| 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 |
| 21.15.832...351.1 |
$x^{21} - 15 x^{19} - 4 x^{18} + 67 x^{17} + 60 x^{16} - 81 x^{15} - 268 x^{14} + 17 x^{13} + 474 x^{12} - 514 x^{11} - 401 x^{10} + 1233 x^{9} + 103 x^{8} - 842 x^{7} - 75 x^{6} + 200 x^{5} + 73 x^{4} - 7 x^{3} - 19 x^{2} - 2 x + 1$ |
$21$ |
[15,3] |
$-\,7^{14}\cdot 107^{3}\cdot 21557^{3}$ |
$3$ |
$29.6752719459$ |
$5557.567460027927$ |
|
|
? |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$17$ |
$132259826.87$ |
| 21.15.901...807.1 |
$x^{21} - 20 x^{19} + 135 x^{17} - 16 x^{16} - 350 x^{15} + 149 x^{14} + 182 x^{13} - 477 x^{12} + 307 x^{11} + 641 x^{10} + 150 x^{9} - 233 x^{8} - 566 x^{7} - 26 x^{6} + 272 x^{5} + 5 x^{4} - 31 x^{3} + 7 x^{2} - 2 x - 1$ |
$21$ |
[15,3] |
$-\,7^{14}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3}$ |
$4$ |
$29.7890234139$ |
$5632.486985444207$ |
|
|
? |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$17$ |
$126151281.589$ |
| 21.15.303...199.1 |
$x^{21} - 7 x^{20} + 4 x^{19} + 78 x^{18} - 172 x^{17} - 227 x^{16} + 1027 x^{15} - 237 x^{14} - 2424 x^{13} + 2147 x^{12} + 2451 x^{11} - 3882 x^{10} - 561 x^{9} + 3295 x^{8} - 1120 x^{7} - 1109 x^{6} + 907 x^{5} - 79 x^{4} - 154 x^{3} + 74 x^{2} - 14 x + 1$ |
$21$ |
[15,3] |
$-\,107^{3}\cdot 313^{2}\cdot 5023^{2}\cdot 21557^{3}$ |
$4$ |
$31.5601884029$ |
$20534827.556795347$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$17$ |
$239141569.892$ |
| 21.15.383...559.1 |
$x^{21} - 7 x^{20} + 4 x^{19} + 76 x^{18} - 158 x^{17} - 247 x^{16} + 951 x^{15} + 33 x^{14} - 2574 x^{13} + 1625 x^{12} + 3365 x^{11} - 4136 x^{10} - 1183 x^{9} + 3929 x^{8} - 1250 x^{7} - 1233 x^{6} + 995 x^{5} - 101 x^{4} - 152 x^{3} + 74 x^{2} - 14 x + 1$ |
$21$ |
[15,3] |
$-\,107^{3}\cdot 21557^{3}\cdot 1767079^{2}$ |
$3$ |
$31.9133777479$ |
$22198486.248570334$ |
|
|
✓ |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$17$ |
$267663117.46$ |
| 21.15.444...216.1 |
$x^{21} - 7 x^{20} - x^{19} + 149 x^{18} - 531 x^{17} + 390 x^{16} + 1944 x^{15} - 5031 x^{14} + 1026 x^{13} + 11764 x^{12} - 13674 x^{11} - 8132 x^{10} + 22878 x^{9} - 4419 x^{8} - 15252 x^{7} + 8130 x^{6} + 3505 x^{5} - 3016 x^{4} + 142 x^{3} + 159 x^{2} - 25 x + 1$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 37^{8}\cdot 199^{3}\cdot 461^{3}$ |
$4$ |
$32.1390570349$ |
$2924.586875530735$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$17$ |
$286086892.589$ |
| 21.15.376...791.1 |
$x^{21} - 8 x^{20} + 16 x^{19} + 19 x^{18} - 103 x^{17} + 160 x^{16} - 174 x^{15} + 66 x^{14} - 206 x^{13} + 39 x^{12} + 4498 x^{11} - 10908 x^{10} + 7867 x^{9} + 6766 x^{8} - 19649 x^{7} + 7824 x^{6} + 13595 x^{5} - 6802 x^{4} - 4602 x^{3} + 1044 x^{2} + 735 x + 79$ |
$21$ |
[15,3] |
$-\,3^{7}\cdot 107^{8}\cdot 21557^{3}$ |
$3$ |
$35.5814011607$ |
$2630.550702799701$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$17$ |
$875237315.142$ |
| 21.15.832...771.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5146 x^{7} - 588 x^{6} + 2065 x^{5} + 392 x^{4} - 357 x^{3} - 98 x^{2} + 7 x + 1$ |
$21$ |
[15,3] |
$-\,7^{35}\cdot 13^{3}$ |
$2$ |
$36.9514510973$ |
|
|
|
✓ |
$D_7\wr C_3$ (as 21T45) |
trivial |
$2$ |
$17$ |
$2097411544.97$ |
| 21.15.923...827.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 4 x^{14} + 2940 x^{13} + 56 x^{12} - 5733 x^{11} - 308 x^{10} + 7007 x^{9} + 840 x^{8} - 5142 x^{7} - 1176 x^{6} + 2037 x^{5} + 784 x^{4} - 301 x^{3} - 196 x^{2} - 21 x + 1$ |
$21$ |
[15,3] |
$-\,7^{35}\cdot 29^{3}$ |
$2$ |
$41.4391399314$ |
|
|
|
✓ |
$D_7\wr C_3$ (as 21T45) |
trivial |
$2$ |
$17$ |
$6207597526.74$ |
| 21.15.184...963.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} + 2940 x^{13} - 5733 x^{11} + 7007 x^{9} - 5149 x^{7} + 2086 x^{5} - 399 x^{3} + 28 x - 1$ |
$21$ |
[15,3] |
$-\,7^{21}\cdot 229^{7}$ |
$2$ |
$42.8262322085$ |
|
|
|
✓ |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$17$ |
$17738220712.6$ |
| 21.15.413...551.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - x^{14} + 2940 x^{13} + 14 x^{12} - 5733 x^{11} - 77 x^{10} + 7007 x^{9} + 210 x^{8} - 5149 x^{7} - 294 x^{6} + 2086 x^{5} + 196 x^{4} - 399 x^{3} - 49 x^{2} + 28 x + 3$ |
$21$ |
[15,3] |
$-\,7^{21}\cdot 257^{7}$ |
$2$ |
$44.5050282581$ |
|
|
|
✓ |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$17$ |
$21946306658.9$ |
| 21.15.627...751.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 3 x^{14} + 2940 x^{13} + 42 x^{12} - 5733 x^{11} - 231 x^{10} + 7007 x^{9} + 630 x^{8} - 5145 x^{7} - 882 x^{6} + 2058 x^{5} + 588 x^{4} - 343 x^{3} - 147 x^{2} + 3$ |
$21$ |
[15,3] |
$-\,3^{28}\cdot 7^{21}\cdot 17^{3}$ |
$3$ |
$45.3981473698$ |
|
|
|
✓ |
$D_7^3:C_3^2$ (as 21T70) |
trivial |
$2$ |
$17$ |
$20836082403.4$ |
| 21.15.246...583.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 56 x^{16} - 896 x^{15} - 424 x^{14} + 2509 x^{13} + 1657 x^{12} - 4002 x^{11} - 3518 x^{10} + 3205 x^{9} + 3917 x^{8} - 741 x^{7} - 2043 x^{6} - 373 x^{5} + 369 x^{4} + 143 x^{3} - 10 x^{2} - 10 x - 1$ |
$21$ |
[15,3] |
$-\,7^{14}\cdot 13\cdot 743\cdot 2267\cdot 5167\cdot 409333\cdot 7835549$ |
$7$ |
$48.4498485337$ |
$2204361726077.8794$ |
|
|
? |
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$17$ |
$26504767223.2$ |
| 21.15.274...875.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5148 x^{7} - 588 x^{6} + 2079 x^{5} + 392 x^{4} - 385 x^{3} - 98 x^{2} + 21 x + 5$ |
$21$ |
[15,3] |
$-\,5^{3}\cdot 7^{21}\cdot 13^{14}$ |
$3$ |
$48.7057011094$ |
|
|
|
✓ |
$D_7^3:C_3^2$ (as 21T70) |
trivial |
$2$ |
$17$ |
$49453805524.3$ |
| 21.15.781...463.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 58 x^{16} - 894 x^{15} - 452 x^{14} + 2477 x^{13} + 1803 x^{12} - 3797 x^{11} - 3830 x^{10} + 2593 x^{9} + 4018 x^{8} - 11 x^{7} - 1637 x^{6} - 453 x^{5} + 235 x^{4} + 116 x^{3} - 3 x^{2} - 8 x - 1$ |
$21$ |
[15,3] |
$-\,7^{14}\cdot 13\cdot 113\cdot 784852972712844077323$ |
$4$ |
$51.1916554902$ |
$3929196468265.053$ |
|
|
✓ |
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$17$ |
$67580414506.4$ |
| 21.15.139...064.1 |
$x^{21} - 24 x^{19} - 16 x^{18} + 189 x^{17} + 252 x^{16} - 321 x^{15} - 810 x^{14} - 1917 x^{13} - 3792 x^{12} + 2403 x^{11} + 18618 x^{10} + 23083 x^{9} + 3420 x^{8} - 20487 x^{7} - 31006 x^{6} - 31212 x^{5} - 25560 x^{4} - 15440 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3}$ |
$4$ |
$52.629314108$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$17$ |
$72608566989.9$ |
| 21.15.139...064.2 |
$x^{21} - 24 x^{19} - 16 x^{18} + 189 x^{17} + 252 x^{16} - 348 x^{15} - 864 x^{14} - 1467 x^{13} - 2504 x^{12} + 1026 x^{11} + 10284 x^{10} + 15673 x^{9} + 12996 x^{8} + 6033 x^{7} - 5438 x^{6} - 18252 x^{5} - 22104 x^{4} - 15056 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3}$ |
$4$ |
$52.629314108$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$17$ |
$58374793410.9$ |
| 21.15.348...648.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 46 x^{16} - 906 x^{15} - 284 x^{14} + 2669 x^{13} + 927 x^{12} - 4946 x^{11} - 1796 x^{10} + 5779 x^{9} + 2197 x^{8} - 4067 x^{7} - 1691 x^{6} + 1503 x^{5} + 733 x^{4} - 175 x^{3} - 126 x^{2} - 20 x - 1$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 37^{7}\cdot 349\cdot 10765241\cdot 595830643430851$ |
$5$ |
$76.3735624702$ |
$14446862362894.004$ |
|
|
✓ |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$17$ |
$3473783434490$ |
| 21.15.480...208.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 58 x^{16} - 894 x^{15} - 452 x^{14} + 2477 x^{13} + 1803 x^{12} - 3798 x^{11} - 3832 x^{10} + 2599 x^{9} + 4033 x^{8} - 15 x^{7} - 1667 x^{6} - 473 x^{5} + 237 x^{4} + 121 x^{3} - 2 x^{2} - 8 x - 1$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 37^{7}\cdot 3089859034734508131528239$ |
$3$ |
$77.5547009139$ |
$16972931523198.04$ |
|
|
✓ |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$17$ |
$3867678769990$ |
| 21.15.575...523.1 |
$x^{21} - 5 x^{20} - 9 x^{19} + 74 x^{18} + 9 x^{17} - 456 x^{16} + 171 x^{15} + 1521 x^{14} - 850 x^{13} - 2991 x^{12} + 1808 x^{11} + 3549 x^{10} - 2032 x^{9} - 2512 x^{8} + 1235 x^{7} + 1025 x^{6} - 388 x^{5} - 231 x^{4} + 57 x^{3} + 25 x^{2} - 3 x - 1$ |
$21$ |
[15,3] |
$-\,57\!\cdots\!23$ |
$1$ |
$78.2221440051$ |
$7.585112248351778e+19$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$17$ |
$10568359055900$ |
| 21.15.157...996.1 |
$x^{21} - 5 x^{20} - 9 x^{19} + 74 x^{18} + 9 x^{17} - 456 x^{16} + 171 x^{15} + 1521 x^{14} - 850 x^{13} - 2991 x^{12} + 1808 x^{11} + 3549 x^{10} - 2032 x^{9} - 2512 x^{8} + 1235 x^{7} + 1025 x^{6} - 388 x^{5} - 229 x^{4} + 56 x^{3} + 25 x^{2} - 3 x - 1$ |
$21$ |
[15,3] |
$-\,2^{2}\cdot 7\cdot 1747\cdot 34519\cdot 93\!\cdots\!99$ |
$5$ |
$82.0768706472$ |
|
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$17$ |
$20147555888400$ |
| 21.15.249...472.1 |
$x^{21} - 21 x^{19} - 8 x^{18} + 189 x^{17} + 144 x^{16} - 945 x^{15} - 1080 x^{14} + 2835 x^{13} + 4432 x^{12} - 5103 x^{11} - 11064 x^{10} + 4903 x^{9} + 17712 x^{8} - 387 x^{7} - 17960 x^{6} - 5400 x^{5} + 9264 x^{4} + 5656 x^{3} - 288 x^{2} - 768 x - 128$ |
$21$ |
[15,3] |
$-\,2^{38}\cdot 3^{21}\cdot 31\cdot 809^{6}$ |
$4$ |
$83.8883896315$ |
|
|
|
|
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$17$ |
$110368762734000$ |
| 21.15.595...176.1 |
$x^{21} - 27 x^{19} - 18 x^{18} + 234 x^{17} + 312 x^{16} - 436 x^{15} - 1080 x^{14} - 2502 x^{13} - 4912 x^{12} + 2538 x^{11} + 22188 x^{10} + 33506 x^{9} + 27432 x^{8} + 1611 x^{7} - 61842 x^{6} - 138564 x^{5} - 157608 x^{4} - 105712 x^{3} - 42336 x^{2} - 9408 x - 896$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 7^{2}\cdot 577^{9}$ |
$4$ |
$87.42879826$ |
|
|
|
? |
$C_3^7:C_2\wr D_7$ (as 21T131) |
trivial |
$2$ |
$17$ |
$18710380374300$ |
| 21.15.601...656.1 |
$x^{21} - 24 x^{19} - 16 x^{18} + 153 x^{17} + 204 x^{16} + 365 x^{15} + 594 x^{14} - 4545 x^{13} - 13088 x^{12} - 9774 x^{11} + 5484 x^{10} + 48407 x^{9} + 147132 x^{8} + 233967 x^{7} + 213694 x^{6} + 121932 x^{5} + 49752 x^{4} + 18128 x^{3} + 6048 x^{2} + 1344 x + 128$ |
$21$ |
[15,3] |
$-\,2^{27}\cdot 3^{21}\cdot 11\cdot 3967^{6}$ |
$4$ |
$87.4746081533$ |
|
|
|
|
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$17$ |
$76439189215900$ |
| 21.15.112...256.1 |
$x^{21} - 63 x^{19} - 42 x^{18} + 1665 x^{17} + 2220 x^{16} - 23155 x^{15} - 47790 x^{14} + 168858 x^{13} + 528168 x^{12} - 449145 x^{11} - 3043422 x^{10} - 1732173 x^{9} + 7496316 x^{8} + 13524411 x^{7} + 1957846 x^{6} - 18965124 x^{5} - 27585864 x^{4} - 19533296 x^{3} - 7904736 x^{2} - 1756608 x - 167296$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 29\cdot 239^{3}\cdot 431^{3}\cdot 1307^{2}$ |
$7$ |
$90.1346220581$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$17$ |
$16402886226500$ |
| 21.15.235...144.1 |
$x^{21} - 63 x^{19} - 42 x^{18} + 1674 x^{17} + 2232 x^{16} - 23583 x^{15} - 48654 x^{14} + 176382 x^{13} + 549640 x^{12} - 500931 x^{11} - 3278442 x^{10} - 1739618 x^{9} + 8547336 x^{8} + 15049899 x^{7} + 1418766 x^{6} - 22842756 x^{5} - 32687784 x^{4} - 23073776 x^{3} - 9332064 x^{2} - 2073792 x - 197504$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 47\cdot 107^{3}\cdot 1543^{2}\cdot 21557^{3}$ |
$6$ |
$93.3429533912$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$17$ |
$19309249738700$ |
| 21.15.237...000.1 |
$x^{21} - 24 x^{19} - 16 x^{18} + 153 x^{17} + 204 x^{16} + 176 x^{15} + 216 x^{14} - 3420 x^{13} - 9472 x^{12} - 1485 x^{11} + 22506 x^{10} + 34207 x^{9} + 20844 x^{8} + 873 x^{7} - 13470 x^{6} - 22572 x^{5} - 23256 x^{4} - 15184 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 6679^{6}$ |
$4$ |
$93.3874102746$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$17$ |
$20396068390900$ |
| 21.15.330...344.1 |
$x^{21} - 27 x^{19} - 18 x^{18} + 234 x^{17} + 312 x^{16} - 409 x^{15} - 1026 x^{14} - 2547 x^{13} - 5120 x^{12} + 621 x^{11} + 16422 x^{10} + 28117 x^{9} + 31140 x^{8} + 25446 x^{7} + 1924 x^{6} - 30024 x^{5} - 42480 x^{4} - 29920 x^{3} - 12096 x^{2} - 2688 x - 256$ |
$21$ |
[15,3] |
$-\,2^{15}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}$ |
$4$ |
$94.8710580569$ |
|
|
|
|
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$17$ |
$371198961249000$ |
| 21.15.127...328.1 |
$x^{21} - 21 x^{19} - 4 x^{18} + 189 x^{17} + 72 x^{16} - 1001 x^{15} - 540 x^{14} + 3675 x^{13} + 2512 x^{12} - 10143 x^{11} - 9084 x^{10} + 19679 x^{9} + 24840 x^{8} - 19971 x^{7} - 40932 x^{6} - 1080 x^{5} + 28512 x^{4} + 15200 x^{3} - 1536 x - 256$ |
$21$ |
[15,3] |
$-\,2^{26}\cdot 3^{21}\cdot 73^{12}\cdot 79$ |
$4$ |
$101.144942949$ |
|
|
|
? |
$C_3^7.C_2\wr C_7:C_3$ (as 21T137) |
trivial |
$2$ |
$17$ |
$218265619129000$ |
| 21.15.131...528.1 |
$x^{21} - 27 x^{19} - 18 x^{18} + 171 x^{17} + 228 x^{16} + 1129 x^{15} + 2106 x^{14} - 14553 x^{13} - 42240 x^{12} + 16497 x^{11} + 177918 x^{10} + 192220 x^{9} - 93312 x^{8} - 395361 x^{7} - 420282 x^{6} - 259956 x^{5} - 121032 x^{4} - 51248 x^{3} - 18144 x^{2} - 4032 x - 384$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{19}\cdot 1601^{9}$ |
$3$ |
$101.316078035$ |
|
|
|
|
$C_3^7:C_2\wr D_7$ (as 21T131) |
trivial |
$2$ |
$17$ |
$143659732725000$ |
| 21.15.378...328.1 |
$x^{21} - 21 x^{19} - 17 x^{18} + 189 x^{17} + 306 x^{16} - 1007 x^{15} - 2295 x^{14} + 3765 x^{13} + 9292 x^{12} - 10683 x^{11} - 21999 x^{10} + 22299 x^{9} + 30834 x^{8} - 31401 x^{7} - 24457 x^{6} + 27378 x^{5} + 8880 x^{4} - 13080 x^{3} + 288 x^{2} + 2304 x - 512$ |
$21$ |
[15,3] |
$-\,2^{12}\cdot 3^{21}\cdot 313^{12}$ |
$3$ |
$118.895038223$ |
|
|
|
|
$C_3^7.C_2\wr C_7:C_3$ (as 21T137) |
trivial |
$2$ |
$17$ |
$783544192002000$ |
| 21.15.199...576.1 |
$x^{21} - 21 x^{19} - 4 x^{18} + 189 x^{17} + 72 x^{16} - 1045 x^{15} - 540 x^{14} + 4335 x^{13} + 1944 x^{12} - 14103 x^{11} - 2268 x^{10} + 32519 x^{9} - 5832 x^{8} - 46431 x^{7} + 21084 x^{6} + 35532 x^{5} - 21528 x^{4} - 11616 x^{3} + 6048 x^{2} + 1152 x - 512$ |
$21$ |
[15,3] |
$-\,2^{15}\cdot 3^{21}\cdot 2029^{9}$ |
$3$ |
$128.691324823$ |
|
|
|
|
$C_3^7:C_2\wr D_7$ (as 21T131) |
trivial |
$2$ |
$17$ |
$13402669848900000$ |
| 21.15.318...064.1 |
$x^{21} - 42 x^{19} - 28 x^{18} + 567 x^{17} + 756 x^{16} - 2205 x^{15} - 4914 x^{14} - 4977 x^{13} - 5264 x^{12} + 12474 x^{11} + 54684 x^{10} + 75264 x^{9} + 50400 x^{8} + 14613 x^{7} - 7966 x^{6} - 20412 x^{5} - 22680 x^{4} - 15120 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 7^{37}$ |
$3$ |
$146.821676726$ |
|
|
|
? |
$C_3^7:C_2\wr C_7$ (as 21T123) |
trivial |
$2$ |
$17$ |
$3816744292220000$ |
| 21.15.148...920.1 |
$x^{21} - 24 x^{19} - 16 x^{18} + 135 x^{17} + 180 x^{16} + 573 x^{15} + 1026 x^{14} - 4500 x^{13} - 13672 x^{12} - 13581 x^{11} - 5334 x^{10} + 43067 x^{9} + 172764 x^{8} + 247614 x^{7} + 71204 x^{6} - 239976 x^{5} - 374256 x^{4} - 268384 x^{3} - 108864 x^{2} - 24192 x - 2304$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{23}\cdot 5\cdot 7^{12}\cdot 173^{9}$ |
$5$ |
$157.982181052$ |
|
|
|
? |
$C_3^7.C_2\wr F_7$ (as 21T142) |
trivial |
$2$ |
$17$ |
$73405955830000000$ |
| 21.15.203...528.1 |
$x^{21} - 48 x^{19} - 32 x^{18} + 846 x^{17} + 1128 x^{16} - 6266 x^{15} - 13284 x^{14} + 12042 x^{13} + 53760 x^{12} + 51354 x^{11} + 10188 x^{10} - 87483 x^{9} - 301644 x^{8} - 426411 x^{7} - 152694 x^{6} + 337284 x^{5} + 555336 x^{4} + 401904 x^{3} + 163296 x^{2} + 36288 x + 3456$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{36}\cdot 587^{9}$ |
$3$ |
$160.386570456$ |
|
|
|
|
$C_3^7:C_2\wr D_7$ (as 21T131) |
trivial |
$2$ |
$17$ |
$32437834846700000$ |
| 21.15.206...824.1 |
$x^{21} - 4 x^{20} - 135 x^{19} + 447 x^{18} + 7426 x^{17} - 14742 x^{16} - 235889 x^{15} + 81863 x^{14} + 4535217 x^{13} + 6003126 x^{12} - 45995423 x^{11} - 152176849 x^{10} + 82861724 x^{9} + 1302489123 x^{8} + 2491180274 x^{7} - 865406655 x^{6} - 12974841396 x^{5} - 29235206700 x^{4} - 36570332305 x^{3} - 28144706275 x^{2} - 12639229484 x - 2567394257$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 107^{3}\cdot 331^{2}\cdot 21557^{3}\cdot 31033^{2}\cdot 98779^{2}$ |
$6$ |
$179.118886543$ |
|
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T149) |
$[3]$ |
$2$ |
$17$ |
$7050261971610000$ |
| 21.15.501...592.1 |
$x^{21} - 48 x^{19} - 32 x^{18} + 540 x^{17} + 720 x^{16} + 4344 x^{15} + 8208 x^{14} - 77472 x^{13} - 219968 x^{12} - 213408 x^{11} - 72384 x^{10} + 2770880 x^{9} + 11033856 x^{8} + 13320192 x^{7} - 7201280 x^{6} - 38873088 x^{5} - 50079744 x^{4} - 34594816 x^{3} - 13934592 x^{2} - 3096576 x - 294912$ |
$21$ |
[15,3] |
$-\,2^{12}\cdot 3^{23}\cdot 7^{12}\cdot 173^{9}\cdot 677$ |
$5$ |
$186.828975607$ |
|
|
|
? |
$C_3^7.C_2\wr F_7$ (as 21T142) |
trivial |
$2$ |
$17$ |
$67132704014200000$ |
| 21.15.727...336.1 |
$x^{21} - 3 x^{19} - 2 x^{18} - 162 x^{17} - 216 x^{16} + 873 x^{15} + 1890 x^{14} + 4338 x^{13} + 8488 x^{12} - 17064 x^{11} - 80592 x^{10} - 106609 x^{9} - 54468 x^{8} + 116223 x^{7} + 527006 x^{6} + 1015308 x^{5} + 1115352 x^{4} + 741328 x^{3} + 296352 x^{2} + 65856 x + 6272$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 7^{5}\cdot 43^{18}$ |
$4$ |
$190.168051486$ |
|
|
|
? |
$C_3^7:C_2\wr C_7$ (as 21T123) |
trivial |
$2$ |
$17$ |
$65917490471100000$ |
| 21.15.102...048.1 |
$x^{21} - 27 x^{19} - 18 x^{18} + 216 x^{17} + 288 x^{16} - 66 x^{15} - 324 x^{14} - 3861 x^{13} - 9768 x^{12} - 4617 x^{11} + 12690 x^{10} + 37269 x^{9} + 76356 x^{8} + 100539 x^{7} + 60774 x^{6} - 15876 x^{5} - 55944 x^{4} - 44016 x^{3} - 18144 x^{2} - 4032 x - 384$ |
$21$ |
[15,3] |
$-\,2^{39}\cdot 3^{41}\cdot 13^{15}$ |
$3$ |
$193.308957625$ |
|
|
|
? |
$C_3^7.C_2\wr F_7$ (as 21T142) |
trivial |
$2$ |
$17$ |
$384598316425000000$ |
| 21.15.243...200.1 |
$x^{21} - 42 x^{19} - 28 x^{18} + 108 x^{17} + 144 x^{16} + 10470 x^{15} + 20844 x^{14} - 34056 x^{13} - 124784 x^{12} - 741690 x^{11} - 2102892 x^{10} - 1453054 x^{9} + 3319272 x^{8} + 10472130 x^{7} + 19267908 x^{6} + 27279720 x^{5} + 27096912 x^{4} + 17500768 x^{3} + 6955200 x^{2} + 1545600 x + 147200$ |
$21$ |
[15,3] |
$-\,2^{32}\cdot 3^{21}\cdot 5^{2}\cdot 23^{2}\cdot 73^{12}\cdot 179$ |
$6$ |
$201.430486694$ |
|
|
|
? |
$C_3^7.C_2\wr C_7:C_3$ (as 21T137) |
trivial |
$2$ |
$17$ |
$432606800132000000$ |
| 21.15.509...352.1 |
$x^{21} - 24 x^{19} - 16 x^{18} + 81 x^{17} + 108 x^{16} + 2061 x^{15} + 4050 x^{14} - 15687 x^{13} - 48432 x^{12} - 15984 x^{11} + 88368 x^{10} + 224896 x^{9} + 424512 x^{8} + 469797 x^{7} - 11902 x^{6} - 758268 x^{5} - 1046808 x^{4} - 733712 x^{3} - 296352 x^{2} - 65856 x - 6272$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 7^{6}\cdot 43^{18}$ |
$4$ |
$208.631711326$ |
|
|
|
|
$C_3^7:C_2\wr C_7$ (as 21T123) |
trivial |
$2$ |
$17$ |
$294377911758000000$ |
| 21.15.604...704.1 |
$x^{21} - 54 x^{19} - 36 x^{18} + 864 x^{17} + 1152 x^{16} - 912 x^{15} - 2592 x^{14} - 60048 x^{13} - 155904 x^{12} + 7776 x^{11} + 475200 x^{10} + 1694016 x^{9} + 4402944 x^{8} + 5853312 x^{7} + 1908480 x^{6} - 4935168 x^{5} - 7934976 x^{4} - 5720064 x^{3} - 2322432 x^{2} - 516096 x - 49152$ |
$21$ |
[15,3] |
$-\,2^{35}\cdot 3^{41}\cdot 13^{15}\cdot 23\cdot 41$ |
$5$ |
$234.723377726$ |
|
|
|
? |
$C_3^7.C_2\wr F_7$ (as 21T142) |
trivial |
$2$ |
$17$ |
$3737343832840000000$ |
| 21.15.248...496.1 |
$x^{21} - 10 x^{20} - 137 x^{19} + 1872 x^{18} + 3512 x^{17} - 125638 x^{16} + 254464 x^{15} + 3804068 x^{14} - 18436401 x^{13} - 41021470 x^{12} + 471129383 x^{11} - 504783236 x^{10} - 5179107104 x^{9} + 17759404554 x^{8} + 7828934422 x^{7} - 152839367696 x^{6} + 283190814248 x^{5} + 156238042640 x^{4} - 1431442633860 x^{3} + 2489193126240 x^{2} - 2022049207736 x + 669652484632$ |
$21$ |
[15,3] |
$-\,2^{22}\cdot 19^{2}\cdot 37^{4}\cdot 4129^{6}\cdot 4207717^{2}$ |
$5$ |
$251.082252684$ |
$396784318.31862247$ |
|
|
|
$C_3^7.C_2^4:\GL(3,2)$ (as 21T136) |
trivial |
$2$ |
$17$ |
$6828490345850000000$ |
| 21.15.264...816.1 |
$x^{21} - 3 x^{20} - 209 x^{19} + 866 x^{18} + 17488 x^{17} - 100813 x^{16} - 699289 x^{15} + 6055386 x^{14} + 9100112 x^{13} - 197774167 x^{12} + 303373804 x^{11} + 3145126908 x^{10} - 13632017727 x^{9} - 6799234698 x^{8} + 179226043197 x^{7} - 434862711589 x^{6} - 215531886603 x^{5} + 3436111182819 x^{4} - 8653636855724 x^{3} + 11225010417085 x^{2} - 7833213610116 x + 2346733148869$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 107^{3}\cdot 21557^{3}\cdot 597049^{2}\cdot 60696949^{2}$ |
$5$ |
$251.786738861$ |
|
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T149) |
$[3]$ |
$2$ |
$17$ |
$262762283957000000$ |
| 21.15.679...056.1 |
$x^{21} - 5 x^{20} - 147 x^{19} + 855 x^{18} + 8313 x^{17} - 59101 x^{16} - 213419 x^{15} + 2133399 x^{14} + 1553594 x^{13} - 42723266 x^{12} + 42772372 x^{11} + 449457876 x^{10} - 1079884938 x^{9} - 1761084678 x^{8} + 8758478200 x^{7} - 5404777968 x^{6} - 17906984544 x^{5} + 38312104852 x^{4} - 48599758344 x^{3} + 67992573696 x^{2} - 64614140288 x + 23767712416$ |
$21$ |
[15,3] |
$-\,2^{22}\cdot 4129^{6}\cdot 571755108853^{2}$ |
$3$ |
$293.898646611$ |
$13264573906.00381$ |
|
|
|
$C_3^7.C_2^4:\GL(3,2)$ (as 21T136) |
$[3]$ |
$2$ |
$17$ |
$41775063679700000000$ |
| 21.15.281...000.1 |
$x^{21} - 45 x^{19} - 30 x^{18} + 594 x^{17} + 792 x^{16} - 897 x^{15} - 2322 x^{14} - 17910 x^{13} - 43976 x^{12} - 10098 x^{11} + 92388 x^{10} + 258803 x^{9} + 551340 x^{8} + 841095 x^{7} + 929166 x^{6} + 845100 x^{5} + 656280 x^{4} + 387920 x^{3} + 151200 x^{2} + 33600 x + 3200$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 3^{21}\cdot 5^{7}\cdot 71^{18}$ |
$4$ |
$314.478377591$ |
|
|
|
|
$C_3^7:C_2\wr C_7$ (as 21T123) |
trivial |
$2$ |
$17$ |
$55032853386800000000$ |
| 21.15.283...256.1 |
$x^{21} - 6 x^{20} - 129 x^{19} + 738 x^{18} + 6841 x^{17} - 34182 x^{16} - 206917 x^{15} + 754770 x^{14} + 4078383 x^{13} - 7593138 x^{12} - 52093363 x^{11} + 8626390 x^{10} + 365734083 x^{9} + 439496302 x^{8} - 804532503 x^{7} - 2198991242 x^{6} - 1696579116 x^{5} - 3038803440 x^{4} - 11303652912 x^{3} - 18939196800 x^{2} - 14663981568 x - 4441714880$ |
$21$ |
[15,3] |
$-\,2^{26}\cdot 13^{2}\cdot 73^{12}\cdot 1699^{2}\cdot 19440739^{2}$ |
$5$ |
$351.034784071$ |
|
|
|
? |
$C_3^7.F_8:C_6$ (as 21T117) |
$[3]$ |
$2$ |
$17$ |
$48439163443900000000$ |
| 21.15.262...824.1 |
$x^{21} - 8 x^{20} - 133 x^{19} + 730 x^{18} + 9557 x^{17} - 20774 x^{16} - 408565 x^{15} - 231634 x^{14} + 9621995 x^{13} + 27029686 x^{12} - 96185103 x^{11} - 598120396 x^{10} - 342043949 x^{9} + 4693867170 x^{8} + 13668773237 x^{7} + 3878121300 x^{6} - 56490630556 x^{5} - 147123786832 x^{4} - 185267123790 x^{3} - 132188180172 x^{2} - 51125595528 x - 8334777958$ |
$21$ |
[15,3] |
$-\,2^{26}\cdot 73^{12}\cdot 1747^{2}\cdot 2366049313^{2}$ |
$4$ |
$435.52560765$ |
|
|
|
? |
$C_3^7.F_8:C_6$ (as 21T117) |
$[3]$ |
$2$ |
$17$ |
$350038202896000000000$ |
| 21.15.199...704.1 |
$x^{21} - 6 x^{20} - 203 x^{19} + 838 x^{18} + 14852 x^{17} - 59663 x^{16} - 530509 x^{15} + 2576288 x^{14} + 9166942 x^{13} - 66398244 x^{12} - 28436177 x^{11} + 936461376 x^{10} - 1582339958 x^{9} - 5167321863 x^{8} + 23210975798 x^{7} - 20434819891 x^{6} - 69789330828 x^{5} + 247971929908 x^{4} - 375341626400 x^{3} + 321030524262 x^{2} - 151939714933 x + 31214514281$ |
$21$ |
[15,3] |
$-\,2^{14}\cdot 29^{18}\cdot 7608122372761^{2}$ |
$3$ |
$479.688154766$ |
|
|
|
? |
$C_3^7:(C_2\times F_8)$ (as 21T112) |
$[3]$ |
$2$ |
$17$ |
$236029735693000000000$ |
| 21.15.131...827.1 |
$x^{21} - 2 x^{20} - 278 x^{19} + 1209 x^{18} + 28609 x^{17} - 188663 x^{16} - 1265361 x^{15} + 12878599 x^{14} + 13360899 x^{13} - 429530466 x^{12} + 780621370 x^{11} + 6395176809 x^{10} - 27439148621 x^{9} - 14072788600 x^{8} + 293371856110 x^{7} - 536805970235 x^{6} - 490924632667 x^{5} + 3155238661458 x^{4} - 4701437594680 x^{3} + 2873237146615 x^{2} - 294214513112 x - 270275728417$ |
$21$ |
[15,3] |
$-\,3^{7}\cdot 29^{18}\cdot 157^{2}\cdot 3307^{2}\cdot 3943^{2}\cdot 26083^{2}$ |
$6$ |
$524.695209274$ |
$44027436841.07632$ |
|
|
? |
$C_3^7:(C_2\times F_8)$ (as 21T112) |
$[3]$ |
$2$ |
$17$ |
$616510170935000000000$ |
