| 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 |
| 22.6.440...573.1 |
$x^{22} - 11 x^{21} + 64 x^{20} - 255 x^{19} + 770 x^{18} - 1857 x^{17} + 3688 x^{16} - 6146 x^{15} + 8690 x^{14} - 10480 x^{13} + 10777 x^{12} - 9386 x^{11} + 6807 x^{10} - 3960 x^{9} + 1680 x^{8} - 341 x^{7} - 170 x^{6} + 212 x^{5} - 109 x^{4} + 28 x^{3} + 3 x^{2} - 5 x + 1$ |
$22$ |
[6,8] |
$37\cdot 163^{2}\cdot 14281\cdot 177106931^{2}$ |
$4$ |
$16.2585616162$ |
$123507051.11934274$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$42752.2517797$ |
| 22.6.144...125.1 |
$x^{22} - 2 x^{21} - x^{20} + 18 x^{19} - 17 x^{18} - 44 x^{17} + 110 x^{16} - 3 x^{15} - 254 x^{14} + 59 x^{13} + 240 x^{12} - 102 x^{11} - 552 x^{10} - 230 x^{9} + 307 x^{8} + 320 x^{7} - 3 x^{6} - 154 x^{5} - 62 x^{4} + 18 x^{3} + 19 x^{2} + 2 x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}$ |
$4$ |
$17.1621719232$ |
$2844.1679033165196$ |
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$13$ |
$95631.3345105$ |
| 22.6.261...704.1 |
$x^{22} - 6 x^{20} + 16 x^{18} - 18 x^{16} + 4 x^{14} - 6 x^{12} + 25 x^{10} - 3 x^{8} - 19 x^{6} + 4 x^{4} + 4 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$17.6294938054$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$107375.053215$ |
| 22.6.302...024.1 |
$x^{22} - x^{18} - x^{16} - 2 x^{14} + x^{10} + 2 x^{8} + 2 x^{6} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ |
$4$ |
$17.7482593697$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$118028.692249$ |
| 22.6.452...625.1 |
$x^{22} - 3 x^{21} - 5 x^{20} + 20 x^{19} + 6 x^{18} - 46 x^{17} - 22 x^{16} + 88 x^{15} + 102 x^{14} - 250 x^{13} - 116 x^{12} + 460 x^{11} - 50 x^{10} - 559 x^{9} + 321 x^{8} + 395 x^{7} - 287 x^{6} - 315 x^{5} + 200 x^{4} + 136 x^{3} + 14 x^{2} - 70 x + 5$ |
$22$ |
[6,8] |
$5^{5}\cdot 7^{6}\cdot 83^{4}\cdot 127^{4}\cdot 997$ |
$5$ |
$18.0748826004$ |
$146075.47938051051$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$13$ |
$180581.627765$ |
| 22.6.111...149.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 111 x^{18} + 372 x^{17} - 61 x^{16} - 838 x^{15} + 563 x^{14} + 1153 x^{13} - 1030 x^{12} - 1191 x^{11} + 1050 x^{10} + 987 x^{9} - 634 x^{8} - 630 x^{7} + 192 x^{6} + 264 x^{5} - 3 x^{4} - 53 x^{3} - 10 x^{2} + x - 1$ |
$22$ |
[6,8] |
$83\cdot 199\cdot 937\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ |
$6$ |
$18.8334111471$ |
$644951594.8448861$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$231636.713172$ |
| 22.6.184...625.1 |
$x^{22} - 7 x^{21} + 16 x^{20} - 3 x^{19} - 51 x^{18} + 101 x^{17} - 62 x^{16} - 50 x^{15} + 49 x^{14} + 124 x^{13} - 271 x^{12} + 166 x^{11} + 113 x^{10} - 102 x^{9} - 51 x^{8} - 34 x^{7} + 128 x^{6} - 78 x^{5} - 37 x^{4} + 36 x^{3} + 14 x^{2} - 8 x + 1$ |
$22$ |
[6,8] |
$5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2}$ |
$5$ |
$19.2655473485$ |
$89805.47415981455$ |
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$416442.121837$ |
| 22.6.304...125.1 |
$x^{22} - 8 x^{19} - 4 x^{16} + 116 x^{15} - 47 x^{14} - 228 x^{13} + 179 x^{12} + 177 x^{11} - 108 x^{10} + 58 x^{9} + 78 x^{8} + 4 x^{7} + 37 x^{6} - 13 x^{5} - 40 x^{4} - x^{3} + 10 x^{2} + x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$19.7103732789$ |
$353296.357899427$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$13$ |
$376545.621481$ |
| 22.6.315...616.1 |
$x^{22} - 6 x^{20} + 14 x^{18} - 15 x^{16} - 6 x^{14} + 47 x^{12} - 75 x^{10} + 21 x^{8} + 101 x^{6} - 110 x^{4} + 55 x^{2} - 11$ |
$22$ |
[6,8] |
$2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$19.7420863372$ |
|
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$13$ |
$496007.27434$ |
| 22.6.334...125.1 |
$x^{22} - 3 x^{20} - 4 x^{19} - 13 x^{18} + x^{17} + 41 x^{16} + 85 x^{15} - 10 x^{14} - 177 x^{13} + 9 x^{12} + 233 x^{11} - 32 x^{10} - 26 x^{9} + 38 x^{8} - 74 x^{7} + 18 x^{6} + 22 x^{5} - 25 x^{4} + 6 x^{2} - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 14851^{2}\cdot 1762627^{2}$ |
$3$ |
$19.7955824892$ |
$361778.7554362473$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$13$ |
$408757.310974$ |
| 22.6.458...896.1 |
$x^{22} - 12 x^{20} + 59 x^{18} - 154 x^{16} + 229 x^{14} - 193 x^{12} + 96 x^{10} - 57 x^{8} + 54 x^{6} - 24 x^{4} + x^{2} - 1$ |
$22$ |
[6,8] |
$2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$20.081203729$ |
|
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$827089.731554$ |
| 22.6.156...136.1 |
$x^{22} + x^{20} - 4 x^{18} - x^{16} + 5 x^{14} - 7 x^{12} - 7 x^{10} + 5 x^{8} + 7 x^{6} + 3 x^{4} - x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 610429790897^{2}$ |
$2$ |
$23.5749849842$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$2599985.98276$ |
| 22.6.157...784.1 |
$x^{22} - 4 x^{21} + 8 x^{20} - 8 x^{19} - 2 x^{18} + 20 x^{17} - 32 x^{16} + 22 x^{15} + 9 x^{14} - 38 x^{13} + 40 x^{12} - 12 x^{11} - 20 x^{10} + 30 x^{9} - 15 x^{8} - 6 x^{7} + 12 x^{6} - 8 x^{5} - x^{4} + 4 x^{3} - 2 x^{2} + 1$ |
$22$ |
[6,8] |
$2^{33}\cdot 3^{2}\cdot 47\cdot 311\cdot 1391443157437409$ |
$5$ |
$23.5814622235$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$2$ |
$13$ |
$3877614.43912$ |
| 22.6.181...869.1 |
$x^{22} - 11 x^{21} + 64 x^{20} - 255 x^{19} + 769 x^{18} - 1848 x^{17} + 3647 x^{16} - 6022 x^{15} + 8418 x^{14} - 10032 x^{13} + 10228 x^{12} - 8926 x^{11} + 6647 x^{10} - 4183 x^{9} + 2160 x^{8} - 829 x^{7} + 136 x^{6} + 111 x^{5} - 114 x^{4} + 47 x^{3} - 3 x^{2} - 5 x + 1$ |
$22$ |
[6,8] |
$71^{2}\cdot 73^{2}\cdot 1408829\cdot 219034943^{2}$ |
$4$ |
$23.7362031549$ |
$1264667761.6061795$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$2830046.81958$ |
| 22.6.274...864.1 |
$x^{22} + 2 x^{20} - x^{18} - 4 x^{16} - x^{14} + 5 x^{12} - x^{10} - 8 x^{8} + 3 x^{6} + 5 x^{4} - x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2}$ |
$4$ |
$24.1850829808$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$3357001.4945$ |
| 22.6.379...009.1 |
$x^{22} - x^{21} + 5 x^{20} - 13 x^{19} + 3 x^{18} - 23 x^{17} - 63 x^{16} + 117 x^{15} + 79 x^{14} + 221 x^{13} + 156 x^{12} + 15 x^{11} - 1069 x^{10} - 1131 x^{9} - 164 x^{8} + 1812 x^{7} + 1646 x^{6} - 690 x^{5} - 1234 x^{4} - 363 x^{3} - 6 x^{2} + 10 x + 1$ |
$22$ |
[6,8] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$4141006.01086$ |
| 22.6.176...277.1 |
$x^{22} - 11 x^{21} + 64 x^{20} - 255 x^{19} + 769 x^{18} - 1848 x^{17} + 3645 x^{16} - 6006 x^{15} + 8346 x^{14} - 9808 x^{13} + 9702 x^{12} - 7954 x^{11} + 5209 x^{10} - 2471 x^{9} + 537 x^{8} + 363 x^{7} - 501 x^{6} + 318 x^{5} - 120 x^{4} + 16 x^{3} + 13 x^{2} - 9 x + 1$ |
$22$ |
[6,8] |
$349^{2}\cdot 1697\cdot 1949\cdot 6615221297^{2}$ |
$4$ |
$26.319845242$ |
$2763323578.596047$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$9070498.76166$ |
| 22.6.199...337.1 |
$x^{22} - 3 x^{21} + 7 x^{20} - 13 x^{19} + 18 x^{18} - 21 x^{17} + 18 x^{16} - 9 x^{15} - 5 x^{14} + 16 x^{13} - 24 x^{12} + 25 x^{11} - 16 x^{10} + 6 x^{9} + 3 x^{8} - 12 x^{7} + 9 x^{6} - 6 x^{5} + 4 x^{4} + 2 x^{3} - x^{2} + x - 1$ |
$22$ |
[6,8] |
$3^{4}\cdot 7^{2}\cdot 59\cdot 5851\cdot 36319\cdot 400764924995207263$ |
$6$ |
$26.4677839917$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$13$ |
$21280189.8381$ |
| 22.6.323...608.1 |
$x^{22} - 10 x^{20} + 20 x^{18} + 38 x^{16} + 30 x^{14} - 676 x^{12} + 645 x^{10} + 720 x^{8} - 79 x^{6} - 2438 x^{4} + 2236 x^{2} - 648$ |
$22$ |
[6,8] |
$2^{43}\cdot 43793^{4}$ |
$2$ |
$27.0563104099$ |
|
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$13$ |
$50121925.16$ |
| 22.6.190...229.1 |
$x^{22} - x^{21} - 2 x^{20} + 6 x^{19} - 4 x^{18} - 5 x^{17} + 13 x^{16} - 11 x^{15} + 13 x^{13} - 18 x^{12} + 11 x^{11} + 3 x^{10} - 14 x^{9} + 15 x^{8} - 7 x^{7} - 3 x^{6} + 8 x^{5} - 8 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ |
$22$ |
[6,8] |
$1671032183\cdot 114013219157456550332963$ |
$2$ |
$29.3271594903$ |
$1.3802889498200804e+16$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$13$ |
$34540709.9251$ |
| 22.6.237...576.1 |
$x^{22} + 12 x^{20} + 59 x^{18} + 151 x^{16} + 204 x^{14} + 106 x^{12} - 64 x^{10} - 101 x^{8} - 19 x^{6} + 16 x^{4} + 3 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2}$ |
$5$ |
$29.6245630228$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$33577695.3491$ |
| 22.6.529...664.1 |
$x^{22} - 13 x^{20} + 76 x^{18} - 269 x^{16} + 659 x^{14} - 1206 x^{12} + 1700 x^{10} - 1829 x^{8} + 1455 x^{6} - 817 x^{4} + 293 x^{2} - 49$ |
$22$ |
[6,8] |
$2^{22}\cdot 1831^{8}$ |
$2$ |
$30.7228938871$ |
|
|
|
? |
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$13$ |
$81981104.2428$ |
| 22.6.529...664.2 |
$x^{22} - 5 x^{20} - 3 x^{18} + 2 x^{16} + 35 x^{14} + 32 x^{12} + 18 x^{10} - 19 x^{8} - 11 x^{6} - 5 x^{4} + 7 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 1831^{8}$ |
$2$ |
$30.7228938871$ |
|
|
|
? |
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$13$ |
$187145857.636$ |
| 22.6.529...664.3 |
$x^{22} - 12 x^{20} + 56 x^{18} - 131 x^{16} + 203 x^{14} - 316 x^{12} + 394 x^{10} - 346 x^{8} + 245 x^{6} - 127 x^{4} + 49 x^{2} - 9$ |
$22$ |
[6,8] |
$2^{22}\cdot 1831^{8}$ |
$2$ |
$30.722893887080275$ |
|
|
|
? |
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$13$ |
$205729193.43735$ |
| 22.6.128...496.1 |
$x^{22} + 8 x^{20} + 24 x^{18} + 28 x^{16} - 12 x^{14} - 66 x^{12} - 48 x^{10} + 28 x^{8} + 43 x^{6} + 3 x^{4} - 7 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 17524013040643^{2}$ |
$2$ |
$31.9887068235$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$77727642.8873$ |
| 22.6.200...817.1 |
$x^{22} - 11 x^{21} + 63 x^{20} - 245 x^{19} + 714 x^{18} - 1638 x^{17} + 3034 x^{16} - 4586 x^{15} + 5635 x^{14} - 5481 x^{13} + 3863 x^{12} - 1247 x^{11} - 1359 x^{10} + 2985 x^{9} - 3236 x^{8} + 2436 x^{7} - 1301 x^{6} + 435 x^{5} - 37 x^{4} - 42 x^{3} + 18 x^{2} - x - 1$ |
$22$ |
[6,8] |
$37\cdot 131\cdot 431\cdot 31015897276291^{2}$ |
$4$ |
$32.6421033783$ |
$8049470623.358821$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
$[2]$ |
$2$ |
$13$ |
$46350378.7038$ |
| 22.6.223...576.1 |
$x^{22} - 2 x^{21} - x^{20} + 8 x^{19} - 9 x^{18} - 2 x^{17} + 15 x^{16} - 16 x^{15} + 8 x^{14} + 2 x^{13} - 14 x^{12} + 22 x^{11} - 13 x^{10} - 6 x^{9} + 13 x^{8} - 10 x^{7} + 4 x^{6} - 5 x^{4} + 6 x^{3} - x^{2} - 2 x + 1$ |
$22$ |
[6,8] |
$2^{33}\cdot 3^{2}\cdot 11^{2}\cdot 241\cdot 991697156691810497$ |
$5$ |
$32.8006498137$ |
|
|
|
? |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$2$ |
$13$ |
$153402538.471$ |
| 22.6.409...729.1 |
$x^{22} - x^{21} + x^{20} - x^{19} - 22 x^{18} - x^{17} - 114 x^{16} + 160 x^{15} - 22 x^{14} + 390 x^{13} + 806 x^{12} + 712 x^{11} + 1174 x^{10} - 5015 x^{9} - 2690 x^{8} - 5866 x^{7} + 10213 x^{6} - 2646 x^{5} + 2232 x^{4} - 12927 x^{3} + 6786 x^{2} - 806 x + 47$ |
$22$ |
[6,8] |
$23^{21}\cdot 47^{3}$ |
$2$ |
$33.7166533192$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$13$ |
$123704206.751$ |
| 22.6.409...729.2 |
$x^{22} - 5 x^{21} + 2 x^{20} + 36 x^{19} - 111 x^{18} + 141 x^{17} - 107 x^{16} + 558 x^{15} - 1962 x^{14} + 3577 x^{13} - 3027 x^{12} - 2023 x^{11} + 17912 x^{10} - 42755 x^{9} + 54822 x^{8} - 37877 x^{7} + 18311 x^{6} - 12826 x^{5} + 673 x^{4} + 3420 x^{3} + 4336 x^{2} - 3280 x + 47$ |
$22$ |
[6,8] |
$23^{21}\cdot 47^{3}$ |
$2$ |
$33.7166533192$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
$[2]$ |
$2$ |
$13$ |
$76447219.2916$ |
| 22.6.409...729.3 |
$x^{22} - 5 x^{21} + 2 x^{20} + 36 x^{19} - 88 x^{18} + 95 x^{17} - 15 x^{16} - 224 x^{15} + 108 x^{14} + 58 x^{13} + 1642 x^{12} - 5082 x^{11} + 6435 x^{10} + 1474 x^{9} - 21998 x^{8} + 40783 x^{7} - 25274 x^{6} - 17265 x^{5} + 57828 x^{4} - 81220 x^{3} + 54660 x^{2} - 19173 x + 7499$ |
$22$ |
[6,8] |
$23^{21}\cdot 47^{3}$ |
$2$ |
$33.7166533192$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$13$ |
$132400558.372$ |
| 22.6.584...416.1 |
$x^{22} + 2 x^{20} - 4 x^{19} - 3 x^{18} - 6 x^{17} + 12 x^{15} + 10 x^{14} + 12 x^{13} - 9 x^{12} - 16 x^{11} - 16 x^{10} - 8 x^{9} + 11 x^{8} + 10 x^{7} + 9 x^{6} + 2 x^{5} - 5 x^{4} - 2 x^{3} - 2 x^{2} + 1$ |
$22$ |
[6,8] |
$2^{33}\cdot 7\cdot 39297136127\cdot 2474137595057$ |
$4$ |
$34.2655610824$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$2$ |
$13$ |
$239933703.762$ |
| 22.6.616...125.1 |
$x^{22} - 2 x^{21} - x^{20} - 18 x^{19} + 62 x^{18} - 94 x^{16} - 181 x^{15} + 176 x^{14} + 109 x^{13} - 688 x^{12} - 104 x^{11} + 486 x^{10} - 327 x^{9} - 459 x^{8} + 239 x^{7} + 157 x^{6} - 80 x^{5} - 7 x^{4} + 30 x^{3} + 13 x^{2} - 2 x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 1831^{8}$ |
$2$ |
$34.3492395985$ |
$95.68176419778223$ |
|
|
? |
$C_2\times \PSL(2,11)$ (as 22T13) |
trivial |
$2$ |
$13$ |
$185058540.947$ |
| 22.6.616...125.2 |
$x^{22} - 2 x^{21} + 5 x^{20} + 14 x^{19} - 14 x^{18} + 142 x^{17} - 5 x^{16} + 272 x^{15} + 173 x^{14} + 218 x^{13} + 72 x^{12} + 64 x^{11} - 24 x^{10} - 523 x^{9} - 90 x^{8} - 459 x^{7} + 102 x^{6} - 56 x^{5} + 85 x^{4} + 4 x^{3} + 7 x^{2} - 4 x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 1831^{8}$ |
$2$ |
$34.3492395985$ |
$95.68176419778223$ |
|
|
? |
$C_2\times \PSL(2,11)$ (as 22T13) |
trivial |
$2$ |
$13$ |
$185058540.947$ |
| 22.6.671...856.1 |
$x^{22} - 2 x^{21} - x^{20} + 10 x^{19} - 11 x^{18} - 8 x^{17} + 30 x^{16} - 20 x^{15} - 16 x^{14} + 34 x^{13} - 18 x^{12} - 4 x^{11} + 13 x^{10} - 16 x^{9} + 13 x^{8} - 12 x^{6} + 8 x^{5} - 2 x^{4} + x^{2} - 2 x + 1$ |
$22$ |
[6,8] |
$2^{33}\cdot 2399\cdot 3769\cdot 593353\cdot 145817511551$ |
$5$ |
$34.4832098333$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$2$ |
$13$ |
$261757660.238$ |
| 22.6.719...104.1 |
$x^{22} + 13 x^{20} + 58 x^{18} + 76 x^{16} - 157 x^{14} - 555 x^{12} - 497 x^{10} - 62 x^{8} + 93 x^{6} + 22 x^{4} - 4 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$183099783.783$ |
| 22.6.719...104.2 |
$x^{22} + 16 x^{20} + 85 x^{18} + 166 x^{16} - 21 x^{14} - 476 x^{12} - 477 x^{10} + 83 x^{8} + 328 x^{6} + 143 x^{4} + 14 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$181073374.443$ |
| 22.6.719...104.3 |
$x^{22} + 9 x^{20} + 18 x^{18} - 52 x^{16} - 221 x^{14} - 121 x^{12} + 384 x^{10} + 550 x^{8} + 179 x^{6} - 39 x^{4} - 16 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$157258272.203$ |
| 22.6.814...144.1 |
$x^{22} + 6 x^{20} + 3 x^{18} - 36 x^{16} - 53 x^{14} + 44 x^{12} + 116 x^{10} + 29 x^{8} - 55 x^{6} - 42 x^{4} - 11 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{18}\cdot 7786721^{2}\cdot 22641181^{2}$ |
$3$ |
$34.7865405388$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$224751226.386$ |
| 22.6.900...288.1 |
$x^{22} - 9 x^{20} + 38 x^{18} - 104 x^{16} + 209 x^{14} - 331 x^{12} + 429 x^{10} - 453 x^{8} + 376 x^{6} - 227 x^{4} + 89 x^{2} - 17$ |
$22$ |
[6,8] |
$2^{22}\cdot 17\cdot 1831^{8}$ |
$3$ |
$34.945528851$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$13$ |
$487975160.123$ |
| 22.6.127...624.1 |
$x^{22} + 15 x^{20} + 91 x^{18} + 278 x^{16} + 410 x^{14} + 123 x^{12} - 404 x^{10} - 417 x^{8} - 19 x^{6} + 77 x^{4} - 3 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 55029067682009^{2}$ |
$2$ |
$35.495617601$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
$[2]$ |
$2$ |
$13$ |
$132523335.017$ |
| 22.6.165...392.1 |
$x^{22} - 46 x^{18} - 69 x^{16} + 529 x^{14} + 1242 x^{12} - 1196 x^{10} - 5336 x^{8} - 4922 x^{6} - 1932 x^{4} - 345 x^{2} - 23$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{21}$ |
$2$ |
$39.8897313901$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$13$ |
$797145799.796$ |
| 22.6.165...392.2 |
$x^{22} - 46 x^{18} - 92 x^{16} + 529 x^{14} + 2070 x^{12} + 966 x^{10} - 6141 x^{8} - 12213 x^{6} - 9039 x^{4} - 2461 x^{2} - 23$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{21}$ |
$2$ |
$39.88973139007569$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$13$ |
$850348826.1510193$ |
| 22.6.970...784.1 |
$x^{22} + 16 x^{20} + 148 x^{18} + 671 x^{16} + 1205 x^{14} - 5770 x^{12} - 13367 x^{10} - 3297 x^{8} + 124727 x^{6} - 177384 x^{4} + 91550 x^{2} - 16479$ |
$22$ |
[6,8] |
$2^{22}\cdot 1831^{9}$ |
$2$ |
$43.2280989111$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$13$ |
$3934465280.98$ |
| 22.6.266...312.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 44 x^{19} - 231 x^{18} + 825 x^{17} - 550 x^{16} - 1540 x^{15} - 968 x^{14} + 23056 x^{13} - 65956 x^{12} + 98910 x^{11} - 90409 x^{10} + 22077 x^{9} + 172414 x^{8} - 515240 x^{7} + 704264 x^{6} - 400400 x^{5} - 37840 x^{4} + 72512 x^{3} + 32560 x^{2} + 3696 x - 9888$ |
$22$ |
[6,8] |
$2^{24}\cdot 3^{11}\cdot 11^{23}$ |
$3$ |
$45.2569938044$ |
|
|
|
|
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$13$ |
$158674344921$ |
| 22.6.226...241.1 |
$x^{22} - 10 x^{21} + 29 x^{20} + 3 x^{19} - 188 x^{18} + 381 x^{17} + 73 x^{16} - 825 x^{15} - 72 x^{14} + 1868 x^{13} - 351 x^{12} + 2371 x^{11} + 18854 x^{10} + 14453 x^{9} + 97552 x^{8} + 172564 x^{7} + 165961 x^{6} + 92915 x^{5} + 32329 x^{4} + 6644 x^{3} + 718 x^{2} + 72 x + 5$ |
$22$ |
[6,8] |
$1297^{12}$ |
$1$ |
$49.8846879289$ |
$216.12498794754728$ |
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
$[2]$ |
$2$ |
$13$ |
$12826181652.5$ |
| 22.6.226...241.2 |
$x^{22} - x^{21} - 11 x^{20} + 37 x^{19} - 125 x^{18} - 206 x^{17} + 947 x^{16} - 1002 x^{15} + 693 x^{14} - 867 x^{13} - 2005 x^{12} + 50723 x^{11} - 26677 x^{10} - 11638 x^{9} + 87302 x^{8} + 129837 x^{7} + 279630 x^{6} - 109510 x^{5} - 453150 x^{4} - 37802 x^{3} + 155367 x^{2} - 17135 x - 36319$ |
$22$ |
[6,8] |
$1297^{12}$ |
$1$ |
$49.8846879289$ |
$216.12498794754728$ |
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
trivial |
$2$ |
$13$ |
$17417733592.5$ |
| 22.6.565...896.1 |
$x^{22} + 26 x^{20} + 246 x^{18} + 992 x^{16} + 1270 x^{14} - 1382 x^{12} - 3114 x^{10} - 1149 x^{8} + 264 x^{6} + 117 x^{4} - 5 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
trivial |
$2$ |
$13$ |
$32131005113.8$ |
| 22.6.565...896.2 |
$x^{22} + 25 x^{20} + 230 x^{18} + 924 x^{16} + 1202 x^{14} - 2380 x^{12} - 9046 x^{10} - 8766 x^{8} - 865 x^{6} + 1915 x^{4} + 68 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
trivial |
$2$ |
$13$ |
$15857150629.6$ |
| 22.6.113...125.1 |
$x^{22} - 9 x^{21} + 41 x^{20} - 140 x^{19} + 383 x^{18} - 720 x^{17} + 530 x^{16} + 1506 x^{15} - 7373 x^{14} + 22033 x^{13} - 51771 x^{12} + 76979 x^{11} - 19458 x^{10} - 188822 x^{9} + 431163 x^{8} - 422621 x^{7} + 84439 x^{6} + 244344 x^{5} - 239399 x^{4} + 37800 x^{3} + 53515 x^{2} - 17850 x - 6300$ |
$22$ |
[6,8] |
$5^{8}\cdot 7^{15}\cdot 11^{19}$ |
$3$ |
$53.6733511187$ |
$86.67991835373819$ |
|
|
? |
$\PGL(2,11)$ (as 22T14) |
trivial |
$2$ |
$13$ |
$118924316463$ |
| 22.6.163...984.1 |
$x^{22} + 16 x^{20} + 101 x^{18} + 300 x^{16} + 301 x^{14} - 580 x^{12} - 1949 x^{10} - 1883 x^{8} - 328 x^{6} + 387 x^{4} + 80 x^{2} - 29$ |
$22$ |
[6,8] |
$2^{22}\cdot 29\cdot 1297^{10}$ |
$3$ |
$60.6003801224$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$13$ |
$162426572365$ |
