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Label Wt Deg $\mathrm{dim}_{\mathbb{R}}$ $\mathrm{G}^0$ Name $\mathrm{G}/\mathrm{G}^0$ $\mathrm{Pr}[t\!=\!0]$ $\mathrm{E}[a_1^2]$ $\mathrm{E}[a_1^4]$ $\mathrm{E}[a_2]$ Diagonal
1.4.E.8.3a $1$ $4$ $3$ $\mathrm{SU}(2)_{2}$ $J(E_4)$ $8$ $5/8$ $1$ $6$ $1$ $[1, 1, 2, 3, 3, 5, 3, 8, 8, 9]$
1.4.F.8.3a $1$ $4$ $1$ $\mathrm{U}(1)_{2}$ $D_{4,1}$ $8$ $7/8$ $1$ $12$ $1$ $[1, 1, 3, 6, 10, 11, 13, 40, 46, 31]$
1.4.F.8.3b $1$ $4$ $1$ $\mathrm{U}(1)_{2}$ $D_4$ $8$ $5/8$ $2$ $18$ $1$ $[1, 2, 4, 7, 12, 13, 14, 42, 48, 35]$
1.4.F.8.3c $1$ $4$ $1$ $\mathrm{U}(1)_{2}$ $D_{4,2}$ $8$ $5/8$ $2$ $18$ $2$ $[1, 2, 3, 8, 12, 11, 14, 40, 48, 29]$
1.6.I.8.3a $1$ $6$ $6$ $\mathrm{SU}(2)\times\mathrm{SU}(2)_2$ $\mathrm{SU}(2)\times J(E_4)$ $8$ $0$ $2$ $14$ $2$ $[1, 2, 4, 3, 5, 13, 13, 19, 21, 11, 8, 37, 39, 75, 125, 58, 67, 121, 91, 28]$
1.6.J.8.3a $1$ $6$ $4$ $\mathrm{U}(1)\times\mathrm{SU}(2)_2$ $J(J(E_4),J(E_2))$ $8$ $1/4$ $2$ $15$ $2$ $[1, 2, 4, 4, 6, 18, 22, 31, 41, 25, 11, 74, 94, 187, 344, 175, 171, 382, 304, 104]$
1.6.J.8.3b $1$ $6$ $4$ $\mathrm{U}(1)\times\mathrm{SU}(2)_2$ $J(J(E_4),E_4)$ $8$ $1/2$ $2$ $21$ $2$ $[1, 2, 5, 4, 9, 25, 26, 37, 46, 26, 16, 93, 104, 202, 368, 182, 181, 392, 316, 104]$
1.6.J.8.3c $1$ $6$ $4$ $\mathrm{U}(1)\times\mathrm{SU}(2)_2$ $J_1(J(E_4))$ $8$ $0$ $3$ $24$ $2$ $[1, 3, 5, 5, 8, 25, 27, 33, 47, 26, 18, 93, 108, 205, 368, 187, 174, 396, 315, 109]$
1.6.K.8.3a $1$ $6$ $4$ $\mathrm{SU}(2)\times\mathrm{U}(1)_2$ $\mathrm{SU}(2)\times D_{4,1}$ $8$ $0$ $2$ $20$ $2$ $[1, 2, 5, 4, 8, 30, 31, 46, 63, 27, 21, 141, 154, 328, 596, 271, 292, 623, 489, 130]$
1.6.K.8.3b $1$ $6$ $4$ $\mathrm{SU}(2)\times\mathrm{U}(1)_2$ $\mathrm{SU}(2)\times D_4$ $8$ $0$ $3$ $32$ $2$ $[1, 3, 7, 6, 10, 42, 41, 53, 78, 32, 24, 161, 175, 364, 652, 293, 304, 663, 511, 139]$
1.6.K.8.3c $1$ $6$ $4$ $\mathrm{SU}(2)\times\mathrm{U}(1)_2$ $\mathrm{SU}(2)\times D_{4,2}$ $8$ $0$ $3$ $32$ $3$ $[1, 3, 8, 5, 11, 42, 40, 59, 76, 31, 25, 164, 172, 365, 652, 290, 320, 655, 512, 131]$
1.6.L.8.3a $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_{4,1},C_{4,1})$ $8$ $1/2$ $2$ $27$ $2$ $[1, 2, 6, 5, 12, 52, 60, 92, 142, 65, 35, 308, 372, 864, 1712, 849, 884, 2074, 1769, 502]$
1.6.L.8.3b $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_{4,1},D_2)$ $8$ $1/2$ $2$ $27$ $2$ $[1, 2, 6, 6, 12, 52, 61, 93, 144, 71, 36, 308, 382, 866, 1712, 862, 885, 2094, 1777, 528]$
1.6.L.8.3c $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_{4,1},D_{2,1})$ $8$ $1/2$ $2$ $27$ $2$ $[1, 2, 6, 5, 10, 52, 58, 86, 142, 63, 35, 308, 372, 866, 1712, 851, 870, 2074, 1763, 504]$
1.6.L.8.3d $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L_1(D_{4,1})$ $8$ $0$ $3$ $30$ $2$ $[1, 3, 6, 7, 11, 52, 62, 87, 145, 69, 38, 308, 384, 869, 1712, 865, 872, 2096, 1774, 531]$
1.6.L.8.3e $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_4,D_2)$ $8$ $1/4$ $3$ $33$ $2$ $[1, 3, 7, 7, 11, 54, 62, 87, 145, 70, 36, 307, 382, 869, 1712, 865, 869, 2094, 1774, 531]$
1.6.L.8.3f $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_4,C_4)$ $8$ $1/2$ $3$ $45$ $2$ $[1, 3, 9, 7, 15, 76, 78, 107, 173, 72, 46, 375, 432, 975, 1884, 911, 925, 2184, 1834, 517]$
1.6.L.8.3g $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L_1(D_4)$ $8$ $0$ $4$ $48$ $2$ $[1, 4, 9, 10, 16, 76, 83, 109, 178, 84, 50, 375, 454, 980, 1884, 938, 928, 2226, 1853, 570]$
1.6.L.8.3h $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_{4,2},D_{2,1})$ $8$ $1/4$ $3$ $33$ $3$ $[1, 3, 8, 6, 12, 54, 60, 94, 143, 67, 35, 310, 372, 869, 1712, 854, 888, 2074, 1773, 507]$
1.6.L.8.3i $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L(D_{4,2},C_4)$ $8$ $1/2$ $3$ $45$ $3$ $[1, 3, 10, 7, 18, 76, 79, 121, 173, 77, 46, 378, 432, 975, 1884, 911, 959, 2184, 1847, 517]$
1.6.L.8.3j $1$ $6$ $6$ $\mathrm{U}(1)\times\mathrm{U}(1)_2$ $L_1(D_{4,2})$ $8$ $0$ $4$ $48$ $3$ $[1, 4, 10, 8, 15, 76, 78, 109, 174, 73, 48, 378, 434, 980, 1884, 916, 932, 2186, 1838, 522]$
1.6.M.8.3a $1$ $6$ $3$ $\mathrm{SU}(2)_{3}$ $M(D_4)$ $8$ $0$ $2$ $22$ $2$ $[1, 2, 6, 5, 9, 40, 46, 70, 103, 46, 23, 195, 237, 544, 1056, 513, 539, 1220, 1002, 277]$
1.6.N.8.3a $1$ $6$ $1$ $\mathrm{U}(1)_{3}$ $J_s(A(2,2))$ $8$ $1/2$ $3$ $63$ $2$ $[1, 3, 13, 13, 25, 160, 193, 301, 531, 254, 112, 1134, 1464, 3577, 7392, 3891, 3978, 9880, 8778, 2675]$
1.6.N.8.3b $1$ $6$ $1$ $\mathrm{U}(1)_{3}$ $B(1,4)_2$ $8$ $0$ $4$ $66$ $2$ $[1, 4, 12, 16, 25, 160, 198, 298, 536, 266, 116, 1131, 1492, 3584, 7392, 3932, 3967, 9940, 8794, 2764]$
1.6.N.8.3c $1$ $6$ $1$ $\mathrm{U}(1)_{3}$ $J(A(1,4)_2)$ $8$ $1/2$ $3$ $63$ $3$ $[1, 3, 13, 11, 25, 160, 187, 303, 527, 236, 108, 1134, 1436, 3573, 7392, 3853, 3986, 9820, 8748, 2589]$
1.6.N.8.3d $1$ $6$ $1$ $\mathrm{U}(1)_{3}$ $J(A(1,4)_1)$ $8$ $1/2$ $5$ $99$ $4$ $[1, 5, 19, 15, 35, 208, 225, 345, 585, 252, 132, 1262, 1540, 3763, 7664, 3949, 4080, 9988, 8860, 2613]$
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