| 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 |
| 18.16.132...179.1 |
$x^{18} - 9 x^{17} + 25 x^{16} + 4 x^{15} - 137 x^{14} + 175 x^{13} + 179 x^{12} - 515 x^{11} + 116 x^{10} + 542 x^{9} - 442 x^{8} - 181 x^{7} + 375 x^{6} - 49 x^{5} - 136 x^{4} + 35 x^{3} + 20 x^{2} - 3 x - 1$ |
$18$ |
[16,1] |
$-\,67\cdot 2113\cdot 9685993193^{2}$ |
$3$ |
$24.8734949678$ |
$37030470.45780276$ |
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$16$ |
$2541189.23709$ |
| 18.16.363...104.1 |
$x^{18} - 11 x^{16} + 39 x^{14} - 29 x^{12} - 110 x^{10} + 246 x^{8} - 204 x^{6} + 81 x^{4} - 15 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 11779563529^{2}$ |
$2$ |
$26.3053661419$ |
|
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$16$ |
$4351551.84464$ |
| 18.16.708...264.1 |
$x^{18} - 14 x^{16} + 67 x^{14} - 125 x^{12} + 12 x^{10} + 272 x^{8} - 366 x^{6} + 190 x^{4} - 37 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$27.2980167006$ |
|
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$16$ |
$6719357.42451$ |
| 18.16.708...264.2 |
$x^{18} - 9 x^{16} + 21 x^{14} + 25 x^{12} - 182 x^{10} + 303 x^{8} - 229 x^{6} + 85 x^{4} - 15 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$27.2980167006$ |
|
|
|
✓ |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$16$ |
$6734440.44006$ |
| 18.16.756...064.1 |
$x^{18} - 14 x^{16} + 66 x^{14} - 134 x^{12} + 91 x^{10} + 78 x^{8} - 159 x^{6} + 87 x^{4} - 18 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 19^{16}$ |
$2$ |
$27.3968015041$ |
|
|
|
✓ |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$16$ |
$6622236.89355$ |
| 18.16.804...776.1 |
$x^{18} - 10 x^{16} + 21 x^{14} + 67 x^{12} - 362 x^{10} + 621 x^{8} - 495 x^{6} + 183 x^{4} - 26 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
|
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$16$ |
$7254497.19743$ |
| 18.16.804...776.2 |
$x^{18} - 14 x^{16} + 77 x^{14} - 211 x^{12} + 294 x^{10} - 168 x^{8} - 30 x^{6} + 70 x^{4} - 21 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
|
|
|
✓ |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$16$ |
$7249105.72308$ |
| 18.16.104...456.1 |
$x^{18} - 12 x^{16} + 48 x^{14} - 59 x^{12} - 61 x^{10} + 206 x^{8} - 183 x^{6} + 74 x^{4} - 14 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 169457^{2}$ |
$3$ |
$27.889151509$ |
|
|
|
✓ |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$16$ |
$8314487.71114$ |
| 18.16.104...456.2 |
$x^{18} - 15 x^{16} + 83 x^{14} - 202 x^{12} + 168 x^{10} + 150 x^{8} - 365 x^{6} + 207 x^{4} - 27 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 169457^{2}$ |
$3$ |
$27.889151509$ |
|
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$16$ |
$7708598.7876$ |
| 18.16.258...864.1 |
$x^{18} - 9 x^{16} + 9 x^{14} + 96 x^{12} - 333 x^{10} + 450 x^{8} - 306 x^{6} + 108 x^{4} - 18 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 3^{44}$ |
$2$ |
$29.3309679999$ |
|
|
|
✓ |
$C_2\wr C_9$ (as 18T460) |
trivial |
$2$ |
$16$ |
$13048170.477$ |
| 18.16.354...784.1 |
$x^{18} - 10 x^{16} + 29 x^{14} + 8 x^{12} - 188 x^{10} + 361 x^{8} - 292 x^{6} + 109 x^{4} - 18 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4}$ |
$4$ |
$29.8513960413$ |
|
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$16$ |
$15353422.3404$ |
| 18.16.354...784.2 |
$x^{18} - 10 x^{16} + 9 x^{14} + 144 x^{12} - 513 x^{10} + 724 x^{8} - 512 x^{6} + 184 x^{4} - 29 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4}$ |
$4$ |
$29.8513960413$ |
|
|
|
? |
$C_2\times A_4^3.A_4$ (as 18T696) |
trivial |
$2$ |
$16$ |
$16341976.6567$ |
| 18.16.426...688.1 |
$x^{18} - 17 x^{16} + 77 x^{14} + 136 x^{12} - 2044 x^{10} + 6119 x^{8} - 8033 x^{6} + 4835 x^{4} - 1110 x^{2} + 37$ |
$18$ |
[16,1] |
$-\,2^{24}\cdot 37^{7}\cdot 16361^{2}$ |
$3$ |
$30.1599520982$ |
|
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$16$ |
$18241445.1808$ |
| 18.16.737...136.1 |
$x^{18} - 12 x^{16} + 53 x^{14} - 91 x^{12} - 27 x^{10} + 318 x^{8} - 428 x^{6} + 213 x^{4} - 27 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{30}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$31.0922149397$ |
|
|
|
✓ |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$16$ |
$24895921.6054$ |
| 18.16.102...064.1 |
$x^{18} - 12 x^{16} + 42 x^{14} - 11 x^{12} - 243 x^{10} + 579 x^{8} - 559 x^{6} + 234 x^{4} - 33 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$31.6657925274$ |
|
|
|
|
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$16$ |
$31808885.6536$ |
| 18.16.352...875.1 |
$x^{18} - 17 x^{16} - 6 x^{15} + 113 x^{14} + 85 x^{13} - 353 x^{12} - 452 x^{11} + 422 x^{10} + 1084 x^{9} + 287 x^{8} - 1014 x^{7} - 1060 x^{6} - 61 x^{5} + 507 x^{4} + 362 x^{3} + 113 x^{2} + 17 x + 1$ |
$18$ |
[16,1] |
$-\,5^{9}\cdot 7^{12}\cdot 41\cdot 419\cdot 1399\cdot 5419$ |
$6$ |
$33.9132146828$ |
$2952915.8307289123$ |
|
|
✓ |
$C_3^6.C_2\wr C_6$ (as 18T857) |
trivial |
$2$ |
$16$ |
$53586442.5258$ |
| 18.16.521...264.1 |
$x^{18} - 22 x^{16} + 173 x^{14} - 545 x^{12} + 279 x^{10} + 1788 x^{8} - 3122 x^{6} + 1509 x^{4} - 91 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{24}\cdot 19^{6}\cdot 137^{6}$ |
$3$ |
$34.6628858467$ |
|
|
|
? |
$C_2^4.S_4^2:C_2^2$ (as 18T691) |
trivial |
$2$ |
$16$ |
$80568411.1462$ |
| 18.16.710...224.1 |
$x^{18} - 20 x^{16} + 156 x^{14} - 602 x^{12} + 1204 x^{10} - 1197 x^{8} + 504 x^{6} - 24 x^{4} - 24 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ |
$3$ |
$35.2625883929$ |
|
|
|
? |
$C_2\wr C_9.C_3$ (as 18T586) |
trivial |
$2$ |
$16$ |
$81911787.8703$ |
| 18.16.710...224.2 |
$x^{18} - 17 x^{16} + 109 x^{14} - 329 x^{12} + 462 x^{10} - 217 x^{8} - 84 x^{6} + 93 x^{4} - 20 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ |
$3$ |
$35.2625883929$ |
|
|
|
? |
$C_2\wr C_9.C_3$ (as 18T586) |
trivial |
$2$ |
$16$ |
$71840848.746$ |
| 18.16.171...888.1 |
$x^{18} - 25 x^{16} + 246 x^{14} - 1245 x^{12} + 3470 x^{10} - 5082 x^{8} + 2731 x^{6} + 1768 x^{4} - 2704 x^{2} + 832$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 7^{12}\cdot 13^{13}$ |
$3$ |
$37.0339469783$ |
$104.34876482104056$ |
|
|
|
$C_2^9:C_3^2$ (as 18T459) |
trivial |
$2$ |
$16$ |
$169698852.096$ |
| 18.16.225...244.1 |
$x^{18} - 27 x^{16} + 190 x^{14} - 305 x^{12} - 1406 x^{10} + 6214 x^{8} - 8812 x^{6} + 4829 x^{4} - 853 x^{2} + 41$ |
$18$ |
[16,1] |
$-\,2^{2}\cdot 37^{4}\cdot 41\cdot 151^{4}\cdot 613^{4}$ |
$5$ |
$37.6000924591$ |
$23699.626241778584$ |
|
|
? |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$16$ |
$319257414.847$ |
| 18.16.356...368.1 |
$x^{18} - 6 x^{17} + 6 x^{16} + 38 x^{15} - 184 x^{14} + 390 x^{13} + 275 x^{12} - 3166 x^{11} + 4308 x^{10} + 3710 x^{9} - 13016 x^{8} + 7380 x^{7} + 5183 x^{6} - 7128 x^{5} + 2214 x^{4} + 150 x^{3} - 170 x^{2} + 24 x - 1$ |
$18$ |
[16,1] |
$-\,2^{16}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6}$ |
$4$ |
$38.5693843273$ |
$213.39900672429513$ |
|
|
? |
$C_2^5.S_4^2$ (as 18T623) |
trivial |
$2$ |
$16$ |
$753534531.557$ |
| 18.16.442...971.1 |
$x^{18} - 21 x^{16} - 6 x^{15} + 178 x^{14} + 105 x^{13} - 762 x^{12} - 712 x^{11} + 1627 x^{10} + 2311 x^{9} - 1158 x^{8} - 3464 x^{7} - 1237 x^{6} + 1514 x^{5} + 1732 x^{4} + 771 x^{3} + 178 x^{2} + 21 x + 1$ |
$18$ |
[16,1] |
$-\,7^{12}\cdot 71\cdot 181^{3}\cdot 7585403561$ |
$4$ |
$39.0313746424$ |
$36129046.558859244$ |
|
|
✓ |
$S_3^4.\SOPlus(4,2).A_4$ (as 18T926) |
trivial |
$2$ |
$16$ |
$225767940.76$ |
| 18.16.456...744.1 |
$x^{18} - 11 x^{16} + 8 x^{14} + 413 x^{12} - 2634 x^{10} + 7683 x^{8} - 12405 x^{6} + 11296 x^{4} - 5376 x^{2} + 1024$ |
$18$ |
[16,1] |
$-\,2^{24}\cdot 37^{6}\cdot 101^{6}$ |
$3$ |
$39.1033855647$ |
$333.54765559633347$ |
|
|
|
$C_2^5.S_4^2$ (as 18T623) |
trivial |
$2$ |
$16$ |
$317820873.514$ |
| 18.16.465...375.1 |
$x^{18} - 21 x^{16} - 6 x^{15} + 178 x^{14} + 105 x^{13} - 763 x^{12} - 712 x^{11} + 1637 x^{10} + 2314 x^{9} - 1189 x^{8} - 3484 x^{7} - 1210 x^{6} + 1545 x^{5} + 1742 x^{4} + 772 x^{3} + 178 x^{2} + 21 x + 1$ |
$18$ |
[16,1] |
$-\,5^{9}\cdot 89\cdot 3881^{3}\cdot 4582578491$ |
$4$ |
$39.1444368276$ |
$88962459.89173801$ |
|
|
✓ |
$C_3^6.S_4^2:D_4$ (as 18T951) |
trivial |
$2$ |
$16$ |
$174600518.137$ |
| 18.16.701...288.1 |
$x^{18} - 24 x^{16} - 6 x^{15} + 234 x^{14} + 120 x^{13} - 1169 x^{12} - 936 x^{11} + 3031 x^{10} + 3532 x^{9} - 3260 x^{8} - 6302 x^{7} - 866 x^{6} + 3728 x^{5} + 3151 x^{4} + 1178 x^{3} + 234 x^{2} + 24 x + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 127\cdot 257^{6}\cdot 7307849$ |
$4$ |
$40.0442960772$ |
|
|
|
? |
$C_3^6.C_2\wr A_4.C_2$ (as 18T930) |
trivial |
$2$ |
$16$ |
$369031688.66$ |
| 18.16.785...704.1 |
$x^{18} - 27 x^{16} + 186 x^{14} - 399 x^{12} - 333 x^{10} + 2511 x^{8} - 3717 x^{6} + 2430 x^{4} - 729 x^{2} + 81$ |
$18$ |
[16,1] |
$-\,2^{10}\cdot 3^{22}\cdot 367^{6}$ |
$3$ |
$40.2972838793$ |
$640.9814721559633$ |
|
|
? |
$A_4^3.C_2^3:S_4$ (as 18T882) |
trivial |
$2$ |
$16$ |
$700116182.97$ |
| 18.16.955...816.1 |
$x^{18} - 13 x^{16} - 8 x^{14} + 506 x^{12} - 1867 x^{10} + 2559 x^{8} - 1411 x^{6} + 327 x^{4} - 31 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{30}\cdot 2113^{6}$ |
$2$ |
$40.7395747855$ |
$471.76138547121144$ |
|
|
|
$C_2^4.S_4^2:C_2^2$ (as 18T691) |
trivial |
$2$ |
$16$ |
$373676310.678$ |
| 18.16.111...000.1 |
$x^{18} - 21 x^{16} + 178 x^{14} - 793 x^{12} + 2006 x^{10} - 2873 x^{8} + 2141 x^{6} - 616 x^{4} - 40 x^{2} + 16$ |
$18$ |
[16,1] |
$-\,2^{22}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4}$ |
$4$ |
$41.0916358865$ |
$1418.6216080984798$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T772) |
trivial |
$2$ |
$16$ |
$759416175.718$ |
| 18.16.114...688.1 |
$x^{18} - 6 x^{16} - 72 x^{14} + 921 x^{12} - 4239 x^{10} + 10089 x^{8} - 12951 x^{6} + 8208 x^{4} - 1881 x^{2} + 57$ |
$18$ |
[16,1] |
$-\,2^{6}\cdot 3^{33}\cdot 19^{9}$ |
$3$ |
$41.1568788744$ |
|
|
|
|
$C_2^9:\He_3$ (as 18T585) |
trivial |
$2$ |
$16$ |
$684118328.319$ |
| 18.16.139...000.1 |
$x^{18} - 9 x^{16} - 26 x^{14} + 495 x^{12} - 1922 x^{10} + 3399 x^{8} - 3079 x^{6} + 1420 x^{4} - 300 x^{2} + 20$ |
$18$ |
[16,1] |
$-\,2^{20}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4}$ |
$4$ |
$41.6042139221$ |
$1056.2694033177092$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T772) |
trivial |
$2$ |
$16$ |
$1023226107.22$ |
| 18.16.255...875.1 |
$x^{18} - 23 x^{16} - 6 x^{15} + 212 x^{14} + 115 x^{13} - 982 x^{12} - 848 x^{11} + 2281 x^{10} + 2971 x^{9} - 1932 x^{8} - 4792 x^{7} - 1355 x^{6} + 2356 x^{5} + 2396 x^{4} + 991 x^{3} + 212 x^{2} + 23 x + 1$ |
$18$ |
[16,1] |
$-\,5^{9}\cdot 31\cdot 139^{6}\cdot 8951\cdot 65479$ |
$5$ |
$43.0314856801$ |
$8087777.225022904$ |
|
|
✓ |
$S_3^3.S_3\wr C_3.C_6$ (as 18T915) |
trivial |
$2$ |
$16$ |
$497725301.848$ |
| 18.16.350...288.1 |
$x^{18} - 21 x^{16} - 6 x^{15} + 178 x^{14} + 105 x^{13} - 762 x^{12} - 712 x^{11} + 1626 x^{10} + 2311 x^{9} - 1151 x^{8} - 3462 x^{7} - 1247 x^{6} + 1507 x^{5} + 1731 x^{4} + 771 x^{3} + 178 x^{2} + 21 x + 1$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 37^{9}\cdot 4799\cdot 137357761$ |
$4$ |
$43.7924110511$ |
$7839520.539013056$ |
|
|
✓ |
$C_3^6.C_2\wr S_3$ (as 18T874) |
trivial |
$2$ |
$16$ |
$458340466.433$ |
| 18.16.386...528.1 |
$x^{18} - 33 x^{16} + 423 x^{14} - 2733 x^{12} + 9531 x^{10} - 17685 x^{8} + 16020 x^{6} - 5760 x^{4} + 369 x^{2} + 3$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 3^{33}\cdot 19^{8}$ |
$3$ |
$44.0295146215$ |
|
|
|
? |
$C_2^9:\He_3$ (as 18T585) |
trivial |
$2$ |
$16$ |
$952444928.519$ |
| 18.16.409...979.1 |
$x^{18} - 18 x^{16} - 6 x^{15} + 129 x^{14} + 90 x^{13} - 451 x^{12} - 516 x^{11} + 699 x^{10} + 1378 x^{9} - 19 x^{8} - 1578 x^{7} - 1138 x^{6} + 277 x^{5} + 789 x^{4} + 460 x^{3} + 129 x^{2} + 18 x + 1$ |
$18$ |
[16,1] |
$-\,23\cdot 79^{3}\cdot 3391\cdot 15227^{3}\cdot 3017519$ |
$5$ |
$44.1707727942$ |
$532075839.6877492$ |
|
|
✓ |
$C_3^6.(C_2^6.S_6)$ (as 18T962) |
trivial |
$2$ |
$16$ |
$1022313724.56$ |
| 18.16.563...216.1 |
$x^{18} - 16 x^{16} + 91 x^{14} - 228 x^{12} + 234 x^{10} - 181 x^{6} + 135 x^{4} - 39 x^{2} + 4$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ |
$4$ |
$44.9602477996$ |
|
|
|
? |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$16$ |
$1522893441.27$ |
| 18.16.691...184.1 |
$x^{18} - 20 x^{16} + 157 x^{14} - 628 x^{12} + 1403 x^{10} - 1789 x^{8} + 1258 x^{6} - 435 x^{4} + 53 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 1129^{8}$ |
$2$ |
$45.4760629249$ |
|
|
|
? |
$C_2^8.D_{18}$ (as 18T548) |
trivial |
$2$ |
$16$ |
$1010266226.98$ |
| 18.16.691...184.2 |
$x^{18} - 18 x^{16} + 125 x^{14} - 412 x^{12} + 617 x^{10} - 255 x^{8} - 177 x^{6} + 121 x^{4} - 20 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{18}\cdot 1129^{8}$ |
$2$ |
$45.4760629249$ |
|
|
|
? |
$C_2^8.D_{18}$ (as 18T548) |
trivial |
$2$ |
$16$ |
$1036460494.49$ |
| 18.16.706...336.1 |
$x^{18} - 36 x^{16} + 363 x^{14} - 1710 x^{12} + 4317 x^{10} - 5898 x^{8} + 3858 x^{6} - 585 x^{4} - 315 x^{2} + 9$ |
$18$ |
[16,1] |
$-\,2^{10}\cdot 3^{24}\cdot 367^{6}$ |
$3$ |
$45.5291190883$ |
$640.9814721559633$ |
|
|
? |
$A_4^3.C_2^3:S_4$ (as 18T882) |
$[2]$ |
$2$ |
$16$ |
$1922742321.75$ |
| 18.16.761...136.1 |
$x^{18} - 33 x^{16} + 414 x^{14} - 2506 x^{12} + 7476 x^{10} - 9492 x^{8} + 2527 x^{6} - 153 x^{4} - 12 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 29^{4}$ |
$4$ |
$45.71763194$ |
|
|
|
? |
$A_4^3.(C_2^2\times A_4)$ (as 18T766) |
trivial |
$2$ |
$16$ |
$1006634999.14$ |
| 18.16.132...928.1 |
$x^{18} - 24 x^{16} + 180 x^{14} - 351 x^{12} - 1620 x^{10} + 9072 x^{8} - 16497 x^{6} + 12960 x^{4} - 3888 x^{2} + 243$ |
$18$ |
[16,1] |
$-\,2^{16}\cdot 3^{25}\cdot 47^{8}$ |
$3$ |
$47.141699072$ |
|
|
|
? |
$A_4^3.C_2^3:S_4$ (as 18T881) |
trivial |
$2$ |
$16$ |
$8397154690.93$ |
| 18.16.241...072.1 |
$x^{18} - 6 x^{17} - 27 x^{16} + 225 x^{15} + 99 x^{14} - 2883 x^{13} + 1709 x^{12} + 17955 x^{11} - 13251 x^{10} - 79555 x^{9} + 48447 x^{8} + 296877 x^{7} - 264292 x^{6} - 523467 x^{5} + 683256 x^{4} + 173607 x^{3} - 426153 x^{2} + 7056 x + 78253$ |
$18$ |
[16,1] |
$-\,2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5}$ |
$4$ |
$48.7455100912$ |
$1089.24799139412$ |
|
|
? |
$A_4^3.(C_2^2\times A_4)$ (as 18T766) |
trivial |
$2$ |
$16$ |
$2876257708.48$ |
| 18.16.325...352.1 |
$x^{18} - 33 x^{16} - 4 x^{15} + 447 x^{14} + 96 x^{13} - 3317 x^{12} - 1032 x^{11} + 15000 x^{10} + 6720 x^{9} - 41586 x^{8} - 26076 x^{7} + 63828 x^{6} + 50472 x^{5} - 44976 x^{4} - 38968 x^{3} + 13200 x^{2} + 9096 x - 2276$ |
$18$ |
[16,1] |
$-\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 67$ |
$4$ |
$49.5638787618$ |
|
|
|
|
$C_2^7.C_6^2:D_6$ (as 18T734) |
trivial |
$2$ |
$16$ |
$2736959265.83$ |
| 18.16.326...659.1 |
$x^{18} - 23 x^{16} - 6 x^{15} + 213 x^{14} + 115 x^{13} - 999 x^{12} - 852 x^{11} + 2381 x^{10} + 3022 x^{9} - 2164 x^{8} - 4992 x^{7} - 1216 x^{6} + 2590 x^{5} + 2496 x^{4} + 1008 x^{3} + 213 x^{2} + 23 x + 1$ |
$18$ |
[16,1] |
$-\,11^{6}\cdot 13^{3}\cdot 43^{7}\cdot 45337\cdot 68053$ |
$5$ |
$49.5688895065$ |
$4355642.969331738$ |
|
|
? |
$C_3^6.C_2\wr (C_2\times S_4)$ (as 18T945) |
trivial |
$2$ |
$16$ |
$1969300588.79$ |
| 18.16.342...000.1 |
$x^{18} - 17 x^{16} - 6 x^{15} + 110 x^{14} + 85 x^{13} - 316 x^{12} - 440 x^{11} + 256 x^{10} + 973 x^{9} + 591 x^{8} - 682 x^{7} - 1177 x^{6} - 371 x^{5} + 341 x^{4} + 325 x^{3} + 110 x^{2} + 17 x + 1$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 5^{9}\cdot 37^{6}\cdot 166946971879$ |
$4$ |
$49.7029492963$ |
$8821893.306542935$ |
|
|
? |
$C_3^6.C_2\wr D_6$ (as 18T903) |
trivial |
$2$ |
$16$ |
$1304272731.89$ |
| 18.16.369...056.1 |
$x^{18} - 6 x^{17} - 15 x^{16} + 170 x^{15} - 186 x^{14} - 1392 x^{13} + 4226 x^{12} + 678 x^{11} - 20544 x^{10} + 29008 x^{9} + 12396 x^{8} - 66546 x^{7} + 50014 x^{6} + 16776 x^{5} - 41670 x^{4} + 19786 x^{3} - 2589 x^{2} - 114 x - 1$ |
$18$ |
[16,1] |
$-\,2^{28}\cdot 3^{24}\cdot 19\cdot 37^{6}$ |
$4$ |
$49.9121559813$ |
|
|
|
? |
$C_2^7.C_6^2:D_6$ (as 18T734) |
trivial |
$2$ |
$16$ |
$5430919987.53$ |
| 18.16.440...336.1 |
$x^{18} - 17 x^{16} + 72 x^{14} + 143 x^{12} - 1593 x^{10} + 3357 x^{8} - 2463 x^{6} + 608 x^{4} - 48 x^{2} + 1$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 32009^{6}$ |
$2$ |
$50.4015662569$ |
|
|
|
|
$C_2^4:A_4^2.D_6$ (as 18T662) |
trivial |
$2$ |
$16$ |
$2720974998.17$ |
| 18.16.440...336.2 |
$x^{18} - 12 x^{16} + 15 x^{14} + 380 x^{12} - 2294 x^{10} + 5736 x^{8} - 7145 x^{6} + 4236 x^{4} - 944 x^{2} + 64$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 32009^{6}$ |
$2$ |
$50.4015662569$ |
|
|
|
|
$C_2^4:A_4^2.D_6$ (as 18T662) |
trivial |
$2$ |
$16$ |
$2830119595.29$ |
| 18.16.105...943.1 |
$x^{18} - 41 x^{16} + 706 x^{14} - 6650 x^{12} + 37313 x^{10} - 126731 x^{8} + 250624 x^{6} - 254274 x^{4} + 86032 x^{2} + 15023$ |
$18$ |
[16,1] |
$-\,7^{12}\cdot 83^{5}\cdot 181^{5}$ |
$3$ |
$52.9186648968$ |
$1956.454374658169$ |
|
|
? |
$A_4^3.C_2^3:A_4$ (as 18T839) |
trivial |
$2$ |
$16$ |
$4313992998.07$ |
| 18.16.109...111.1 |
$x^{18} - 9 x^{17} + 18 x^{16} + 60 x^{15} - 253 x^{14} + 7 x^{13} + 1019 x^{12} - 823 x^{11} - 1809 x^{10} + 2313 x^{9} + 1408 x^{8} - 2719 x^{7} - 213 x^{6} + 1477 x^{5} - 276 x^{4} - 336 x^{3} + 114 x^{2} + 21 x - 9$ |
$18$ |
[16,1] |
$-\,3^{8}\cdot 7\cdot 53^{4}\cdot 107^{8}\cdot 1753$ |
$5$ |
$53.0071738273$ |
$118532.10546278152$ |
|
|
|
$A_4^3.C_2^3:S_4$ (as 18T881) |
trivial |
$2$ |
$16$ |
$29443873028.0$ |
