ |
$52236$ |
$13$ |
$1308$ |
$228690$ |
|
✓ |
$[1, 3, 7, 6, 10, 42, 41, 53, 78, 32, 24, 161, 175, 364, 652, 293, 304, 663, 511, 139]$ |
1.6.K.8.3c |
$1$ |
$6$ |
$4$ |
$\mathrm{SU}(2)\times\mathrm{U}(1)_2$ |
$\mathrm{SU}(2)\times D_{4,2}$ |
$8$ |
$0$ |
$3$ |
$32$ |
$535$ |
$10934$ |
$251874$ |
$251874$ |
$3$ |
$13$ |
$75$ |
$568$ |
$5168$ |
$52530$ |
$14$ |
$1318$ |
$228800$ |
|
✓ |
$[1, 3, 8, 5, 11, 42, 40, 59, 76, 31, 25, 164, 172, 365, 652, 290, 320, 655, 512, 131]$ |
1.6.L.8.3a |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{4,1},C_{4,1})$ |
$8$ |
$1/2$ |
$2$ |
$27$ |
$620$ |
$16835$ |
$489132$ |
$489132$ |
$2$ |
$9$ |
$65$ |
$660$ |
$7742$ |
$96666$ |
$9$ |
$1785$ |
$483300$ |
|
✓ |
$[1, 2, 6, 5, 12, 52, 60, 92, 142, 65, 35, 308, 372, 864, 1712, 849, 884, 2074, 1769, 502]$ |
1.6.L.8.3b |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{4,1},D_2)$ |
$8$ |
$1/2$ |
$2$ |
$27$ |
$620$ |
$16835$ |
$489132$ |
$489132$ |
$2$ |
$9$ |
$65$ |
$660$ |
$7742$ |
$96666$ |
$10$ |
$1794$ |
$483400$ |
|
✓ |
$[1, 2, 6, 6, 12, 52, 61, 93, 144, 71, 36, 308, 382, 866, 1712, 862, 885, 2094, 1777, 528]$ |
1.6.L.8.3c |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{4,1},D_{2,1})$ |
$8$ |
$1/2$ |
$2$ |
$27$ |
$620$ |
$16835$ |
$489132$ |
$489132$ |
$2$ |
$9$ |
$65$ |
$660$ |
$7742$ |
$96666$ |
$11$ |
$1809$ |
$483620$ |
|
✓ |
$[1, 2, 6, 5, 10, 52, 58, 86, 142, 63, 35, 308, 372, 866, 1712, 851, 870, 2074, 1763, 504]$ |
1.6.L.8.3d |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(D_{4,1})$ |
$8$ |
$0$ |
$3$ |
$30$ |
$630$ |
$16870$ |
$489258$ |
$489258$ |
$2$ |
$9$ |
$65$ |
$660$ |
$7742$ |
$96666$ |
$12$ |
$1818$ |
$483720$ |
|
✓ |
$[1, 3, 6, 7, 11, 52, 62, 87, 145, 69, 38, 308, 384, 869, 1712, 865, 872, 2096, 1774, 531]$ |
1.6.L.8.3e |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_4,D_2)$ |
$8$ |
$1/4$ |
$3$ |
$33$ |
$660$ |
$17115$ |
$491148$ |
$491148$ |
$2$ |
$10$ |
$71$ |
$693$ |
$7912$ |
$97516$ |
$14$ |
$1890$ |
$485960$ |
|
✓ |
$[1, 3, 7, 7, 11, 54, 62, 87, 145, 70, 36, 307, 382, 869, 1712, 865, 869, 2094, 1774, 531]$ |
1.6.L.8.3f |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_4,C_4)$ |
$8$ |
$1/2$ |
$3$ |
$45$ |
$930$ |
$22435$ |
$595098$ |
$595098$ |
$2$ |
$12$ |
$95$ |
$933$ |
$10192$ |
$118926$ |
$16$ |
$2466$ |
$569440$ |
|
✓ |
$[1, 3, 9, 7, 15, 76, 78, 107, 173, 72, 46, 375, 432, 975, 1884, 911, 925, 2184, 1834, 517]$ |
1.6.L.8.3g |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(D_4)$ |
$8$ |
$0$ |
$4$ |
$48$ |
$940$ |
$22470$ |
$595224$ |
$595224$ |
$2$ |
$12$ |
$95$ |
$933$ |
$10192$ |
$118926$ |
$18$ |
$2484$ |
$569640$ |
|
✓ |
$[1, 4, 9, 10, 16, 76, 83, 109, 178, 84, 50, 375, 454, 980, 1884, 938, 928, 2226, 1853, 570]$ |
1.6.L.8.3h |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{4,2},D_{2,1})$ |
$8$ |
$1/4$ |
$3$ |
$33$ |
$660$ |
$17115$ |
$491148$ |
$491148$ |
$3$ |
$13$ |
$81$ |
$724$ |
$8008$ |
$97810$ |
$15$ |
$1905$ |
$486180$ |
|
✓ |
$[1, 3, 8, 6, 12, 54, 60, 94, 143, 67, 35, 310, 372, 869, 1712, 854, 888, 2074, 1773, 507]$ |
1.6.L.8.3i |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L(D_{4,2},C_4)$ |
$8$ |
$1/2$ |
$3$ |
$45$ |
$930$ |
$22435$ |
$595098$ |
$595098$ |
$3$ |
$15$ |
$105$ |
$964$ |
$10288$ |
$119220$ |
$16$ |
$2466$ |
$569440$ |
|
✓ |
$[1, 3, 10, 7, 18, 76, 79, 121, 173, 77, 46, 378, 432, 975, 1884, 911, 959, 2184, 1847, 517]$ |
1.6.L.8.3j |
$1$ |
$6$ |
$6$ |
$\mathrm{U}(1)\times\mathrm{U}(1)_2$ |
$L_1(D_{4,2})$ |
$8$ |
$0$ |
$4$ |
$48$ |
$940$ |
$22470$ |
$595224$ |
$595224$ |
$3$ |
$15$ |
$105$ |
$964$ |
$10288$ |
$119220$ |
$20$ |
$2514$ |
$570080$ |
|
✓ |
$[1, 4, 10, 8, 15, 76, 78, 109, 174, 73, 48, 378, 434, 980, 1884, 916, 932, 2186, 1838, 522]$ |
1.6.M.8.3a |
$1$ |
$6$ |
$3$ |
$\mathrm{SU}(2)_{3}$ |
$M(D_4)$ |
$8$ |
$0$ |
$2$ |
$22$ |
$460$ |
$11494$ |
$310044$ |
$310044$ |
$2$ |
$9$ |
$59$ |
$539$ |
$5772$ |
$66783$ |
$9$ |
$1388$ |
$320178$ |
|
✓ |
$[1, 2, 6, 5, 9, 40, 46, 70, 103, 46, 23, 195, 237, 544, 1056, 513, 539, 1220, 1002, 277]$ |
1.6.N.8.3a |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J_s(A(2,2))$ |
$8$ |
$1/2$ |
$3$ |
$63$ |
$1830$ |
$57435$ |
$1860138$ |
$1860138$ |
$2$ |
$16$ |
$161$ |
$2002$ |
$26597$ |
$363733$ |
$22$ |
$5910$ |
$1932070$ |
|
✓ |
$[1, 3, 13, 13, 25, 160, 193, 301, 531, 254, 112, 1134, 1464, 3577, 7392, 3891, 3978, 9880, 8778, 2675]$ |
1.6.N.8.3b |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$B(1,4)_2$ |
$8$ |
$0$ |
$4$ |
$66$ |
$1840$ |
$57470$ |
$1860264$ |
$1860264$ |
$2$ |
$15$ |
$158$ |
$1991$ |
$26562$ |
$363621$ |
$24$ |
$5932$ |
$1932360$ |
|
✓ |
$[1, 4, 12, 16, 25, 160, 198, 298, 536, 266, 116, 1131, 1492, 3584, 7392, 3932, 3967, 9940, 8794, 2764]$ |
1.6.N.8.3c |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(A(1,4)_2)$ |
$8$ |
$1/2$ |
$3$ |
$63$ |
$1830$ |
$57435$ |
$1860138$ |
$1860138$ |
$3$ |
$18$ |
$168$ |
$2022$ |
$26658$ |
$363915$ |
$22$ |
$5910$ |
$1932070$ |
|
✓ |
$[1, 3, 13, 11, 25, 160, 187, 303, 527, 236, 108, 1134, 1436, 3573, 7392, 3853, 3986, 9820, 8748, 2589]$ |
1.6.N.8.3d |
$1$ |
$6$ |
$1$ |
$\mathrm{U}(1)_{3}$ |
$J(A(1,4)_1)$ |
$8$ |
$1/2$ |
$5$ |
$99$ |
$2450$ |
$68355$ |
$2056950$ |
$2056950$ |
$4$ |
$26$ |
$235$ |
$2586$ |
$31489$ |
$405911$ |
$34$ |
$7222$ |
$2086690$ |
|
✓ |
$[1, 5, 19, 15, 35, 208, 225, 345, 585, 252, 132, 1262, 1540, 3763, 7664, 3949, 4080, 9988, 8860, 2613]$ |