| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 12.4.12293120000000.1 |
$x^{12} - 2 x^{10} - 5 x^{8} - 4 x^{6} - x^{4} - 10 x^{2} + 5$ |
$12$ |
(4, 4) |
$2^{16}\cdot 5^{7}\cdot 7^{4}$ |
$3$ |
$12.325517900267316$ |
$26.50985484327206$ |
|
|
? |
$C_4\times S_4$ (as 12T53) |
trivial |
trivial |
$2$ |
$7$ |
$74.86133582325681$ |
$4$ |
$7$ |
| 12.4.6221455499788288.1 |
$x^{12} - 4 x^{11} + 9 x^{10} + 2 x^{9} - 42 x^{8} + 112 x^{7} - 99 x^{6} - 84 x^{5} + 366 x^{4} - 314 x^{3} + 137 x^{2} - 16 x - 1$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{7}$ |
$2$ |
$20.7089303088$ |
$44.95542621736403$ |
|
|
? |
$A_4:C_4$ (as 12T30) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$959.198751967$ |
$4$ |
$37$ |
| 12.8.6221455499788288.1 |
$x^{12} - 4 x^{11} + 3 x^{10} + 22 x^{9} - 76 x^{8} + 88 x^{7} + 59 x^{6} - 396 x^{5} + 624 x^{4} - 370 x^{3} - 33 x^{2} + 108 x - 27$ |
$12$ |
(8, 2) |
$2^{16}\cdot 37^{7}$ |
$2$ |
$20.7089303088$ |
$44.95542621736403$ |
|
|
? |
$C_2^3.S_4$ (as 12T107) |
trivial |
$[2]$ |
$2$ |
$9$ |
$4026.8619158$ |
$7$ |
$37$ |
| 12.4.6221455499788288.2 |
$x^{12} - 10 x^{10} + 43 x^{8} - 100 x^{6} + 143 x^{4} - 130 x^{2} + 37$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{7}$ |
$2$ |
$20.7089303088$ |
$44.95542621736403$ |
|
|
? |
$C_2^3.S_4$ (as 12T102) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1120.15946834$ |
$4$ |
$37$ |
| 12.4.118210688000000000.1 |
$x^{12} - 2 x^{11} - 2 x^{10} - 8 x^{9} + 46 x^{8} + 56 x^{7} - 376 x^{6} + 112 x^{5} + 768 x^{4} - 304 x^{3} - 332 x^{2} - 664 x - 4$ |
$12$ |
(4, 4) |
$2^{16}\cdot 5^{9}\cdot 31^{4}$ |
$3$ |
$26.4680164212$ |
$98.87795117748159$ |
|
|
? |
$A_4^2:C_4$ (as 12T159) |
trivial |
$[2]$ |
$2$ |
$7$ |
$8075.99960902$ |
$3$ |
$31$ |
| 12.4.126546736084484096.1 |
$x^{12} - 2 x^{11} + 4 x^{10} - 4 x^{9} - 8 x^{8} + 20 x^{7} - 36 x^{6} + 60 x^{5} - 16 x^{4} - 24 x^{3} + 64 x^{2} - 248 x - 100$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{4}\cdot 101^{3}$ |
$3$ |
$26.6187451948$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
trivial |
$[2]$ |
$2$ |
$7$ |
$9503.79911049$ |
$3$ |
$101$ |
| 12.4.220399211520000000.1 |
$x^{12} - 3 x^{10} + 18 x^{8} + 37 x^{6} + 18 x^{4} - 27 x^{2} + 5$ |
$12$ |
(4, 4) |
$2^{16}\cdot 3^{16}\cdot 5^{7}$ |
$3$ |
$27.878378044494372$ |
$43.35308454357693$ |
|
|
? |
$C_2^3.S_4$ (as 12T102) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$12429.980367857583$ |
$4$ |
$5$ |
| 12.4.344305662203068416.1 |
$x^{12} - 4 x^{11} + 9 x^{10} - 20 x^{9} + 28 x^{8} - 20 x^{7} - 3 x^{6} - 22 x^{5} + 54 x^{4} + 50 x^{3} + 31 x^{2} + 10 x - 1$ |
$12$ |
(4, 4) |
$2^{16}\cdot 3^{3}\cdot 37^{4}\cdot 47^{3}$ |
$4$ |
$28.9342356206$ |
$216.44185373499275$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$7863.72441263$ |
$4$ |
$47$ |
| 12.4.345438387690078208.1 |
$x^{12} - 2 x^{11} - 4 x^{10} - 4 x^{9} + 16 x^{8} + 12 x^{7} - 140 x^{6} + 28 x^{5} + 144 x^{4} - 24 x^{3} - 176 x^{2} - 296 x - 148$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{3}\cdot 101^{4}$ |
$3$ |
$28.942156206346073$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
trivial |
$[2]$ |
$2$ |
$7$ |
$27007.552444694287$ |
$3$ |
$101$ |
| 12.0.173...424.1 |
$x^{12} - 4 x^{11} + 19 x^{10} - 88 x^{9} + 336 x^{8} - 976 x^{7} + 2299 x^{6} - 3930 x^{5} + 5422 x^{4} - 5254 x^{3} + 3585 x^{2} - 1646 x + 391$ |
$12$ |
(0, 6) |
$2^{16}\cdot 37^{6}\cdot 101^{3}$ |
$3$ |
$48.590854115782896$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$37353.89360784618$ |
$0$ |
$101$ |
| 12.4.173...424.1 |
$x^{12} - 4 x^{11} + 10 x^{10} - 52 x^{9} + 148 x^{8} - 192 x^{7} + 228 x^{6} - 232 x^{5} - 1348 x^{4} + 4240 x^{3} - 5184 x^{2} + 4856 x - 2404$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{6}\cdot 101^{3}$ |
$3$ |
$48.590854115782896$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$88277.54820927241$ |
$4$ |
$101$ |
| 12.4.173...424.2 |
$x^{12} - 2 x^{11} - 11 x^{10} + 6 x^{9} + 72 x^{8} + 38 x^{7} - 223 x^{6} - 336 x^{5} + 656 x^{4} - 52 x^{3} - 303 x^{2} + 568 x + 137$ |
$12$ |
(4, 4) |
$2^{16}\cdot 37^{6}\cdot 101^{3}$ |
$3$ |
$48.590854115782896$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 12T239) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$90703.94429783209$ |
$4$ |
$101$ |
| 15.7.554...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 387 x^{5} + 100 x^{4} + 185 x^{3} - 50 x^{2} - 60 x + 8$ |
$15$ |
(7, 4) |
$2^{18}\cdot 5^{15}\cdot 37^{5}$ |
$3$ |
$38.2771775947$ |
|
|
|
? |
$D_5^3.D_6$ (as 15T68) |
trivial |
trivial |
$2$ |
$10$ |
$5557858.58989$ |
$7$ |
$37$ |
| 16.12.272...456.1 |
$x^{16} - 11 x^{14} + 30 x^{12} + 53 x^{10} - 330 x^{8} + 337 x^{6} + 49 x^{4} - 92 x^{2} + 16$ |
$16$ |
(12, 2) |
$2^{16}\cdot 3^{4}\cdot 8461^{4}$ |
$3$ |
$25.2444395331$ |
$477.4218610180042$ |
|
|
? |
$C_2^4.C_2^6:S_4$ (as 16T1815) |
trivial |
trivial |
$2$ |
$13$ |
$447406.814747$ |
$12$ |
$8461$ |
| 16.0.141...016.1 |
$x^{16} - 5 x^{15} + 41 x^{14} - 259 x^{13} + 1372 x^{12} - 5406 x^{11} + 18891 x^{10} - 56655 x^{9} + 166716 x^{8} - 446154 x^{7} + 1812061 x^{6} - 5194431 x^{5} + 14474071 x^{4} - 33842039 x^{3} + 51923808 x^{2} - 54532972 x + 32633056$ |
$16$ |
(0, 8) |
$2^{16}\cdot 7^{8}\cdot 373^{8}$ |
$3$ |
$102.195890328$ |
$672.9169538973321$ |
✓ |
|
|
$C_2^7.S_4$ (as 16T1528) |
$[2, 2, 2, 1340]$ |
$[2, 2, 2, 1340]$ |
$2$ |
$7$ |
$1832893.2546$ |
$0$ |
$373$ |
| 16.0.528...968.1 |
$x^{16} - 2 x^{15} + 58 x^{14} - 102 x^{13} + 1579 x^{12} - 3700 x^{11} + 24583 x^{10} - 57538 x^{9} + 267399 x^{8} - 549368 x^{7} + 1493175 x^{6} - 1428550 x^{5} + 4310250 x^{4} - 4357918 x^{3} - 45383791 x^{2} + 50182964 x + 463221588$ |
$16$ |
(0, 8) |
$2^{16}\cdot 7^{8}\cdot 373^{9}$ |
$3$ |
$147.9671243231501$ |
$672.9169538973321$ |
✓ |
|
|
$C_2^7.S_4$ (as 16T1522) |
$[2, 2, 2680]$ |
$[2, 2, 2680]$ |
$2$ |
$7$ |
$25730913.19761381$ |
$0$ |
$373$ |
| 18.2.221...824.1 |
$x^{18} - 5 x^{17} + 5 x^{16} + 30 x^{15} - 98 x^{14} + 24 x^{13} + 378 x^{12} - 630 x^{11} - 275 x^{10} + 1781 x^{9} - 1269 x^{8} - 1486 x^{7} + 2494 x^{6} - 388 x^{5} - 558 x^{4} - 446 x^{3} + 59 x^{2} + 479 x - 197$ |
$18$ |
(2, 8) |
$2^{20}\cdot 11^{9}\cdot 19^{7}$ |
$3$ |
$22.5147527779$ |
$90.4466258093427$ |
|
|
|
$C_2^4.S_4^2$ (as 18T550) |
trivial |
$[2]$ |
$2$ |
$9$ |
$110487.747201$ |
$1$ |
$19$ |
| 18.2.113...936.1 |
$x^{18} - x^{17} + 3 x^{16} + 10 x^{15} + 2 x^{14} + 4 x^{13} + 24 x^{12} + 142 x^{11} - 225 x^{10} + 297 x^{9} + 373 x^{8} - 6 x^{7} + 1840 x^{6} - 4732 x^{5} + 1422 x^{4} + 3542 x^{3} - 927 x^{2} - 1349 x - 257$ |
$18$ |
(2, 8) |
$2^{20}\cdot 11^{6}\cdot 19^{10}$ |
$3$ |
$24.661945586896625$ |
$90.4466258093427$ |
|
|
|
$C_2^4.S_4^2$ (as 18T545) |
trivial |
$[2]$ |
$2$ |
$9$ |
$223875.4921708372$ |
$1$ |
$19$ |
| 18.6.229...464.2 |
$x^{18} - 12 x^{16} + 96 x^{14} - 531 x^{12} + 1974 x^{10} - 5124 x^{8} + 9261 x^{6} - 10584 x^{4} + 6174 x^{2} - 1029$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$33.116050347$ |
|
|
|
? |
$C_2^4.S_4^2$ (as 18T546) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$18946965.7706$ |
$4$ |
$7$ |
| 18.10.285...984.1 |
$x^{18} + 2 x^{16} - 85 x^{14} - 244 x^{12} + 887 x^{10} + 610 x^{8} - 1555 x^{6} - 288 x^{4} + 224 x^{2} - 16$ |
$18$ |
(10, 4) |
$2^{20}\cdot 37^{6}\cdot 101^{6}$ |
$3$ |
$33.5211419845$ |
$183.1860403967972$ |
|
|
|
$C_2^6:S_3^2$ (as 18T373) |
trivial |
trivial |
$2$ |
$13$ |
$24318155.1468$ |
$10$ |
$101$ |
| 18.10.285...984.2 |
$x^{18} - 10 x^{16} - 21 x^{14} + 184 x^{12} - x^{10} - 778 x^{8} + 693 x^{6} + 140 x^{4} - 176 x^{2} - 16$ |
$18$ |
(10, 4) |
$2^{20}\cdot 37^{6}\cdot 101^{6}$ |
$3$ |
$33.5211419845$ |
$183.1860403967972$ |
|
|
|
$C_2^6:S_3^2$ (as 18T373) |
trivial |
trivial |
$2$ |
$13$ |
$19355196.3347$ |
$10$ |
$101$ |
| 18.10.105...408.1 |
$x^{18} - 6 x^{17} + x^{16} + 52 x^{15} - 77 x^{14} - 110 x^{13} + 167 x^{12} + 628 x^{11} - 124 x^{10} - 3760 x^{9} + 916 x^{8} + 8144 x^{7} + 508 x^{6} - 12000 x^{5} - 4344 x^{4} + 7704 x^{3} + 1372 x^{2} - 1528 x + 148$ |
$18$ |
(10, 4) |
$2^{20}\cdot 37^{7}\cdot 101^{6}$ |
$3$ |
$40.967656703$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 18T376) |
trivial |
$[2]$ |
$2$ |
$13$ |
$347353162.895$ |
$9$ |
$101$ |
| 18.6.105...408.1 |
$x^{18} + 14 x^{16} + 18 x^{14} - 407 x^{12} - 1636 x^{10} - 1376 x^{8} + 1059 x^{6} + 1274 x^{4} + 18 x^{2} - 37$ |
$18$ |
(6, 6) |
$2^{20}\cdot 37^{7}\cdot 101^{6}$ |
$3$ |
$40.967656703$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 18T376) |
trivial |
$[2]$ |
$2$ |
$11$ |
$139931042.542$ |
$5$ |
$101$ |
| 18.10.105...408.2 |
$x^{18} - 6 x^{17} + 84 x^{15} - 248 x^{14} + 104 x^{13} + 951 x^{12} - 2366 x^{11} + 1684 x^{10} + 2916 x^{9} - 8092 x^{8} + 5786 x^{7} + 4085 x^{6} - 8608 x^{5} + 3866 x^{4} + 120 x^{3} - 502 x^{2} + 98 x - 1$ |
$18$ |
(10, 4) |
$2^{20}\cdot 37^{7}\cdot 101^{6}$ |
$3$ |
$40.967656703$ |
$183.1860403967972$ |
|
|
? |
$C_2^6:S_3^2$ (as 18T376) |
trivial |
$[2]$ |
$2$ |
$13$ |
$387352588.648$ |
$9$ |
$101$ |
| 18.6.262...384.1 |
$x^{18} - 27 x^{16} + 180 x^{14} - 270 x^{13} - 633 x^{12} + 2250 x^{11} + 3516 x^{10} + 5512 x^{9} + 23415 x^{8} + 31770 x^{7} + 39825 x^{6} + 113874 x^{5} + 191892 x^{4} + 229320 x^{3} + 262134 x^{2} + 197172 x + 59322$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$43.09049381891572$ |
$104.1620784659052$ |
|
|
? |
$C_2^4.S_4^2$ (as 18T545) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$217086717.51119798$ |
$4$ |
$7$ |
| 18.6.103...000.1 |
$x^{18} + 29 x^{16} + 138 x^{14} - 83 x^{12} - 1210 x^{10} - 719 x^{8} + 2221 x^{6} + 1664 x^{4} - 592 x^{2} - 148$ |
$18$ |
(6, 6) |
$2^{20}\cdot 5^{4}\cdot 37^{9}\cdot 59^{4}$ |
$4$ |
$46.4973253548$ |
$1992.1871302009247$ |
|
|
? |
$A_4^3.S_4$ (as 18T717) |
trivial |
$[2]$ |
$2$ |
$11$ |
$642233875.37$ |
$5$ |
$59$ |
| 18.6.395...000.1 |
$x^{18} - 6 x^{17} + 16 x^{16} - 38 x^{15} - 143 x^{14} + 1736 x^{13} - 8444 x^{12} + 34704 x^{11} - 103525 x^{10} + 241450 x^{9} - 487144 x^{8} + 669658 x^{7} - 464501 x^{6} - 56456 x^{5} + 453512 x^{4} - 266620 x^{3} - 23004 x^{2} + 87780 x - 3404$ |
$18$ |
(6, 6) |
$2^{22}\cdot 5^{6}\cdot 53^{5}\cdot 229^{6}$ |
$4$ |
$73.5347971077$ |
|
|
|
? |
$A_4^3.(C_2^2\times S_4)$ (as 18T835) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$11$ |
$13642380533.8$ |
$3$ |
$229$ |
| 18.14.457...816.1 |
$x^{18} + 18 x^{16} - 882 x^{14} + 9177 x^{12} - 39816 x^{10} + 84672 x^{8} - 90993 x^{6} + 44982 x^{4} - 6174 x^{2} - 1029$ |
$18$ |
(14, 2) |
$2^{20}\cdot 3^{37}\cdot 7^{13}$ |
$3$ |
$84.2511045409$ |
|
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T590) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$1206769213680$ |
$12$ |
$7$ |
| 18.6.462...576.2 |
$x^{18} + 39 x^{16} + 468 x^{14} + 1852 x^{12} + 1038 x^{10} - 2910 x^{8} - 652 x^{6} + 828 x^{4} + 105 x^{2} - 1$ |
$18$ |
(6, 6) |
$2^{20}\cdot 3^{32}\cdot 47^{8}$ |
$3$ |
$84.3039532574$ |
$153.95792733529305$ |
|
|
|
$C_2^4.\PSOPlus(4,3)$ (as 18T466) |
$[6]$ |
$[2, 6]$ |
$2$ |
$11$ |
$19363177112.2$ |
$5$ |
$47$ |
| 18.14.636...784.1 |
$x^{18} - 30 x^{16} + 195 x^{14} + 1984 x^{12} - 29169 x^{10} + 107634 x^{8} - 80067 x^{6} - 88164 x^{4} + 87984 x^{2} - 9024$ |
$18$ |
(14, 2) |
$2^{26}\cdot 3^{25}\cdot 47^{9}$ |
$3$ |
$85.8101069284$ |
|
|
|
? |
$A_4:S_4^2.S_4$ (as 18T842) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$881725103387$ |
$11$ |
$47$ |
| 18.10.166...904.1 |
$x^{18} - x^{17} - 68 x^{16} + 89 x^{15} + 2057 x^{14} - 1606 x^{13} - 40921 x^{12} + 27359 x^{11} + 479099 x^{10} - 676118 x^{9} - 2160917 x^{8} + 6546211 x^{7} - 2964313 x^{6} - 11568026 x^{5} + 18623925 x^{4} - 24137575 x^{3} + 32448224 x^{2} - 2988729 x - 16312767$ |
$18$ |
(10, 4) |
$2^{20}\cdot 3^{4}\cdot 37^{2}\cdot 101^{6}\cdot 1161031^{2}$ |
$5$ |
$90.5165544787$ |
$8420337.149006974$ |
|
|
|
$C_3^6.C_4^3:S_4$ (as 18T927) |
trivial |
trivial |
$2$ |
$13$ |
$355664115457$ |
$10$ |
$1161031$ |
| 18.6.418...032.1 |
$x^{18} - 36 x^{16} + 234 x^{14} + 1857 x^{12} - 1728 x^{10} - 20394 x^{8} - 27417 x^{6} - 7794 x^{4} - 342 x^{2} - 3$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{37}\cdot 7^{12}$ |
$3$ |
$95.2728252261$ |
|
|
|
? |
$C_2^3:A_4^2.S_4$ (as 18T658) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$210832117966$ |
$5$ |
$7$ |
| 18.6.418...032.2 |
$x^{18} + 18 x^{16} - 162 x^{14} - 5325 x^{12} - 33462 x^{10} + 5364 x^{8} + 634065 x^{6} + 1461330 x^{4} - 15300 x^{2} - 363$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{37}\cdot 7^{12}$ |
$3$ |
$95.2728252261$ |
|
|
|
? |
$C_2^3:A_4^2.S_4$ (as 18T658) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$353444488280$ |
$4$ |
$7$ |
| 18.18.975...408.1 |
$x^{18} - 63 x^{16} + 1530 x^{14} - 19224 x^{12} + 138096 x^{10} - 582498 x^{8} + 1409982 x^{6} - 1801800 x^{4} + 984375 x^{2} - 109375$ |
$18$ |
(18, 0) |
$2^{26}\cdot 3^{36}\cdot 7^{13}$ |
$3$ |
$99.8647453103$ |
|
|
|
? |
$C_2^3:A_4^2.S_4$ (as 18T658) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$14027256565500$ |
$16$ |
$7$ |
| 18.6.652...216.3 |
$x^{18} + 60 x^{16} + 1104 x^{14} + 992 x^{12} - 166656 x^{10} - 1277184 x^{8} + 1652992 x^{6} + 24376320 x^{4} - 13750272 x^{2} - 2310144$ |
$18$ |
(6, 6) |
$2^{20}\cdot 3^{33}\cdot 47^{9}$ |
$3$ |
$110.98109417248871$ |
$153.95792733529305$ |
|
|
? |
$C_2^4.\PSOPlus(4,3)$ (as 18T464) |
$[2, 6]$ |
$[2, 2, 2, 6]$ |
$2$ |
$11$ |
$170261837446.71686$ |
$4$ |
$47$ |
| 18.6.131...776.1 |
$x^{18} - 4 x^{17} - 138 x^{16} + 696 x^{15} + 7427 x^{14} - 48052 x^{13} - 174252 x^{12} + 1690984 x^{11} + 573423 x^{10} - 31022940 x^{9} + 53414302 x^{8} + 239764776 x^{7} - 965195683 x^{6} + 374024484 x^{5} + 4350189816 x^{4} - 11199995144 x^{3} + 12808586512 x^{2} - 7360366800 x + 1729630192$ |
$18$ |
(6, 6) |
$2^{20}\cdot 37^{10}\cdot 2011^{2}\cdot 80282263^{2}$ |
$4$ |
$282.512589537$ |
$1332917399.6125185$ |
|
|
|
$C_3^6:(C_2^3.S_4)$ (as 18T818) |
$[3]$ |
$[3]$ |
$2$ |
$11$ |
$864185479262000$ |
$6$ |
$80282263$ |
| 18.14.142...000.1 |
$x^{18} - 126 x^{16} - 48 x^{15} + 3132 x^{14} + 7992 x^{13} + 144816 x^{12} - 398088 x^{11} - 5797944 x^{10} + 2711216 x^{9} - 15956352 x^{8} + 226818720 x^{7} + 1367392656 x^{6} - 3340243872 x^{5} + 109992960 x^{4} + 2436418944 x^{3} - 639447552 x - 142099456$ |
$18$ |
(14, 2) |
$2^{20}\cdot 3^{24}\cdot 5^{10}\cdot 37^{6}\cdot 151^{2}\cdot 919^{2}$ |
$6$ |
$283.828401803$ |
|
|
|
|
$C_3^6.(C_2^5.D_6)$ (as 18T866) |
trivial |
$[2]$ |
$2$ |
$15$ |
$20019756825100000$ |
$13$ |
$919$ |
| 18.6.430...000.1 |
$x^{18} - 8 x^{17} - 166 x^{16} + 992 x^{15} + 13787 x^{14} - 43792 x^{13} - 683200 x^{12} + 324296 x^{11} + 19442527 x^{10} + 35911624 x^{9} - 252163750 x^{8} - 1135946096 x^{7} - 309415211 x^{6} + 8778440352 x^{5} + 28005842636 x^{4} + 43101138376 x^{3} + 37441670032 x^{2} + 17657640432 x + 3533246224$ |
$18$ |
(6, 6) |
$2^{20}\cdot 5^{4}\cdot 19^{2}\cdot 37^{10}\cdot 30091^{2}\cdot 64621^{2}$ |
$6$ |
$342.926768378$ |
$1458158452.7782567$ |
|
|
|
$C_3^6:(C_2^3.S_4)$ (as 18T818) |
$[3]$ |
$[3]$ |
$2$ |
$11$ |
$5176965044360000$ |
$6$ |
$64621$ |
| 20.0.373...336.1 |
$x^{20} + 9 x^{18} + 65 x^{16} + 437 x^{14} + 1369 x^{12} + 2140 x^{10} + 1768 x^{8} + 760 x^{6} + 144 x^{4} + 16 x^{2} + 16$ |
$20$ |
(0, 10) |
$2^{16}\cdot 11^{8}\cdot 113^{8}$ |
$3$ |
$30.1031850284$ |
$346.42687713514096$ |
|
|
? |
$C_2^9.C_2^4:A_5$ (as 20T933) |
trivial |
trivial |
$2$ |
$9$ |
$8815644.08773$ |
$0$ |
$113$ |
| 20.12.971...216.3 |
$x^{20} - 2 x^{19} - 15 x^{18} + 21 x^{17} + 49 x^{16} - 10 x^{15} - 71 x^{14} + 96 x^{13} + 174 x^{12} - 788 x^{11} - 1551 x^{10} - 565 x^{9} + 2282 x^{8} + 4368 x^{7} + 3726 x^{6} + 1830 x^{5} + 92 x^{4} - 298 x^{3} - 68 x^{2} + 5 x + 1$ |
$20$ |
(12, 4) |
$2^{16}\cdot 33769^{6}$ |
$2$ |
$39.7538739696$ |
$7464.822346743425$ |
|
|
? |
$C_2^9.C_2^4:S_5$ (as 20T962) |
trivial |
trivial |
$2$ |
$15$ |
$604403525.998$ |
$12$ |
$33769$ |
| 20.0.975...000.1 |
$x^{20} + 30 x^{18} + 395 x^{16} + 2930 x^{14} + 13305 x^{12} + 39200 x^{10} + 79900 x^{8} + 109000 x^{6} + 88000 x^{4} + 50000 x^{2} + 10000$ |
$20$ |
(0, 10) |
$2^{28}\cdot 5^{16}\cdot 47^{8}$ |
$3$ |
$44.61255953983532$ |
|
|
|
|
$C_2^9.A_5^2.C_4$ (as 20T1025) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$133777304.43188025$ |
$0$ |
$47$ |
| 20.0.576...000.1 |
$x^{20} + 46 x^{18} + 932 x^{16} + 10957 x^{14} + 82799 x^{12} + 420299 x^{10} + 1451407 x^{8} + 3366365 x^{6} + 5017400 x^{4} + 4337750 x^{2} + 1651225$ |
$20$ |
(0, 10) |
$2^{16}\cdot 5^{6}\cdot 17^{8}\cdot 73^{8}$ |
$4$ |
$48.7555107587$ |
$1157.1052144438684$ |
✓ |
|
? |
$C_2\times C_4^4:A_5$ (as 20T565) |
$[6, 6]$ |
$[6, 6]$ |
$2$ |
$9$ |
$11911856.2581$ |
$0$ |
$73$ |
| 20.16.328...104.1 |
$x^{20} - 6 x^{19} + x^{18} + 21 x^{17} - 102 x^{16} + 1334 x^{15} - 3485 x^{14} - 840 x^{13} + 7595 x^{12} - 40626 x^{11} + 228412 x^{10} - 279903 x^{9} - 634103 x^{8} + 1697024 x^{7} - 862745 x^{6} - 723776 x^{5} + 757692 x^{4} - 108596 x^{3} - 63711 x^{2} + 16233 x - 109$ |
$20$ |
(16, 2) |
$2^{16}\cdot 33769^{7}$ |
$2$ |
$66.9584461153$ |
$27484.27286216627$ |
|
|
? |
$(C_2\times C_4^4).S_5$ (as 20T671) |
trivial |
$[2]$ |
$2$ |
$17$ |
$249520888476$ |
$15$ |
$33769$ |
| 20.20.430...000.1 |
$x^{20} - 57 x^{18} + 1206 x^{16} - 13082 x^{14} + 82149 x^{12} - 313876 x^{10} + 735568 x^{8} - 1025632 x^{6} + 780224 x^{4} - 261632 x^{2} + 18688$ |
$20$ |
(20, 0) |
$2^{24}\cdot 5^{4}\cdot 17^{8}\cdot 73^{9}$ |
$4$ |
$67.8742199201$ |
|
|
|
? |
$C_2^9.C_2\wr A_5$ (as 20T968) |
trivial |
$[2, 2, 2]$ |
$2$ |
$19$ |
$1387265040780$ |
$17$ |
$73$ |
| 20.4.481...144.1 |
$x^{20} + 32 x^{18} + 387 x^{16} + 2136 x^{14} + 4434 x^{12} - 5672 x^{10} - 40306 x^{8} - 57144 x^{6} - 20771 x^{4} + 1256 x^{2} + 959$ |
$20$ |
(4, 8) |
$2^{20}\cdot 7\cdot 11^{8}\cdot 29^{2}\cdot 113^{8}\cdot 137$ |
$6$ |
$68.2573113208$ |
|
|
|
|
$C_2^{10}.C_2\wr A_5$ (as 20T995) |
$[6]$ |
$[2, 2, 6]$ |
$2$ |
$11$ |
$13532493362.9$ |
$2$ |
$137$ |
| 20.12.160...848.1 |
$x^{20} - 12 x^{18} - 9 x^{16} + 408 x^{14} - 270 x^{12} - 3616 x^{10} + 2230 x^{8} + 11688 x^{6} - 5155 x^{4} - 12564 x^{2} + 3203$ |
$20$ |
(12, 4) |
$2^{20}\cdot 11^{8}\cdot 29^{2}\cdot 113^{8}\cdot 3203$ |
$5$ |
$72.4996806949$ |
|
|
|
|
$C_2^{10}.C_2\wr A_5$ (as 20T995) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$886245264778$ |
$9$ |
$3203$ |
| 20.20.201...600.1 |
$x^{20} - 62 x^{18} + 1453 x^{16} - 16912 x^{14} + 111306 x^{12} - 442604 x^{10} + 1088202 x^{8} - 1626688 x^{6} + 1374869 x^{4} - 537990 x^{2} + 42025$ |
$20$ |
(20, 0) |
$2^{28}\cdot 5^{2}\cdot 17^{8}\cdot 73^{10}$ |
$4$ |
$82.2583498334$ |
|
|
|
|
$C_2^9.C_2\wr A_5$ (as 20T963) |
trivial |
$[2, 2, 2]$ |
$2$ |
$19$ |
$10745359176600$ |
$17$ |
$73$ |
| 20.20.134...984.1 |
$x^{20} - 95 x^{18} + 3274 x^{16} - 51403 x^{14} + 408466 x^{12} - 1756047 x^{10} + 4367477 x^{8} - 6483648 x^{6} + 5673192 x^{4} - 2701520 x^{2} + 540304$ |
$20$ |
(20, 0) |
$2^{28}\cdot 33769^{7}$ |
$2$ |
$101.490026045$ |
|
|
|
? |
$(C_2\times C_4^4).S_5$ (as 20T671) |
trivial |
$[2, 2]$ |
$2$ |
$19$ |
$51393314573700$ |
$18$ |
$33769$ |
| 20.0.428...000.1 |
$x^{20} - x^{19} - 38 x^{18} + 116 x^{17} + 248 x^{16} - 1876 x^{15} + 4112 x^{14} - 4824 x^{13} + 3088 x^{12} + 11664 x^{11} - 67904 x^{10} + 109152 x^{9} + 87936 x^{8} - 513792 x^{7} + 459904 x^{6} + 618624 x^{5} - 1293056 x^{4} + 310272 x^{3} + 884736 x^{2} - 940032 x + 331776$ |
$20$ |
(0, 10) |
$2^{22}\cdot 5^{18}\cdot 7^{10}\cdot 31^{2}\cdot 37^{8}\cdot 53^{2}$ |
$6$ |
$214.585051699$ |
|
|
|
|
$C_5^4.C_4^3.A_4.C_4$ (as 20T987) |
trivial |
trivial |
$2$ |
$9$ |
$60794029758500000$ |
$0$ |
$53$ |
| 20.8.126...336.1 |
$x^{20} - 2 x^{19} + 215 x^{18} - 139 x^{17} - 73514 x^{16} - 24888 x^{15} - 9472091 x^{14} + 38501650 x^{13} + 882524587 x^{12} - 487339624 x^{11} + 77538975544 x^{10} - 28188076428 x^{9} + 343782219594 x^{8} - 1555740040772 x^{7} - 37339633831812 x^{6} - 16314854119744 x^{5} - 503801026916788 x^{4} + 2184437076106784 x^{3} + 562008177850824 x^{2} - 2731674661381760 x + 1514333352476884$ |
$20$ |
(8, 6) |
$2^{16}\cdot 33769^{10}$ |
$2$ |
$319.950723501$ |
$27484.27286216627$ |
|
|
? |
$C_2\times C_4^4:S_5$ (as 20T679) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$127493122875000000$ |
$7$ |
$33769$ |
