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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.12.33.1 $x^{12} + 24 x^{11} + 248 x^{10} + 608 x^{9} + 90 x^{8} + 512 x^{7} + 704 x^{6} - 4800 x^{5} - 7252 x^{4} - 5728 x^{3} - 9696 x^{2} - 8448 x - 3016$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 8 t\right) x^{2} + 8 t x + 24 t + 14$
2.12.33.10 $x^{12} - 16 x^{10} + 210 x^{8} + 256 x^{7} - 80 x^{6} - 800 x^{5} + 2588 x^{4} + 2560 x^{3} - 352 x^{2} + 1216 x + 1464$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 4 t\right) x^{2} + 8 t x + 4 t^{2} + 14$
2.12.33.100 $x^{12} + 8 x^{11} + 36 x^{10} + 824 x^{9} + 1162 x^{8} + 3840 x^{7} + 10480 x^{6} + 19680 x^{5} + 24892 x^{4} + 41056 x^{3} + 39568 x^{2} + 21472 x + 32152$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(4 t + 12\right) x^{2} + 8 x + 8 t^{2} + 20 t + 30$
2.12.33.101 $x^{12} + 24 x^{11} + 284 x^{10} + 1056 x^{9} + 3662 x^{8} + 4576 x^{7} + 8112 x^{6} + 18752 x^{5} + 10988 x^{4} + 18784 x^{3} + 26992 x^{2} + 20136$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T99) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 12\right) x^{2} + 16 t + 26$
2.12.33.102 $x^{12} + 24 x^{11} + 268 x^{10} + 992 x^{9} + 3962 x^{8} + 2560 x^{7} + 10512 x^{6} + 6272 x^{5} + 17356 x^{4} + 7840 x^{3} + 22832 x^{2} + 3456 x + 15224$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(12 t^{2} + 12\right) x^{2} + 8 t x + 24 t^{2} + 14$
2.12.33.103 $x^{12} + 24 x^{11} + 192 x^{10} + 512 x^{9} + 18 x^{8} + 960 x^{7} + 8448 x^{6} + 1664 x^{5} + 908 x^{4} + 17440 x^{3} + 1408 x^{2} + 10648$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(12 t^{2} + 8\right) x^{2} + 8 t x + 22$
2.12.33.104 $x^{12} + 24 x^{11} + 212 x^{10} + 816 x^{9} + 1134 x^{8} - 416 x^{7} - 1360 x^{6} + 1760 x^{5} + 4636 x^{4} + 3424 x^{3} + 1744 x^{2} + 384 x + 72$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(8 t^{2} + 12\right) x^{2} + 8 t^{2} x + 4 t^{2} + 4 t + 2$
2.12.33.105 $x^{12} + 92 x^{10} - 288 x^{9} - 222 x^{8} + 160 x^{7} - 1392 x^{6} - 340 x^{4} - 4416 x^{3} + 1776 x^{2} - 3968 x - 744$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t^{2} + 8 t + 12\right) x^{2} + 8 t x + 8 t^{2} + 16 t + 6$
2.12.33.106 $x^{12} + 24 x^{11} + 268 x^{10} + 992 x^{9} + 3846 x^{8} + 2656 x^{7} + 1840 x^{6} + 8640 x^{5} + 4876 x^{4} - 3488 x^{3} + 4272 x^{2} - 3576$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T99) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(12 t^{2} + 12\right) x^{2} + 16 t + 2$
2.12.33.107 $x^{12} + 76 x^{10} - 112 x^{9} - 202 x^{8} + 3424 x^{7} + 3488 x^{6} + 12128 x^{5} + 39004 x^{4} + 25152 x^{3} + 82576 x^{2} + 24576 x + 59688$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T105) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t x^{3} + \left(12 t^{2} + 8 t + 12\right) x^{2} + 8 t^{2} x + 28 t^{2} + 28 t + 26$
2.12.33.108 $x^{12} + 24 x^{11} + 272 x^{10} + 992 x^{9} + 2178 x^{8} + 2304 x^{7} + 1792 x^{6} + 1728 x^{5} - 2292 x^{4} - 4960 x^{3} - 3520 x^{2} - 4608 x - 2344$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 8 t + 8\right) x^{2} + 8 t x + 16 t + 6$
2.12.33.109 $x^{12} + 40 x^{10} - 96 x^{9} - 854 x^{8} - 3040 x^{7} - 5056 x^{6} - 3264 x^{5} + 6508 x^{4} + 6848 x^{3} + 20320 x^{2} + 7168 x + 41848$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t x^{3} + \left(12 t^{2} + 8 t\right) x^{2} + 8 t x + 16 t^{2} + 24 t + 30$
2.12.33.11 $x^{12} + 24 x^{11} + 188 x^{10} + 456 x^{9} + 286 x^{8} + 4032 x^{7} + 1600 x^{6} + 5728 x^{5} + 4348 x^{4} + 3104 x^{3} + 1296 x^{2} + 416 x + 72$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(8 t^{2} + 12 t + 4\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 2$
2.12.33.110 $x^{12} - 16 x^{11} + 312 x^{10} - 192 x^{9} - 650 x^{8} + 480 x^{7} - 528 x^{6} - 896 x^{5} + 1692 x^{4} - 640 x^{3} - 320 x^{2} + 4776$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{2} + 28 t + 18$
2.12.33.111 $x^{12} + 24 x^{11} + 264 x^{10} + 1048 x^{9} + 2694 x^{8} + 4576 x^{7} + 7808 x^{6} + 10208 x^{5} + 13404 x^{4} + 8544 x^{3} + 15008 x^{2} + 1888 x + 13032$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 4 t + 2$
2.12.33.112 $x^{12} + 8 x^{11} + 240 x^{10} + 1784 x^{9} + 2698 x^{8} + 4288 x^{7} + 10048 x^{6} + 9312 x^{5} + 13436 x^{4} + 15200 x^{3} + 1152 x^{2} + 22752 x + 29592$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + \left(8 t^{2} + 4 t\right) x^{2} + 8 x + 12 t + 30$
2.12.33.113 $x^{12} + 80 x^{10} - 344 x^{9} + 106 x^{8} + 2304 x^{7} + 624 x^{6} + 7712 x^{5} + 18396 x^{4} + 16128 x^{3} + 31712 x^{2} + 30752 x + 29016$ $2$ $4$ $3$ $33$ $C_4\wr C_3$ (as 12T94) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t x^{3} + \left(4 t^{2} + 4 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 20 t^{2} + 24 t + 22$
2.12.33.114 $x^{12} + 24 x^{11} + 240 x^{10} + 560 x^{9} + 410 x^{8} + 2112 x^{7} + 7744 x^{6} + 4224 x^{5} + 11100 x^{4} + 25248 x^{3} + 25408 x^{2} + 18112 x + 12056$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 20 t^{2} + 4 t + 22$
2.12.33.115 $x^{12} + 20 x^{10} + 24 x^{9} + 198 x^{8} + 576 x^{7} + 1872 x^{6} + 4000 x^{5} + 8028 x^{4} + 2688 x^{3} + 10448 x^{2} + 1248 x + 3816$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 4 t + 12\right) x^{2} + \left(8 t + 8\right) x + 16 t^{2} + 4 t + 2$
2.12.33.116 $x^{12} + 8 x^{10} - 16 x^{9} - 2 x^{8} - 128 x^{7} + 1088 x^{6} + 2080 x^{5} + 13884 x^{4} + 14336 x^{3} + 48992 x^{2} + 21248 x + 36296$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8\right) x^{2} + 8 t^{2} x + 28 t^{2} + 28 t + 18$
2.12.33.117 $x^{12} + 8 x^{9} + 558 x^{8} + 704 x^{7} + 4560 x^{6} + 8448 x^{5} + 20892 x^{4} + 23552 x^{3} + 29472 x^{2} + 16736 x + 10952$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T142) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(12 t^{2} + 12 t + 8\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 12 t^{2} + 16 t + 18$
2.12.33.118 $x^{12} + 24 x^{11} + 208 x^{10} + 776 x^{9} + 1546 x^{8} + 4224 x^{7} + 6864 x^{6} + 19424 x^{5} + 17052 x^{4} + 39584 x^{3} + 33696 x^{2} + 30752 x + 29016$ $2$ $4$ $3$ $33$ $C_4\wr C_3$ (as 12T94) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(4 t^{2} + 12 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 20 t^{2} + 24 t + 22$
2.12.33.119 $x^{12} - 16 x^{11} + 84 x^{10} + 376 x^{9} + 2042 x^{8} + 2400 x^{7} + 2832 x^{6} + 6240 x^{5} + 13628 x^{4} + 13184 x^{3} + 17552 x^{2} + 8672 x + 4056$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t^{2} x^{3} + \left(8 t^{2} + 4 t + 12\right) x^{2} + 8 x + 8 t^{2} + 20 t + 14$
2.12.33.12 $x^{12} + 12 x^{10} + 8 x^{9} + 262 x^{8} + 544 x^{7} + 256 x^{6} + 832 x^{5} + 3932 x^{4} + 12608 x^{3} + 21328 x^{2} + 19680 x + 19944$ $2$ $4$ $3$ $33$ $D_4\times A_4$ (as 12T51) $[3, 4]$ $[2, 2, 2, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(12 t + 4\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 4 t^{2} + 16 t + 26$
2.12.33.120 $x^{12} + 8 x^{11} - 8 x^{10} + 624 x^{9} + 2042 x^{8} + 4704 x^{7} + 12624 x^{6} + 17472 x^{5} + 20700 x^{4} + 38432 x^{3} + 20928 x^{2} + 28480 x + 44824$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(4 t^{2} + 8 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 20 t + 22$
2.12.33.121 $x^{12} + 24 x^{11} + 216 x^{10} + 880 x^{9} + 1470 x^{8} + 224 x^{7} - 1632 x^{6} - 608 x^{5} + 2556 x^{4} + 8928 x^{3} + 12896 x^{2} + 21504 x + 33352$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + 8 x^{2} + 8 t^{2} x + 28 t^{2} + 12 t + 18$
2.12.33.122 $x^{12} + 16 x^{10} + 8 x^{9} + 226 x^{8} + 160 x^{7} + 1648 x^{6} + 2144 x^{5} + 8956 x^{4} + 8256 x^{3} + 20064 x^{2} + 12320 x + 24504$ $2$ $4$ $3$ $33$ $C_4\wr C_3$ (as 12T94) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(4 t^{2} + 4 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 8 t + 30$
2.12.33.123 $x^{12} + 24 x^{11} + 256 x^{10} + 912 x^{9} + 2658 x^{8} + 4128 x^{7} + 11408 x^{6} + 16000 x^{5} + 25916 x^{4} + 27104 x^{3} + 42400 x^{2} + 25152 x + 26424$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(12 t^{2} + 8 t + 8\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 4 t + 14$
2.12.33.124 $x^{12} + 8 x^{9} + 506 x^{8} + 224 x^{7} + 4048 x^{6} + 8160 x^{5} + 16732 x^{4} + 20416 x^{3} + 22112 x^{2} + 14112 x + 8728$ $2$ $4$ $3$ $33$ $C_4\wr C_3$ (as 12T94) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(12 t^{2} + 12 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 20 t^{2} + 8 t + 6$
2.12.33.125 $x^{12} + 24 x^{11} + 220 x^{10} + 960 x^{9} + 2066 x^{8} + 2432 x^{7} + 3280 x^{6} + 6080 x^{5} + 12972 x^{4} + 20640 x^{3} + 22640 x^{2} + 7552 x + 31576$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(4 t^{2} + 12\right) x^{2} + 8 t x + 24 t^{2} + 16 t + 22$
2.12.33.126 $x^{12} + 24 x^{11} + 216 x^{10} + 920 x^{9} + 2318 x^{8} + 5792 x^{7} + 10720 x^{6} + 20064 x^{5} + 20348 x^{4} + 31840 x^{3} + 23072 x^{2} + 19040 x + 23048$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 28 t + 26$
2.12.33.127 $x^{12} - 16 x^{11} + 76 x^{10} + 416 x^{9} + 3006 x^{8} + 3808 x^{7} + 3648 x^{6} + 192 x^{5} + 6076 x^{4} + 1280 x^{3} + 6480 x^{2} + 712$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T105) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t^{2} x^{3} + \left(12 t^{2} + 4 t + 12\right) x^{2} + 12 t + 10$
2.12.33.128 $x^{12} + 24 x^{11} + 192 x^{10} + 496 x^{9} - 278 x^{8} - 1376 x^{7} - 1088 x^{6} + 3328 x^{5} + 6428 x^{4} + 1760 x^{3} + 2176 x^{2} + 9920 x + 9048$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(8 t^{2} + 8 t\right) x + 20 t^{2} + 4 t + 6$
2.12.33.129 $x^{12} + 24 x^{11} + 192 x^{10} + 536 x^{9} + 382 x^{8} + 1440 x^{7} - 128 x^{6} + 4704 x^{5} + 2748 x^{4} + 4704 x^{3} + 4544 x^{2} + 3168 x + 16456$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + 4 t x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 4 t + 10$
2.12.33.13 $x^{12} + 24 x^{11} + 208 x^{10} + 776 x^{9} + 1502 x^{8} + 3808 x^{7} + 5008 x^{6} + 6912 x^{5} + 7772 x^{4} + 7520 x^{3} + 5088 x^{2} + 3680 x + 1928$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T142) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(4 t^{2} + 12 t + 8\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 12 t^{2} + 2$
2.12.33.130 $x^{12} - 16 x^{11} + 332 x^{10} + 72 x^{9} + 2486 x^{8} + 8032 x^{7} + 18080 x^{6} + 32448 x^{5} + 36892 x^{4} + 37376 x^{3} + 25680 x^{2} + 12000 x + 9000$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T142) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(12 t^{2} + 12 t + 12\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 20 t^{2} + 10$
2.12.33.131 $x^{12} + 24 x^{11} + 184 x^{10} + 392 x^{9} - 222 x^{8} + 2496 x^{7} + 5040 x^{6} - 2016 x^{5} + 9308 x^{4} + 20512 x^{3} - 3904 x^{2} + 5792 x + 20344$ $2$ $4$ $3$ $33$ $C_4\wr C_3$ (as 12T94) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 30$
2.12.33.132 $x^{12} + 8 x^{11} + 268 x^{10} + 1904 x^{9} + 2042 x^{8} + 4512 x^{7} + 15280 x^{6} + 10944 x^{5} + 19932 x^{4} + 43424 x^{3} + 17072 x^{2} + 28480 x + 44824$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + \left(8 t + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 20 t + 22$
2.12.33.133 $x^{12} + 40 x^{10} - 160 x^{9} - 458 x^{8} - 512 x^{7} - 1904 x^{6} - 3648 x^{5} + 10780 x^{4} - 4992 x^{3} + 22848 x^{2} + 26792$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 t x^{3} + \left(12 t^{2} + 4 t\right) x^{2} + 24 t^{2} + 28 t + 18$
2.12.33.134 $x^{12} - 16 x^{11} + 320 x^{10} + 32 x^{9} + 1590 x^{8} + 5952 x^{7} + 5792 x^{6} + 17472 x^{5} + 21420 x^{4} + 15552 x^{3} + 40896 x^{2} + 28296$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T142) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + \left(12 t^{2} + 8 t + 8\right) x^{2} + 24 t^{2} + 24 t + 18$
2.12.33.135 $x^{12} + 24 x^{11} + 252 x^{10} + 624 x^{9} + 1602 x^{8} + 960 x^{7} + 6768 x^{6} + 5184 x^{5} + 7548 x^{4} + 12448 x^{3} + 8688 x^{2} + 6976 x + 3384$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 4 t + 14$
2.12.33.136 $x^{12} + 20 x^{10} - 16 x^{9} + 378 x^{8} + 256 x^{7} + 4848 x^{6} + 5376 x^{5} + 26748 x^{4} + 21248 x^{3} + 59280 x^{2} + 22720 x + 47832$ $2$ $4$ $3$ $33$ $C_2^3.(C_2\times A_4)$ (as 12T104) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 28 t + 22$
2.12.33.137 $x^{12} + 12 x^{10} + 18 x^{8} + 288 x^{7} + 1744 x^{6} + 2880 x^{5} + 11052 x^{4} + 8128 x^{3} + 22192 x^{2} + 8064 x + 13912$ $2$ $4$ $3$ $33$ $C_4^3:C_6$ (as 12T141) $[3, 4]$ $[2, 2, 3, 3, 3, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(12 t^{2} + 12\right) x^{2} + 8 t x + 24 t^{2} + 22$
2.12.33.138 $x^{12} + 24 x^{11} + 180 x^{10} + 304 x^{9} - 618 x^{8} + 2912 x^{7} + 7264 x^{6} + 2912 x^{5} + 12220 x^{4} + 21600 x^{3} + 14704 x^{2} - 640 x + 10344$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T105) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(12 t^{2} + 8 t + 4\right) x^{2} + 8 t^{2} x + 12 t^{2} + 4 t + 26$
2.12.33.139 $x^{12} + 8 x^{11} + 28 x^{10} + 952 x^{9} + 2986 x^{8} + 6400 x^{7} + 10336 x^{6} + 15456 x^{5} + 13084 x^{4} + 15584 x^{3} + 11728 x^{2} + 1248 x + 5976$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(4 t^{2} + 12 t + 12\right) x^{2} + 8 x + 16 t^{2} + 4 t + 14$
2.12.33.14 $x^{12} + 24 x^{11} + 240 x^{10} + 432 x^{9} + 722 x^{8} + 1792 x^{7} + 9248 x^{6} - 256 x^{5} + 7676 x^{4} + 32288 x^{3} - 640 x^{2} - 5184 x + 22136$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + 8 t^{2} x^{2} + \left(8 t^{2} + 8 t\right) x + 4 t^{2} + 4 t + 30$
2.12.33.140 $x^{12} + 8 x^{11} + 252 x^{10} + 1824 x^{9} + 3778 x^{8} + 4224 x^{7} + 7616 x^{6} + 6816 x^{5} + 3388 x^{4} + 8672 x^{3} + 2960 x^{2} - 1344 x + 3384$ $2$ $4$ $3$ $33$ $C_2\wr C_6$ (as 12T134) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + \left(8 t^{2} + 4 t + 4\right) x^{2} + 8 t x + 4 t^{2} + 16 t + 14$
2.12.33.141 $x^{12} + 24 x^{11} + 264 x^{10} + 944 x^{9} + 2262 x^{8} + 4480 x^{7} + 11232 x^{6} + 18656 x^{5} + 20796 x^{4} + 39968 x^{3} + 54688 x^{2} + 23168 x + 52456$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t + 8\right) x^{2} + 8 t^{2} x + 28 t^{2} + 20 t + 26$
2.12.33.142 $x^{12} + 24 x^{11} + 200 x^{10} + 664 x^{9} + 1386 x^{8} + 6048 x^{7} + 8544 x^{6} + 23072 x^{5} + 25532 x^{4} + 42976 x^{3} + 47584 x^{2} + 25312 x + 44696$ $2$ $4$ $3$ $33$ $C_2^4.(C_2\times A_4)$ (as 12T143) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{6}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(8 t^{2} + 12 t + 8\right) x^{2} + 8 x + 16 t^{2} + 28 t + 30$
2.12.33.143 $x^{12} + 24 x^{11} + 216 x^{10} + 904 x^{9} + 2010 x^{8} + 3776 x^{7} + 4208 x^{6} + 6432 x^{5} + 4476 x^{4} + 3104 x^{3} + 1664 x^{2} + 416 x + 88$ $2$ $4$ $3$ $33$ $C_2^4:C_{12}$ (as 12T105) $[3, 4]$ $[2, 2, 3, 7/2, 7/2, 4]^{3}$ $t^{3} + t + 1$ $x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 6$
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