| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 15.7.306...241.1 |
$x^{15} - 6 x^{14} + 13 x^{13} - 10 x^{12} - 9 x^{11} + 30 x^{10} - 38 x^{9} + 45 x^{8} - 19 x^{7} - 48 x^{6} + 47 x^{5} - 38 x^{4} + 34 x^{3} + 5 x^{2} - 7 x + 1$ |
$15$ |
[7,4] |
$11^{12}\cdot 23^{2}\cdot 43^{2}$ |
$3$ |
$17.0794410507$ |
$400.82706302115287$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$10$ |
$3397.28173407$ |
| 15.15.886...529.1 |
$x^{15} - x^{14} - 22 x^{13} + 17 x^{12} + 166 x^{11} - 102 x^{10} - 533 x^{9} + 270 x^{8} + 729 x^{7} - 352 x^{6} - 393 x^{5} + 173 x^{4} + 80 x^{3} - 27 x^{2} - 6 x + 1$ |
$15$ |
[15,0] |
$7^{10}\cdot 11^{12}$ |
$2$ |
$24.9179804908$ |
$24.91798049084744$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$286717.64844$ |
| 15.15.587...409.1 |
$x^{15} - 6 x^{14} + x^{13} + 56 x^{12} - 89 x^{11} - 122 x^{10} + 358 x^{9} - 53 x^{8} - 418 x^{7} + 271 x^{6} + 122 x^{5} - 158 x^{4} + 22 x^{3} + 22 x^{2} - 9 x + 1$ |
$15$ |
[15,0] |
$11^{12}\cdot 109^{2}\cdot 397^{2}$ |
$3$ |
$28.2667849864$ |
$8393.159659599982$ |
|
|
✓ |
$C_3\wr C_5$ (as 15T36) |
trivial |
$2$ |
$14$ |
$850238.217539$ |
| 15.15.848...401.1 |
$x^{15} - 4 x^{14} - 9 x^{13} + 54 x^{12} - 7 x^{11} - 226 x^{10} + 218 x^{9} + 293 x^{8} - 500 x^{7} + 15 x^{6} + 314 x^{5} - 152 x^{4} - 28 x^{3} + 40 x^{2} - 11 x + 1$ |
$15$ |
[15,0] |
$11^{12}\cdot 52009^{2}$ |
$2$ |
$28.9684071107$ |
$9487.821026459433$ |
|
|
✓ |
$C_3\wr C_5$ (as 15T36) |
trivial |
$2$ |
$14$ |
$1056561.55278$ |
| 15.15.109...121.1 |
$x^{15} - 27 x^{13} - 4 x^{12} + 252 x^{11} + 60 x^{10} - 976 x^{9} - 288 x^{8} + 1473 x^{7} + 384 x^{6} - 765 x^{5} - 168 x^{4} + 150 x^{3} + 27 x^{2} - 9 x - 1$ |
$15$ |
[15,0] |
$3^{20}\cdot 11^{12}$ |
$2$ |
$29.4629223441$ |
$29.46292234405376$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$967645.576239$ |
| 15.5.281...072.1 |
$x^{15} - 5 x^{14} + 10 x^{13} + 2 x^{12} - 43 x^{11} + 71 x^{10} - 52 x^{9} + 24 x^{8} - 12 x^{7} - 76 x^{6} + 160 x^{5} - 80 x^{4} - 96 x^{3} + 96 x^{2} - 32$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{12}\cdot 43\cdot 197\cdot 1033$ |
$5$ |
$31.3764023494$ |
$73886.12521996467$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$9$ |
$183908.779975$ |
| 15.7.334...489.1 |
$x^{15} - 6 x^{14} + 14 x^{13} - 2 x^{12} - 81 x^{11} + 267 x^{10} - 478 x^{9} + 345 x^{8} + 603 x^{7} - 1896 x^{6} + 2450 x^{5} - 2082 x^{4} + 445 x^{3} + 2020 x^{2} - 2460 x + 859$ |
$15$ |
[7,4] |
$11^{12}\cdot 23^{2}\cdot 67^{4}$ |
$3$ |
$31.7417699914$ |
$538.7177286092511$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$10$ |
$316012.234645$ |
| 15.11.461...728.1 |
$x^{15} - 18 x^{13} - 12 x^{12} + 90 x^{11} + 120 x^{10} + 13 x^{9} - 54 x^{8} - 522 x^{7} - 1304 x^{6} - 1053 x^{5} + 234 x^{4} + 984 x^{3} + 720 x^{2} + 240 x + 32$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{15}\cdot 11^{12}$ |
$3$ |
$32.42814204$ |
$133.7061122075245$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$12$ |
$1076539.51981$ |
| 15.15.432...129.1 |
$x^{15} - 2 x^{14} - 33 x^{13} + 46 x^{12} + 402 x^{11} - 362 x^{10} - 2214 x^{9} + 1335 x^{8} + 5700 x^{7} - 2740 x^{6} - 6581 x^{5} + 2926 x^{4} + 2758 x^{3} - 1103 x^{2} - 373 x + 131$ |
$15$ |
[15,0] |
$11^{12}\cdot 13^{10}$ |
$2$ |
$37.6480988096$ |
$37.648098809616535$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$5243886.21648$ |
| 15.7.522...529.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 25 x^{12} - 39 x^{11} + 325 x^{10} - 886 x^{9} + 1475 x^{8} - 714 x^{7} - 3448 x^{6} + 9908 x^{5} - 13758 x^{4} + 11749 x^{3} - 6069 x^{2} + 1604 x - 131$ |
$15$ |
[7,4] |
$11^{12}\cdot 23\cdot 38281\cdot 189223$ |
$4$ |
$38.1264600294$ |
$2779435.915025367$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$10$ |
$1332210.24405$ |
| 15.7.106...744.1 |
$x^{15} - 15 x^{13} - 6 x^{12} + 90 x^{11} + 72 x^{10} - 282 x^{9} - 324 x^{8} + 513 x^{7} + 768 x^{6} - 567 x^{5} - 1206 x^{4} + 164 x^{3} + 1080 x^{2} + 480 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 23$ |
$4$ |
$39.9672182762$ |
$614.0458551912413$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$10$ |
$2211657.27405$ |
| 15.11.578...009.2 |
$x^{15} - 27 x^{13} - 31 x^{12} + 252 x^{11} + 564 x^{10} - 664 x^{9} - 3123 x^{8} - 1641 x^{7} + 5490 x^{6} + 8388 x^{5} - 753 x^{4} - 9231 x^{3} - 3159 x^{2} + 3186 x + 659$ |
$15$ |
[11,2] |
$3^{20}\cdot 11^{12}\cdot 23^{2}$ |
$3$ |
$44.7547909169$ |
$291.26858881174$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$12$ |
$11715038.8016$ |
| 15.1.849...496.1 |
$x^{15} + 6 x^{13} - 4 x^{12} - 45 x^{11} + 192 x^{10} + 630 x^{9} + 2088 x^{8} + 252 x^{7} - 6304 x^{6} + 4680 x^{5} + 33888 x^{4} + 101152 x^{3} + 103680 x^{2} + 100608 x - 12288$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 3^{17}\cdot 11^{12}$ |
$3$ |
$62.415659547583$ |
$69.39059404662864$ |
|
|
|
$D_{15}$ (as 15T2) |
$[5]$ |
$2$ |
$7$ |
$2326080105.1566486$ |
| 15.15.257...521.1 |
$x^{15} - 2 x^{14} - 63 x^{13} + 133 x^{12} + 1422 x^{11} - 3182 x^{10} - 14085 x^{9} + 33507 x^{8} + 61557 x^{7} - 157405 x^{6} - 111611 x^{5} + 318268 x^{4} + 77338 x^{3} - 252062 x^{2} - 16054 x + 47081$ |
$15$ |
[15,0] |
$11^{12}\cdot 31^{10}$ |
$2$ |
$67.1978344275$ |
$67.19783442751356$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$920271857.6558672$ |
| 15.15.844...176.1 |
$x^{15} - 4 x^{14} - 111 x^{13} + 405 x^{12} + 4716 x^{11} - 14598 x^{10} - 100506 x^{9} + 230773 x^{8} + 1181513 x^{7} - 1552520 x^{6} - 7465131 x^{5} + 2316335 x^{4} + 20264426 x^{3} + 10868994 x^{2} - 3113004 x - 898633$ |
$15$ |
[15,0] |
$2^{10}\cdot 11^{12}\cdot 23^{2}\cdot 89^{6}$ |
$4$ |
$98.8827477406$ |
$2387.8258297602165$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$14$ |
$15372643736.2$ |
| 15.15.309...129.2 |
$x^{15} - 3 x^{14} - 114 x^{13} + 165 x^{12} + 5277 x^{11} + 309 x^{10} - 119015 x^{9} - 163851 x^{8} + 1201692 x^{7} + 3201011 x^{6} - 2654712 x^{5} - 17750946 x^{4} - 19922550 x^{3} - 3294435 x^{2} + 4535715 x + 831403$ |
$15$ |
[15,0] |
$3^{20}\cdot 7^{10}\cdot 11^{12}$ |
$3$ |
$107.813839968$ |
$107.81383996755932$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
$[3]$ |
$2$ |
$14$ |
$5252645612.166227$ |
| 15.1.406...296.1 |
$x^{15} - 2 x^{14} - 23 x^{13} + 40 x^{12} + 271 x^{11} - 362 x^{10} + 815 x^{9} + 10076 x^{8} - 10840 x^{7} - 64768 x^{6} + 21392 x^{5} + 92864 x^{4} + 48000 x^{3} - 339456 x^{2} + 331776 x - 147456$ |
$15$ |
[1,7] |
$-\,2^{21}\cdot 3^{7}\cdot 7^{10}\cdot 11^{12}$ |
$4$ |
$109.80229587200682$ |
$122.07267524640429$ |
|
|
|
$D_{15}$ (as 15T2) |
$[15]$ |
$2$ |
$7$ |
$387983860119.02954$ |
| 15.15.572...729.1 |
$x^{15} - 2 x^{14} - 123 x^{13} + 152 x^{12} + 5870 x^{11} - 2956 x^{10} - 136528 x^{9} - 22067 x^{8} + 1590440 x^{7} + 1155822 x^{6} - 8394345 x^{5} - 9635844 x^{4} + 13947752 x^{3} + 17818309 x^{2} - 4647121 x - 4845499$ |
$15$ |
[15,0] |
$11^{12}\cdot 67^{10}$ |
$2$ |
$112.330411523$ |
$112.33041152311623$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$35980252831.5571$ |
| 15.15.134...929.1 |
$x^{15} - 2 x^{14} - 133 x^{13} + 326 x^{12} + 6618 x^{11} - 19414 x^{10} - 150182 x^{9} + 529243 x^{8} + 1451632 x^{7} - 6655484 x^{6} - 2779461 x^{5} + 32472178 x^{4} - 23518862 x^{3} - 22419019 x^{2} + 15844999 x + 3358343$ |
$15$ |
[15,0] |
$11^{12}\cdot 73^{10}$ |
$2$ |
$118.940398219$ |
$118.94039821882505$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$35246330370.40924$ |
| 15.15.297...921.1 |
$x^{15} - 2 x^{14} - 143 x^{13} + 8246 x^{11} + 14904 x^{10} - 219872 x^{9} - 786687 x^{8} + 2075724 x^{7} + 14598886 x^{6} + 12430527 x^{5} - 75224192 x^{4} - 235831716 x^{3} - 288431111 x^{2} - 160431365 x - 31658639$ |
$15$ |
[15,0] |
$11^{12}\cdot 79^{10}$ |
$2$ |
$125.371515493$ |
$125.37151549284967$ |
|
✓ |
? |
$C_{15}$ (as 15T1) |
trivial |
$2$ |
$14$ |
$61238384087.82688$ |
| 16.16.111...496.1 |
$x^{16} - 2 x^{15} - 428 x^{14} + 1320 x^{13} + 62092 x^{12} - 220480 x^{11} - 3633464 x^{10} + 12204344 x^{9} + 81935950 x^{8} - 175605868 x^{7} - 729549480 x^{6} + 168712188 x^{5} + 1147884592 x^{4} - 3407876 x^{3} - 91633952 x^{2} + 2724436 x + 1022790$ |
$16$ |
[16,0] |
$2^{30}\cdot 7^{10}\cdot 11^{12}\cdot 43^{8}$ |
$4$ |
$490.225906804$ |
$599.346965909669$ |
|
|
? |
$F_{16}$ (as 16T447) |
trivial |
$2$ |
$15$ |
$99361010062300000$ |
| 20.8.765...089.1 |
$x^{20} - 5 x^{18} - 5 x^{17} + 9 x^{16} + 20 x^{15} + 4 x^{14} - 26 x^{13} - 35 x^{12} - 2 x^{11} + 39 x^{10} + 39 x^{9} - 3 x^{8} - 34 x^{7} - 25 x^{6} + x^{5} + 17 x^{4} + 10 x^{3} - 3 x - 1$ |
$20$ |
[8,6] |
$11^{16}\cdot 23\cdot 38281\cdot 189223$ |
$4$ |
$24.7855408301$ |
$2779435.915025367$ |
|
|
✓ |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$13$ |
$2324096.69771$ |
| 20.0.289...989.1 |
$x^{20} - 4 x^{17} + 25 x^{16} - 31 x^{14} - 36 x^{13} + 184 x^{12} + 60 x^{11} - 157 x^{10} - 149 x^{9} + 445 x^{8} - 27 x^{7} - 180 x^{6} + 67 x^{5} + 156 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 229^{5}$ |
$2$ |
$26.4894547313$ |
$103.04617822247701$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$9$ |
$957497.704734$ |
| 20.4.374...621.1 |
$x^{20} - 4 x^{17} + 5 x^{16} + 2 x^{14} - 16 x^{13} + 10 x^{12} + 5 x^{11} + 6 x^{10} - 24 x^{9} + 8 x^{8} + 10 x^{7} + 6 x^{6} - 17 x^{5} + 3 x^{4} + 5 x^{3} + 2 x^{2} - 4 x + 1$ |
$20$ |
[4,8] |
$11^{16}\cdot 109\cdot 7478768329$ |
$3$ |
$26.8334786166$ |
$6148121.439266359$ |
|
|
✓ |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$11$ |
$2340177.30654$ |
| 20.0.515...177.1 |
$x^{20} + 9 x^{18} - 4 x^{17} + 53 x^{16} - 20 x^{15} + 151 x^{14} - 68 x^{13} + 368 x^{12} - 76 x^{11} + 496 x^{10} - 166 x^{9} + 634 x^{8} - 55 x^{7} + 277 x^{6} + 61 x^{5} + 175 x^{4} + x^{3} + 12 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 257^{5}$ |
$2$ |
$27.2644931779$ |
$109.16431898404717$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$9$ |
$831805.977332$ |
| 20.6.645...571.1 |
$x^{20} - 5 x^{19} + 10 x^{18} - 10 x^{17} + 4 x^{16} + 3 x^{15} - 6 x^{14} + 4 x^{13} - 5 x^{12} + 12 x^{11} - 12 x^{10} + 4 x^{9} + 3 x^{8} - 6 x^{7} + 3 x^{6} + 3 x^{4} - 3 x^{3} - 1$ |
$20$ |
[6,7] |
$-\,11^{16}\cdot 48313\cdot 29095747$ |
$3$ |
$27.5745747786$ |
$8073482.475245251$ |
|
|
✓ |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$12$ |
$4006817.24649$ |
| 20.10.834...523.1 |
$x^{20} - 4 x^{17} - 25 x^{16} - 31 x^{14} + 36 x^{13} + 184 x^{12} + 60 x^{11} + 157 x^{10} - 149 x^{9} - 361 x^{8} + 27 x^{7} - 180 x^{6} - 69 x^{5} + 154 x^{4} + 4 x^{3} + 3 x^{2} - 3 x - 1$ |
$20$ |
[10,5] |
$-\,11^{16}\cdot 283^{5}$ |
$2$ |
$27.9293454037$ |
$114.55323701805673$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$14$ |
$11612148.1752$ |
| 20.10.421...648.1 |
$x^{20} - 10 x^{19} + 48 x^{18} - 144 x^{17} + 273 x^{16} - 258 x^{15} - 130 x^{14} + 778 x^{13} - 1091 x^{12} + 624 x^{11} + 195 x^{10} - 538 x^{9} + 281 x^{8} + 28 x^{7} - 66 x^{6} + 10 x^{5} - 6 x^{4} + 4 x^{3} - x^{2} + 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 11^{16}\cdot 43\cdot 197\cdot 1033$ |
$5$ |
$30.2862772678$ |
|
|
|
? |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$14$ |
$29995717.6677$ |
| 20.8.482...344.1 |
$x^{20} - 2 x^{19} - 14 x^{18} + 22 x^{17} + 65 x^{16} - 56 x^{15} + 4 x^{14} - 276 x^{13} - 1269 x^{12} + 2222 x^{11} + 5220 x^{10} - 5048 x^{9} - 8450 x^{8} + 1138 x^{7} + 2760 x^{6} + 3332 x^{5} + 10791 x^{4} + 7590 x^{3} - 6996 x^{2} - 10164 x - 3883$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 43^{2}$ |
$4$ |
$38.3865225313$ |
|
|
|
? |
$C_2^{10}.C_3:S_3^4:C_5$ (as 20T1043) |
trivial |
$2$ |
$13$ |
$190494394.012$ |
| 20.12.482...344.1 |
$x^{20} - 6 x^{19} + 26 x^{18} - 50 x^{17} - 34 x^{16} + 578 x^{15} - 1974 x^{14} + 2608 x^{13} + 3033 x^{12} - 20388 x^{11} + 38182 x^{10} - 7852 x^{9} - 83941 x^{8} + 122334 x^{7} - 50050 x^{6} - 10512 x^{5} + 8489 x^{4} - 440 x^{3} - 296 x^{2} + 40 x - 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 43^{2}$ |
$4$ |
$38.3865225313$ |
|
|
|
? |
$C_2^{10}.C_3:S_3^4:C_5$ (as 20T1043) |
trivial |
$2$ |
$15$ |
$511143231.37$ |
| 20.8.482...344.2 |
$x^{20} - 6 x^{19} + 12 x^{18} - 28 x^{17} + 100 x^{16} + 68 x^{15} - 1134 x^{14} + 1656 x^{13} + 1524 x^{12} - 5802 x^{11} + 4430 x^{10} + 4166 x^{9} - 13167 x^{8} + 5002 x^{7} + 14782 x^{6} - 8746 x^{5} - 10182 x^{4} + 4510 x^{3} + 4130 x^{2} - 546 x - 529$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 43^{2}$ |
$4$ |
$38.3865225313$ |
|
|
|
? |
$C_2^{10}.C_3:S_3^4:C_5$ (as 20T1043) |
trivial |
$2$ |
$13$ |
$217512044.033$ |
| 20.20.758...777.1 |
$x^{20} - x^{19} - 39 x^{18} + 28 x^{17} + 593 x^{16} - 302 x^{15} - 4531 x^{14} + 1664 x^{13} + 18779 x^{12} - 5250 x^{11} - 42734 x^{10} + 10050 x^{9} + 52063 x^{8} - 11604 x^{7} - 32303 x^{6} + 7629 x^{5} + 8990 x^{4} - 2522 x^{3} - 785 x^{2} + 296 x - 23$ |
$20$ |
[20,0] |
$11^{16}\cdot 2777^{5}$ |
$2$ |
$49.4319926992$ |
$358.8410245617943$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$19$ |
$40125051391.3$ |
| 20.0.139...336.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 4 x^{17} + 90 x^{16} - 100 x^{15} + 340 x^{14} - 216 x^{13} + 1704 x^{12} + 208 x^{11} + 4144 x^{10} + 848 x^{9} + 7512 x^{8} - 1024 x^{7} + 6032 x^{6} - 3104 x^{5} + 3600 x^{4} - 1344 x^{3} + 480 x^{2} + 32$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{10}\cdot 11^{16}$ |
$3$ |
$50.9575056884$ |
$70.47869191420928$ |
|
|
? |
$C_5\times A_4$ (as 20T14) |
trivial |
$2$ |
$9$ |
$421620502.283$ |
| 20.0.618...625.1 |
$x^{20} - x^{19} - 4 x^{18} - 9 x^{17} + 40 x^{16} + 38 x^{15} - 353 x^{14} + 132 x^{13} + 2003 x^{12} + 428 x^{11} - 4601 x^{10} - 9617 x^{9} + 18106 x^{8} + 6013 x^{7} - 28464 x^{6} + 21165 x^{5} + 34436 x^{4} - 9024 x^{3} - 1728 x^{2} - 2304 x + 1024$ |
$20$ |
[0,10] |
$5^{10}\cdot 11^{16}\cdot 13^{10}$ |
$3$ |
$54.8998081068$ |
$84.18370816193149$ |
|
|
? |
$C_5\times A_4$ (as 20T14) |
$[2]$ |
$2$ |
$9$ |
$509760612.569$ |
| 20.12.892...056.1 |
$x^{20} - 8 x^{19} + 14 x^{18} + 48 x^{17} - 387 x^{16} + 1778 x^{15} - 3590 x^{14} - 6284 x^{13} + 47515 x^{12} - 114702 x^{11} + 172804 x^{10} + 35890 x^{9} - 1233511 x^{8} + 2908084 x^{7} - 1327992 x^{6} - 4901324 x^{5} + 8497166 x^{4} - 3917990 x^{3} - 2027746 x^{2} + 2551222 x - 680681$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 43^{4}$ |
$4$ |
$55.9146507185$ |
|
|
|
? |
$C_2^{10}.C_3:S_3^4:C_5$ (as 20T1043) |
trivial |
$2$ |
$15$ |
$20272351260.4$ |
| 20.0.923...256.1 |
$x^{20} + 12 x^{18} - 40 x^{17} + 92 x^{16} - 384 x^{15} + 1178 x^{14} - 2624 x^{13} + 7088 x^{12} - 17968 x^{11} + 36882 x^{10} - 73536 x^{9} + 150601 x^{8} - 269536 x^{7} + 417008 x^{6} - 620176 x^{5} + 882554 x^{4} - 1024768 x^{3} + 841468 x^{2} - 427248 x + 105137$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}\cdot 109^{2}\cdot 397^{2}$ |
$4$ |
$56.0119692985$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2, 2]$ |
$2$ |
$9$ |
$311476767.066$ |
| 20.0.133...784.1 |
$x^{20} + 8 x^{18} - 40 x^{17} + 64 x^{16} - 256 x^{15} + 998 x^{14} - 1984 x^{13} + 4748 x^{12} - 14032 x^{11} + 29430 x^{10} - 53280 x^{9} + 114733 x^{8} - 226976 x^{7} + 351560 x^{6} - 510416 x^{5} + 795266 x^{4} - 1072320 x^{3} + 1000716 x^{2} - 556976 x + 144497$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}\cdot 52009^{2}$ |
$3$ |
$57.0514900925$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2, 2]$ |
$2$ |
$9$ |
$397498342.144$ |
| 20.8.724...952.1 |
$x^{20} + 12 x^{18} - 16 x^{17} - 150 x^{16} - 576 x^{15} - 1256 x^{14} + 288 x^{13} + 5709 x^{12} + 29536 x^{11} + 73686 x^{10} + 113424 x^{9} + 198148 x^{8} + 363984 x^{7} + 727182 x^{6} + 1227680 x^{5} + 1433244 x^{4} + 1189152 x^{3} + 644976 x^{2} + 171720 x + 10449$ |
$20$ |
[8,6] |
$2^{40}\cdot 3^{15}\cdot 11^{16}$ |
$3$ |
$62.0890593736$ |
|
|
|
? |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$13$ |
$20351269618.0$ |
| 20.4.257...264.1 |
$x^{20} - 8 x^{19} + 28 x^{18} - 96 x^{17} + 182 x^{16} - 196 x^{15} + 1152 x^{14} - 632 x^{13} + 896 x^{12} - 6896 x^{11} - 23856 x^{10} - 34352 x^{9} - 17944 x^{8} + 95568 x^{7} + 340224 x^{6} + 768736 x^{5} + 1042864 x^{4} + 988800 x^{3} + 876320 x^{2} + 541568 x + 128864$ |
$20$ |
[4,8] |
$2^{30}\cdot 7^{10}\cdot 11^{16}\cdot 43^{2}$ |
$4$ |
$74.2258205267$ |
|
|
|
? |
$C_2^{10}:C_{15}$ (as 20T469) |
$[2]$ |
$2$ |
$11$ |
$33781347314.4$ |
| 20.12.488...424.1 |
$x^{20} - 54 x^{18} - 24 x^{17} + 1105 x^{16} + 192 x^{15} - 13082 x^{14} + 9072 x^{13} + 134752 x^{12} - 87632 x^{11} - 929712 x^{10} + 436832 x^{9} + 4288819 x^{8} - 2676352 x^{7} - 21289878 x^{6} - 12913408 x^{5} + 26267507 x^{4} + 31059248 x^{3} - 570370 x^{2} - 7533576 x + 978121$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 109^{2}\cdot 397^{2}$ |
$5$ |
$76.6396699353$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2]$ |
$2$ |
$15$ |
$278012462254$ |
| 20.8.488...424.1 |
$x^{20} - 2 x^{19} - 4 x^{18} + 44 x^{17} - 409 x^{16} + 1830 x^{15} - 4016 x^{14} + 4288 x^{13} + 6983 x^{12} - 55644 x^{11} + 116416 x^{10} - 888 x^{9} - 614364 x^{8} + 592280 x^{7} + 1061212 x^{6} - 1557242 x^{5} + 276207 x^{4} + 1864944 x^{3} - 1802916 x^{2} - 629648 x + 754469$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}\cdot 23^{2}\cdot 109^{2}\cdot 397^{2}$ |
$5$ |
$76.6396699353$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2]$ |
$2$ |
$13$ |
$91728824952.5$ |
| 20.8.246...616.1 |
$x^{20} - 24 x^{18} - 56 x^{17} + 216 x^{16} + 1920 x^{15} - 2098 x^{14} - 18832 x^{13} - 13196 x^{12} + 165712 x^{11} + 282510 x^{10} - 1360880 x^{9} - 932811 x^{8} + 3985568 x^{7} + 11536648 x^{6} - 37320112 x^{5} + 16993074 x^{4} + 40402304 x^{3} - 43803716 x^{2} + 390352 x + 10182481$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}\cdot 43^{2}\cdot 52009^{2}$ |
$4$ |
$83.1024518799$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2]$ |
$2$ |
$13$ |
$254611690444$ |
| 20.20.608...689.1 |
$x^{20} - x^{19} - 54 x^{18} + 39 x^{17} + 1162 x^{16} - 590 x^{15} - 12841 x^{14} + 4472 x^{13} + 78424 x^{12} - 18184 x^{11} - 265853 x^{10} + 38670 x^{9} + 479629 x^{8} - 35258 x^{7} - 425102 x^{6} - 2135 x^{5} + 161071 x^{4} + 17687 x^{3} - 18671 x^{2} - 3172 x + 89$ |
$20$ |
[20,0] |
$11^{16}\cdot 163^{10}$ |
$2$ |
$86.937660744$ |
$203.19166282197943$ |
|
|
? |
$C_5\times A_4$ (as 20T14) |
trivial |
$2$ |
$19$ |
$8339520574340$ |
| 20.4.476...136.1 |
$x^{20} - 2 x^{19} + 4 x^{18} + 132 x^{17} - 393 x^{16} + 3316 x^{15} - 14578 x^{14} + 68392 x^{13} - 219002 x^{12} + 538754 x^{11} - 1627260 x^{10} + 2923088 x^{9} - 7858263 x^{8} + 8813532 x^{7} - 26963500 x^{6} + 56906872 x^{5} - 81308073 x^{4} + 83086834 x^{3} - 72271464 x^{2} - 1589366 x + 1848527$ |
$20$ |
[4,8] |
$2^{30}\cdot 7^{10}\cdot 11^{16}\cdot 43^{4}$ |
$4$ |
$108.118958305$ |
|
|
|
? |
$C_2^4:F_{16}$ (as 20T286) |
$[2]$ |
$2$ |
$11$ |
$1369167289030$ |
| 20.4.476...136.2 |
$x^{20} - 2 x^{19} - 12 x^{18} - 108 x^{17} + 407 x^{16} + 2268 x^{15} - 9038 x^{14} - 12122 x^{13} - 14007 x^{12} + 1180778 x^{11} - 2104380 x^{10} - 17855632 x^{9} + 45649766 x^{8} + 111481254 x^{7} - 357164692 x^{6} - 245791604 x^{5} + 1099871635 x^{4} - 515976992 x^{3} + 2168329358 x^{2} - 5808046808 x + 3054850787$ |
$20$ |
[4,8] |
$2^{30}\cdot 7^{10}\cdot 11^{16}\cdot 43^{4}$ |
$4$ |
$108.118958305$ |
|
|
|
? |
$C_2^4:F_{16}$ (as 20T286) |
$[2]$ |
$2$ |
$11$ |
$1372243846190$ |
| 20.12.119...544.1 |
$x^{20} - 2 x^{19} - 56 x^{18} + 30 x^{17} + 1349 x^{16} + 1404 x^{15} - 14840 x^{14} - 43292 x^{13} + 21494 x^{12} + 366224 x^{11} + 866544 x^{10} + 16744 x^{9} - 4600674 x^{8} - 9573004 x^{7} - 2793624 x^{6} + 16777068 x^{5} + 26423321 x^{4} + 13368514 x^{3} - 2661256 x^{2} - 5077526 x - 1406131$ |
$20$ |
[12,4] |
$2^{30}\cdot 7^{10}\cdot 11^{16}\cdot 2927^{2}$ |
$4$ |
$113.201044445$ |
|
|
|
? |
$C_2^{10}:C_{15}$ (as 20T469) |
trivial |
$2$ |
$15$ |
$21174642209500$ |
| 20.16.172...312.1 |
$x^{20} - 96 x^{18} - 12 x^{17} + 3312 x^{16} + 6096 x^{15} - 82032 x^{14} - 284292 x^{13} + 2238009 x^{12} + 2743680 x^{11} - 37413276 x^{10} + 34372428 x^{9} + 242746961 x^{8} - 533123712 x^{7} - 454083576 x^{6} + 2097916288 x^{5} - 327486861 x^{4} - 3230722656 x^{3} + 1236902076 x^{2} + 1841553468 x - 306437823$ |
$20$ |
[16,2] |
$2^{40}\cdot 3^{15}\cdot 11^{16}\cdot 23^{2}\cdot 67^{2}$ |
$5$ |
$129.358611214$ |
|
|
|
? |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$17$ |
$268984531076000$ |
| 20.12.235...384.1 |
$x^{20} - 2 x^{19} - 66 x^{18} - 98 x^{17} + 548 x^{16} + 10270 x^{15} + 46280 x^{14} - 145168 x^{13} - 1021802 x^{12} + 714226 x^{11} + 8706426 x^{10} - 6629896 x^{9} - 43677913 x^{8} + 61903176 x^{7} + 119198458 x^{6} - 277683878 x^{5} - 100202484 x^{4} + 560840682 x^{3} - 167260584 x^{2} - 416045820 x + 259669871$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}\cdot 4201^{2}\cdot 52009^{2}$ |
$4$ |
$131.402086136$ |
|
|
|
? |
$C_2^{10}:C_3\wr C_5$ (as 20T979) |
$[2]$ |
$2$ |
$15$ |
$49858582072000$ |
| 20.16.372...688.1 |
$x^{20} - 4 x^{19} - 65 x^{18} + 308 x^{17} + 1131 x^{16} - 7728 x^{15} - 7477 x^{14} + 94038 x^{13} + 10143 x^{12} - 623082 x^{11} + 122444 x^{10} + 2311702 x^{9} - 792927 x^{8} - 4720220 x^{7} + 2228987 x^{6} + 4914024 x^{5} - 2964154 x^{4} - 2018402 x^{3} + 1379021 x^{2} + 269666 x - 197363$ |
$20$ |
[16,2] |
$2^{20}\cdot 3^{15}\cdot 11^{16}\cdot 617^{2}\cdot 3761^{2}$ |
$5$ |
$134.44477683$ |
|
|
|
? |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
$[2]$ |
$2$ |
$17$ |
$132262791398000$ |
| 20.12.497...729.1 |
$x^{20} - 10 x^{19} - 37 x^{18} + 427 x^{17} + 1421 x^{16} - 7544 x^{15} - 39006 x^{14} + 24488 x^{13} + 503487 x^{12} + 974660 x^{11} - 1416665 x^{10} - 9380203 x^{9} - 16149571 x^{8} - 4880690 x^{7} + 27588657 x^{6} + 52874139 x^{5} + 42671405 x^{4} + 10685344 x^{3} - 8383586 x^{2} - 7169631 x - 1655149$ |
$20$ |
[12,4] |
$11^{16}\cdot 23\cdot 38281\cdot 189223\cdot 25504931^{2}$ |
$5$ |
$136.414587817$ |
$14036820345.89747$ |
|
|
? |
$C_2^{10}.S_3\wr C_5$ (as 20T1050) |
trivial |
$2$ |
$15$ |
$161847187657000$ |
