| 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 |
| 21.5.162...041.1 |
$x^{21} - x^{20} - 6 x^{19} + 8 x^{18} + 15 x^{17} - 28 x^{16} - 39 x^{15} + 74 x^{14} + 112 x^{13} - 127 x^{12} - 227 x^{11} + 89 x^{10} + 306 x^{9} + x^{8} - 244 x^{7} - 55 x^{6} + 122 x^{5} + 40 x^{4} - 41 x^{3} - 6 x^{2} + 8 x - 1$ |
$21$ |
[5,8] |
$13^{8}\cdot 109^{8}$ |
$2$ |
$15.8679874279$ |
$37.64306044943742$ |
|
|
? |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$17240.5464964$ |
| 21.5.267...304.1 |
$x^{21} - 5 x^{20} + 11 x^{19} - 16 x^{18} + 25 x^{17} - 38 x^{16} + 36 x^{15} - 25 x^{14} + 18 x^{13} - 4 x^{12} - 3 x^{11} - 17 x^{10} - 23 x^{9} - 12 x^{8} + 55 x^{7} + 18 x^{6} - 46 x^{5} - 17 x^{4} + 19 x^{3} + 9 x^{2} - 2 x - 1$ |
$21$ |
[5,8] |
$2^{18}\cdot 317^{8}$ |
$2$ |
$16.2483846421$ |
$32.251902756545775$ |
|
|
? |
$\PSL(2,7)$ (as 21T14) |
trivial |
$2$ |
$12$ |
$25357.2549184$ |
| 21.5.855...849.1 |
$x^{21} - 4 x^{19} + 23 x^{17} - 4 x^{16} - 54 x^{15} + 19 x^{14} + 94 x^{13} - 41 x^{12} - 115 x^{11} + 59 x^{10} + 30 x^{9} - 81 x^{8} + 20 x^{7} + 46 x^{6} - 18 x^{5} - 5 x^{4} + 13 x^{3} - 3 x^{2} + 1$ |
$21$ |
[5,8] |
$23^{8}\cdot 239^{3}\cdot 431^{3}$ |
$3$ |
$17.1742778909$ |
$1539.2228558594106$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$12$ |
$45009.9851463$ |
| 21.5.123...001.1 |
$x^{21} - 2 x^{19} - x^{18} - 8 x^{17} + 16 x^{15} + 16 x^{14} + 21 x^{13} - 27 x^{12} - 29 x^{11} - 63 x^{10} - 3 x^{9} + 86 x^{8} + 60 x^{7} + 11 x^{6} - 69 x^{5} - 49 x^{4} + 30 x^{3} + 16 x^{2} - 6 x - 1$ |
$21$ |
[5,8] |
$7^{9}\cdot 12503^{5}$ |
$2$ |
$21.7602786875$ |
$295.8394835041462$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$564369.598704$ |
| 21.5.279...288.1 |
$x^{21} - 2 x^{19} - 7 x^{18} - 5 x^{17} + 11 x^{16} + 17 x^{15} + 34 x^{14} - 32 x^{13} - 19 x^{12} - 120 x^{11} - 65 x^{10} - 276 x^{9} + 43 x^{8} + 539 x^{7} + 983 x^{6} + 606 x^{5} + 280 x^{4} + 121 x^{3} + 40 x^{2} - 13 x - 5$ |
$21$ |
[5,8] |
$2^{27}\cdot 181^{9}$ |
$2$ |
$22.6263811101$ |
$38.05259518088089$ |
|
|
|
$\PGL(2,7)$ (as 21T20) |
trivial |
$2$ |
$12$ |
$2296254.50823$ |
| 21.5.348...177.1 |
$x^{21} - 2 x^{20} - 5 x^{18} + 12 x^{17} - 5 x^{16} + 4 x^{15} - 27 x^{14} + 16 x^{13} - 8 x^{12} + 8 x^{11} - 22 x^{10} - 8 x^{9} - 2 x^{8} + 9 x^{7} + 15 x^{6} + 12 x^{5} + 13 x^{4} + 2 x^{3} - x^{2} - 2 x - 1$ |
$21$ |
[5,8] |
$3^{8}\cdot 37^{5}\cdot 2381^{5}$ |
$3$ |
$22.8629450794$ |
$514.0924041454026$ |
|
|
? |
$S_7$ (as 21T38) |
trivial |
$2$ |
$12$ |
$1358971.01083$ |
| 21.5.417...153.1 |
$x^{21} - 3 x^{19} - 2 x^{18} + 15 x^{17} + 6 x^{16} - 23 x^{15} - 30 x^{14} + 23 x^{13} + 44 x^{12} + 12 x^{11} - 43 x^{10} - 61 x^{9} + 51 x^{8} + 34 x^{7} - 5 x^{6} - 30 x^{5} - 9 x^{4} + 13 x^{3} + 7 x^{2} - 1$ |
$21$ |
[5,8] |
$23^{7}\cdot 107^{3}\cdot 21557^{3}$ |
$3$ |
$23.062442084$ |
$7283.665080163969$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$12$ |
$895675.424859$ |
| 21.5.115...601.1 |
$x^{21} - 6 x^{20} + 61 x^{18} - 66 x^{17} - 276 x^{16} + 428 x^{15} + 753 x^{14} - 1425 x^{13} - 1350 x^{12} + 3009 x^{11} + 1563 x^{10} - 4228 x^{9} - 1029 x^{8} + 3927 x^{7} + 143 x^{6} - 2298 x^{5} + 384 x^{4} + 686 x^{3} - 288 x^{2} - 21 x + 31$ |
$21$ |
[5,8] |
$3^{32}\cdot 53^{8}$ |
$2$ |
$24.2052130678$ |
|
|
|
? |
$A_7$ (as 21T33) |
trivial |
$2$ |
$12$ |
$3200562.51046$ |
| 21.5.124...789.1 |
$x^{21} - 7 x^{20} + 22 x^{19} - 36 x^{18} + 16 x^{17} + 90 x^{16} - 359 x^{15} + 819 x^{14} - 1304 x^{13} + 1479 x^{12} - 987 x^{11} - 415 x^{10} + 2526 x^{9} - 4472 x^{8} + 5201 x^{7} - 4365 x^{6} + 2658 x^{5} - 1122 x^{4} + 291 x^{3} - 23 x^{2} - 4 x - 1$ |
$21$ |
[5,8] |
$1709^{9}$ |
$1$ |
$24.2918664051$ |
$41.340053217188775$ |
|
|
? |
$\PGL(2,7)$ (as 21T20) |
trivial |
$2$ |
$12$ |
$5054661.69478$ |
| 21.5.159...441.1 |
$x^{21} - 2 x^{20} - 2 x^{19} + 26 x^{18} - 25 x^{17} - 37 x^{16} + 153 x^{15} - 69 x^{14} - 124 x^{13} + 277 x^{12} - 70 x^{11} - 106 x^{10} + 228 x^{9} - 76 x^{8} - 41 x^{7} + 116 x^{6} - 32 x^{5} - 16 x^{4} + 25 x^{3} - 2 x^{2} - 2 x + 1$ |
$21$ |
[5,8] |
$11^{14}\cdot 29^{10}$ |
$2$ |
$24.583391024$ |
$69.62404259846498$ |
|
|
? |
$A_7$ (as 21T33) |
trivial |
$2$ |
$12$ |
$2549812.08882$ |
| 21.5.933...688.1 |
$x^{21} - 21 x^{19} - 16 x^{18} + 189 x^{17} + 288 x^{16} - 841 x^{15} - 2160 x^{14} + 1275 x^{13} + 8272 x^{12} + 4257 x^{11} - 15024 x^{10} - 22193 x^{9} + 3456 x^{8} + 32877 x^{7} + 27088 x^{6} - 4104 x^{5} - 23856 x^{4} - 20464 x^{3} - 8928 x^{2} - 2112 x - 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{15}\cdot 71^{3}\cdot 173\cdot 8623^{3}$ |
$5$ |
$29.8375785031$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$12$ |
$19802837.2105$ |
| 21.5.393...824.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 961 x^{15} + 3075 x^{13} - 6543 x^{11} + 9503 x^{9} - 9387 x^{7} - 32 x^{6} + 6048 x^{5} + 192 x^{4} - 2352 x^{3} - 288 x^{2} + 576 x + 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 8623^{3}$ |
$4$ |
$31.9529021298$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$12$ |
$26711678.1083$ |
| 21.5.933...053.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 49 x^{16} - 903 x^{15} - 326 x^{14} + 2621 x^{13} + 1146 x^{12} - 4665 x^{11} - 2317 x^{10} + 5020 x^{9} + 2746 x^{8} - 3078 x^{7} - 1856 x^{6} + 916 x^{5} + 648 x^{4} - 62 x^{3} - 89 x^{2} - 17 x - 1$ |
$21$ |
[5,8] |
$23^{7}\cdot 7013\cdot 101221\cdot 386091589202563$ |
$4$ |
$37.1533585556$ |
$2510708654803.8076$ |
|
|
✓ |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$12$ |
$194180619.332$ |
| 21.5.111...288.1 |
$x^{21} - 6 x^{19} - 4 x^{18} + 108 x^{15} + 216 x^{14} - 261 x^{13} - 1048 x^{12} - 1080 x^{11} - 480 x^{10} + 1378 x^{9} + 5832 x^{8} + 7533 x^{7} - 1566 x^{6} - 16092 x^{5} - 21528 x^{4} - 14992 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{37}\cdot 73^{6}$ |
$3$ |
$37.4719966449$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$12$ |
$378342584.891$ |
| 21.5.138...288.1 |
$x^{21} - 6 x^{19} - 4 x^{18} - 9 x^{17} - 12 x^{16} + 104 x^{15} + 216 x^{14} + 144 x^{13} + 32 x^{12} - 729 x^{11} - 2430 x^{10} - 3969 x^{9} - 5076 x^{8} - 3393 x^{7} + 5790 x^{6} + 18252 x^{5} + 22104 x^{4} + 15056 x^{3} + 6048 x^{2} + 1344 x + 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6}$ |
$4$ |
$37.8616297577$ |
|
|
|
? |
$C_3^7.C_2^4:\GL(3,2)$ (as 21T136) |
trivial |
$2$ |
$12$ |
$182407030.672$ |
| 21.5.971...016.1 |
$x^{21} - 21 x^{19} - 12 x^{18} + 189 x^{17} + 216 x^{16} - 897 x^{15} - 1620 x^{14} + 2115 x^{13} + 6440 x^{12} - 783 x^{11} - 14100 x^{10} - 8033 x^{9} + 15336 x^{8} + 18837 x^{7} - 4012 x^{6} - 16416 x^{5} - 5736 x^{4} + 4368 x^{3} + 3744 x^{2} + 1152 x + 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 7\cdot 13^{6}\cdot 109^{6}$ |
$5$ |
$41.5376639148$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$12$ |
$835220003.258$ |
| 21.5.114...625.1 |
$x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 52 x^{16} - 900 x^{15} - 368 x^{14} + 2573 x^{13} + 1365 x^{12} - 4381 x^{11} - 2832 x^{10} + 4243 x^{9} + 3250 x^{8} - 2077 x^{7} - 1933 x^{6} + 383 x^{5} + 551 x^{4} + 34 x^{3} - 55 x^{2} - 14 x - 1$ |
$21$ |
[5,8] |
$5^{3}\cdot 31^{7}\cdot 3343677482854966554307$ |
$3$ |
$41.8732324588$ |
$719909723397.677$ |
|
|
✓ |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$12$ |
$844154506.063$ |
| 21.5.209...328.1 |
$x^{21} - 21 x^{19} - 18 x^{18} + 189 x^{17} + 324 x^{16} - 897 x^{15} - 2430 x^{14} + 2115 x^{13} + 9736 x^{12} - 783 x^{11} - 22062 x^{10} - 8161 x^{9} + 27108 x^{8} + 19989 x^{7} - 14274 x^{6} - 19872 x^{5} - 2160 x^{4} + 7760 x^{3} + 5184 x^{2} + 1344 x + 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6}$ |
$4$ |
$43.0823524279$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$12$ |
$958995676.947$ |
| 21.5.455...872.1 |
$x^{21} - 6 x^{19} - 4 x^{18} + 54 x^{15} + 108 x^{14} - 90 x^{13} - 416 x^{12} + 54 x^{11} + 1428 x^{10} + 2128 x^{9} + 1440 x^{8} - 3894 x^{7} - 20348 x^{6} - 40824 x^{5} - 45360 x^{4} - 30240 x^{3} - 12096 x^{2} - 2688 x - 256$ |
$21$ |
[5,8] |
$2^{32}\cdot 3^{21}\cdot 317^{6}$ |
$3$ |
$44.7117830875$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$12$ |
$4674516561.29$ |
| 21.5.513...656.1 |
$x^{21} - 21 x^{19} - 16 x^{18} + 189 x^{17} + 288 x^{16} - 845 x^{15} - 2160 x^{14} + 1335 x^{13} + 8328 x^{12} + 3897 x^{11} - 15696 x^{10} - 21465 x^{9} + 6480 x^{8} + 34425 x^{7} + 22352 x^{6} - 12636 x^{5} - 27192 x^{4} - 13840 x^{3} + 2880 x^{2} + 6528 x + 2432$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 37\cdot 109^{6}$ |
$5$ |
$44.9651013726$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$12$ |
$1160913998.94$ |
| 21.5.524...728.1 |
$x^{21} - 4 x^{18} - 36 x^{17} + 12 x^{16} - 32 x^{15} + 198 x^{14} - 45 x^{13} + 328 x^{12} - 1395 x^{11} - 120 x^{10} - 551 x^{9} + 3384 x^{8} + 135 x^{7} + 868 x^{6} - 5328 x^{5} - 2856 x^{4} + 1248 x^{3} + 1152 x^{2} - 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 23^{4}\cdot 239^{3}\cdot 431^{3}$ |
$5$ |
$45.0100684716$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$12$ |
$1065397003.93$ |
| 21.5.778...976.1 |
$x^{21} + 21 x^{19} - 14 x^{18} + 162 x^{17} - 216 x^{16} + 585 x^{15} - 1026 x^{14} + 846 x^{13} - 584 x^{12} - 1755 x^{11} + 7098 x^{10} - 11146 x^{9} + 12312 x^{8} - 9693 x^{7} - 1278 x^{6} + 16092 x^{5} - 21528 x^{4} + 14992 x^{3} - 6048 x^{2} + 1344 x - 128$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{21}\cdot 37\cdot 107^{3}\cdot 21557^{3}$ |
$5$ |
$45.8648740549$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$12$ |
$1439410720.51$ |
| 21.5.911...744.1 |
$x^{21} + 3 x^{19} - 14 x^{18} - 45 x^{17} + 12 x^{16} - 99 x^{15} + 522 x^{14} + 171 x^{13} + 272 x^{12} - 513 x^{11} - 954 x^{10} - 4555 x^{9} + 4032 x^{8} + 5343 x^{7} - 770 x^{6} - 4356 x^{5} - 1224 x^{4} - 880 x^{3} + 288 x^{2} + 576 x + 128$ |
$21$ |
[5,8] |
$2^{33}\cdot 3^{21}\cdot 317^{6}$ |
$3$ |
$46.2122114022$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$12$ |
$5471497408.33$ |
| 21.5.112...600.1 |
$x^{21} - x^{20} - 3 x^{19} + 10 x^{18} - 9 x^{17} - 5 x^{16} + 83 x^{15} - 139 x^{14} - 436 x^{13} - 411 x^{12} - 872 x^{11} - 742 x^{10} + 583 x^{9} + 984 x^{8} + 1484 x^{7} + 1498 x^{6} - 868 x^{5} - 1614 x^{4} - 396 x^{3} - 242 x^{2} - 180 x + 50$ |
$21$ |
[5,8] |
$2^{8}\cdot 5^{2}\cdot 13^{6}\cdot 229^{6}\cdot 159191^{2}$ |
$5$ |
$46.6848227731$ |
$1641376.5539579347$ |
|
|
? |
$C_3^7.C_2^6:A_7$ (as 21T148) |
trivial |
$2$ |
$12$ |
$5375052288.55$ |
| 21.5.635...152.1 |
$x^{21} - 3 x^{20} - 2 x^{19} + 16 x^{18} - 12 x^{17} - 27 x^{16} + 46 x^{15} + 13 x^{14} - 76 x^{13} + 26 x^{12} + 79 x^{11} - 73 x^{10} - 38 x^{9} + 86 x^{8} - 18 x^{7} - 47 x^{6} + 34 x^{5} + 6 x^{4} - 15 x^{3} + 4 x^{2} + 3 x - 1$ |
$21$ |
[5,8] |
$2^{3}\cdot 3^{3}\cdot 6959\cdot 382373449525433\cdot 1105105461718151$ |
$5$ |
$50.6873540503$ |
|
|
|
? |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$12$ |
$12446002569.2$ |
| 21.5.497...652.1 |
$x^{21} - 3 x^{20} - 2 x^{19} + 16 x^{18} - 12 x^{17} - 27 x^{16} + 46 x^{15} + 13 x^{14} - 76 x^{13} + 26 x^{12} + 79 x^{11} - 73 x^{10} - 38 x^{9} + 86 x^{8} - 18 x^{7} - 47 x^{6} + 34 x^{5} + 6 x^{4} - 14 x^{3} + 4 x^{2} + 2 x - 1$ |
$21$ |
[5,8] |
$2^{2}\cdot 8543\cdot 38299\cdot 309599\cdot 11606649319\cdot 1057328219989$ |
$6$ |
$55.905676613$ |
$1.7698795129084938e+18$ |
|
|
✓ |
$S_{21}$ (as 21T164) |
trivial |
$2$ |
$12$ |
$30185117768.0$ |
| 21.5.870...336.1 |
$x^{21} + 6 x^{19} - 16 x^{18} - 36 x^{17} - 144 x^{16} - 390 x^{15} - 270 x^{14} - 2019 x^{13} - 784 x^{12} - 9594 x^{11} - 2886 x^{10} - 15678 x^{9} + 10368 x^{8} + 15135 x^{7} + 33164 x^{6} + 52632 x^{5} + 28944 x^{4} + 22256 x^{3} + 12096 x^{2} + 5376 x + 896$ |
$21$ |
[5,8] |
$2^{21}\cdot 3^{21}\cdot 7^{2}\cdot 13^{6}\cdot 109^{6}$ |
$5$ |
$57.4153694592$ |
|
|
|
? |
$C_3^7.C_2^4:\GL(3,2)$ (as 21T136) |
trivial |
$2$ |
$12$ |
$15001188795.8$ |
| 21.5.446...224.1 |
$x^{21} + 18 x^{19} - 72 x^{18} + 33 x^{17} - 1080 x^{16} - 1098 x^{15} - 6357 x^{14} - 5688 x^{13} + 745 x^{12} - 3288 x^{11} - 9459 x^{10} - 59991 x^{9} - 82185 x^{8} - 50031 x^{7} + 2277 x^{6} + 5016 x^{5} + 693 x^{4} + 235 x^{3} - 24 x^{2} - 9 x - 3$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{34}\cdot 73^{6}\cdot 1039^{2}$ |
$4$ |
$62.0645161589$ |
|
|
|
? |
$C_3^7.C_2^6:A_7$ (as 21T148) |
trivial |
$2$ |
$12$ |
$56856654321.9$ |
| 21.5.732...656.1 |
$x^{21} - 21 x^{15} - 18 x^{14} - 1176 x^{9} - 2016 x^{8} - 864 x^{7} - 343 x^{3} - 882 x^{2} - 756 x - 216$ |
$21$ |
[5,8] |
$2^{18}\cdot 3^{35}\cdot 7^{21}$ |
$3$ |
$79.127207972$ |
|
|
|
|
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$12$ |
$2604814902030$ |
| 21.5.378...336.1 |
$x^{21} - 9 x^{20} + x^{19} + 247 x^{18} - 1128 x^{17} + 1844 x^{16} + 1538 x^{15} - 10782 x^{14} + 6884 x^{13} + 36114 x^{12} - 29952 x^{11} - 179184 x^{10} + 356326 x^{9} + 190336 x^{8} - 1475463 x^{7} + 2097737 x^{6} - 1307021 x^{5} + 514117 x^{4} - 539862 x^{3} + 463496 x^{2} - 103930 x - 22322$ |
$21$ |
[5,8] |
$2^{24}\cdot 11^{18}\cdot 67^{8}$ |
$3$ |
$85.5665705694$ |
$180.8026103790633$ |
|
|
|
$\PSL(3,4)$ (as 21T67) |
$[3]$ |
$2$ |
$12$ |
$10194481907400$ |
| 21.5.378...336.2 |
$x^{21} - 4 x^{20} - 34 x^{19} + 250 x^{18} + 49 x^{17} - 4806 x^{16} + 10924 x^{15} + 35134 x^{14} - 181415 x^{13} + 42258 x^{12} + 1174704 x^{11} - 2046920 x^{10} - 2612752 x^{9} + 11070150 x^{8} - 4343266 x^{7} - 21914184 x^{6} + 22487749 x^{5} + 21732094 x^{4} - 35335382 x^{3} - 9878676 x^{2} + 29752822 x - 9397944$ |
$21$ |
[5,8] |
$2^{24}\cdot 11^{18}\cdot 67^{8}$ |
$3$ |
$85.5665705694$ |
$180.8026103790633$ |
|
|
|
$\PSL(3,4)$ (as 21T67) |
$[3]$ |
$2$ |
$12$ |
$10194481907400$ |
| 21.5.101...904.1 |
$x^{21} - 27 x^{19} - 10 x^{18} + 216 x^{17} + 210 x^{16} + 725 x^{15} + 288 x^{14} - 19932 x^{13} - 38346 x^{12} + 76410 x^{11} + 234948 x^{10} + 296881 x^{9} + 400932 x^{8} - 2455545 x^{7} - 3096076 x^{6} + 984564 x^{5} + 2353416 x^{4} - 412432 x^{3} + 313056 x^{2} + 208704 x - 139136$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{28}\cdot 593^{3}\cdot 1033^{3}\cdot 1087^{2}$ |
$5$ |
$89.691127993$ |
|
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T149) |
trivial |
$2$ |
$12$ |
$1820587529600$ |
| 21.5.305...704.1 |
$x^{21} + 24 x^{19} - 16 x^{18} + 27 x^{17} - 36 x^{16} - 1662 x^{15} + 3348 x^{14} + 6192 x^{13} - 21968 x^{12} + 113589 x^{11} - 313734 x^{10} - 769213 x^{9} + 4433508 x^{8} - 9942741 x^{7} + 17192778 x^{6} - 23957316 x^{5} + 23677128 x^{4} - 15268592 x^{3} + 6066144 x^{2} - 1348032 x + 128384$ |
$21$ |
[5,8] |
$2^{14}\cdot 3^{28}\cdot 13^{6}\cdot 17^{2}\cdot 59^{2}\cdot 109^{6}$ |
$6$ |
$105.457605626$ |
|
|
|
? |
$C_3^7.C_2^3:\GL(3,2)$ (as 21T125) |
trivial |
$2$ |
$12$ |
$12933156465800$ |
| 21.5.147...864.1 |
$x^{21} - 2 x^{20} - 31 x^{19} + 14 x^{18} + 391 x^{17} + 839 x^{16} - 3642 x^{15} - 12906 x^{14} + 21946 x^{13} + 71319 x^{12} - 68080 x^{11} - 360180 x^{10} + 640978 x^{9} + 2101569 x^{8} - 6970238 x^{7} - 4352809 x^{6} + 28605427 x^{5} + 1130039 x^{4} - 63367644 x^{3} - 20310040 x^{2} + 139664899 x - 45933317$ |
$21$ |
[5,8] |
$2^{14}\cdot 37^{2}\cdot 71^{4}\cdot 211^{2}\cdot 8623^{4}\cdot 10243^{2}$ |
$6$ |
$113.661855637$ |
|
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T150) |
$[3]$ |
$2$ |
$12$ |
$6213329276080$ |
| 21.5.347...229.1 |
$x^{21} - 4 x^{20} - 90 x^{19} + 411 x^{18} + 3197 x^{17} - 18197 x^{16} - 51735 x^{15} + 435956 x^{14} + 181775 x^{13} - 5893180 x^{12} + 6396148 x^{11} + 41981559 x^{10} - 100640498 x^{9} - 107519374 x^{8} + 577043557 x^{7} - 292735101 x^{6} - 1092656431 x^{5} + 1385415391 x^{4} - 168690307 x^{3} + 1127770366 x^{2} - 3401414294 x + 2197928707$ |
$21$ |
[5,8] |
$13^{8}\cdot 109^{7}\cdot 2767^{2}\cdot 5516617^{2}$ |
$4$ |
$118.406628102$ |
$439837335.4833772$ |
|
|
? |
$C_3^7:C_2^4.\GL(3,2)$ (as 21T135) |
$[3]$ |
$2$ |
$12$ |
$11521415360300$ |
| 21.5.382...816.1 |
$x^{21} - 6 x^{20} - 32 x^{19} + 220 x^{18} - 71 x^{17} - 902 x^{16} + 5320 x^{15} - 32524 x^{14} + 54335 x^{13} + 52730 x^{12} - 451160 x^{11} + 2325392 x^{10} - 6659517 x^{9} + 11243466 x^{8} - 15644640 x^{7} + 4239088 x^{6} + 54407188 x^{5} - 141705136 x^{4} + 265754960 x^{3} - 413258960 x^{2} + 333108324 x - 162458072$ |
$21$ |
[5,8] |
$2^{36}\cdot 11^{19}\cdot 71^{7}$ |
$3$ |
$118.946034221$ |
$350.64554459156545$ |
|
|
|
$\PSL(3,4).C_2$ (as 21T85) |
trivial |
$2$ |
$12$ |
$2512137314520000$ |
| 21.5.384...288.1 |
$x^{21} - 7 x^{15} - 6 x^{14} - 98 x^{9} - 168 x^{8} - 72 x^{7} + 343 x^{3} + 882 x^{2} + 756 x + 216$ |
$21$ |
[5,8] |
$2^{18}\cdot 3^{18}\cdot 7^{35}$ |
$3$ |
$118.98261768$ |
|
|
|
? |
$S_7\wr C_3$ (as 21T159) |
trivial |
$2$ |
$12$ |
$61739221128300$ |
| 21.5.133...901.1 |
$x^{21} - 6 x^{20} - 109 x^{19} + 852 x^{18} + 4054 x^{17} - 49056 x^{16} - 19772 x^{15} + 1439643 x^{14} - 2914462 x^{13} - 20959603 x^{12} + 93601933 x^{11} + 73773944 x^{10} - 1209292466 x^{9} + 1909889766 x^{8} + 5378436465 x^{7} - 23689051810 x^{6} + 21160307927 x^{5} + 56749396678 x^{4} - 187732639665 x^{3} + 241813432964 x^{2} - 156262915354 x + 41965405847$ |
$21$ |
[5,8] |
$3^{12}\cdot 19^{2}\cdot 271^{2}\cdot 2377^{2}\cdot 8689^{2}\cdot 280909^{3}$ |
$6$ |
$126.232512572$ |
|
|
|
? |
$C_3^6.(S_3\times S_7)$ (as 21T144) |
$[3]$ |
$2$ |
$12$ |
$31233390232100$ |
| 21.5.197...553.1 |
$x^{21} - 4 x^{20} - 88 x^{19} + 492 x^{18} + 2722 x^{17} - 23456 x^{16} - 18278 x^{15} + 554053 x^{14} - 909739 x^{13} - 6314467 x^{12} + 25005205 x^{11} + 14407592 x^{10} - 254496351 x^{9} + 409718150 x^{8} + 801650743 x^{7} - 3772994826 x^{6} + 3833766726 x^{5} + 6136704108 x^{4} - 22567165772 x^{3} + 29014890807 x^{2} - 18533507650 x + 4925133913$ |
$21$ |
[5,8] |
$13^{7}\cdot 109^{7}\cdot 193^{2}\cdot 277^{2}\cdot 2457529^{2}$ |
$5$ |
$128.636667759$ |
$972841476.3030767$ |
|
|
? |
$C_3^7.(C_2\times \GL(3,2))$ (as 21T119) |
$[3]$ |
$2$ |
$12$ |
$29091941771600$ |
| 21.5.269...016.1 |
$x^{21} - 21 x^{15} - 18 x^{14} - 196 x^{9} - 336 x^{8} - 144 x^{7} - 343 x^{3} - 882 x^{2} - 756 x - 216$ |
$21$ |
[5,8] |
$2^{18}\cdot 3^{18}\cdot 7^{36}$ |
$3$ |
$130.53479252$ |
|
|
|
? |
$A_7^3.A_4$ (as 21T158) |
trivial |
$2$ |
$12$ |
$153129409051000$ |
| 21.5.269...016.2 |
$x^{21} - 119 x^{15} - 102 x^{14} + 490 x^{9} + 840 x^{8} + 360 x^{7} - 343 x^{3} - 882 x^{2} - 756 x - 216$ |
$21$ |
[5,8] |
$2^{18}\cdot 3^{18}\cdot 7^{36}$ |
$3$ |
$130.53479252$ |
|
|
|
? |
$A_7^3.A_4$ (as 21T158) |
trivial |
$2$ |
$12$ |
$185340932015000$ |
| 21.5.967...744.1 |
$x^{21} - 2 x^{20} - 107 x^{19} + 12 x^{18} + 5113 x^{17} + 8402 x^{16} - 127817 x^{15} - 435638 x^{14} + 1472941 x^{13} + 9521630 x^{12} + 1053675 x^{11} - 96583342 x^{10} - 208880543 x^{9} + 261576550 x^{8} + 1797849401 x^{7} + 2472649678 x^{6} - 2118845476 x^{5} - 12591311834 x^{4} - 20851985164 x^{3} - 18493569810 x^{2} - 8864880926 x - 1810155266$ |
$21$ |
[5,8] |
$2^{24}\cdot 127^{2}\cdot 317^{6}\cdot 1867^{2}\cdot 1005409^{2}$ |
$5$ |
$138.731201278$ |
|
|
|
? |
$C_3^7.C_2^6:\GL(3,2)$ (as 21T145) |
$[3]$ |
$2$ |
$12$ |
$258301252893000$ |
| 21.5.219...257.1 |
$x^{21} - 10 x^{20} - 64 x^{19} + 1060 x^{18} - 414 x^{17} - 43164 x^{16} + 143514 x^{15} + 756375 x^{14} - 5147167 x^{13} - 1076463 x^{12} + 81715797 x^{11} - 172342538 x^{10} - 513277027 x^{9} + 2674733564 x^{8} - 1554424873 x^{7} - 14048843964 x^{6} + 35554134906 x^{5} - 7390105232 x^{4} - 106207754284 x^{3} + 210434894369 x^{2} - 176222639918 x + 58288245703$ |
$21$ |
[5,8] |
$13^{7}\cdot 109^{7}\cdot 437789723053^{2}$ |
$3$ |
$144.260879334$ |
$2170344291.6055818$ |
|
|
? |
$C_3^7.(C_2\times \GL(3,2))$ (as 21T119) |
$[3]$ |
$2$ |
$12$ |
$128035498196000$ |
| 21.5.411...632.1 |
$x^{21} - 21 x^{15} - 18 x^{14} - 49 x^{9} - 84 x^{8} - 36 x^{7} + 686 x^{3} + 1764 x^{2} + 1512 x + 432$ |
$21$ |
[5,8] |
$2^{22}\cdot 3^{12}\cdot 7^{21}\cdot 229^{7}$ |
$4$ |
$165.849948809$ |
|
|
|
? |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$12$ |
$6802834166480000$ |
| 21.5.459...209.1 |
$x^{21} - 10 x^{20} - 103 x^{19} + 1448 x^{18} + 2152 x^{17} - 83871 x^{16} + 149173 x^{15} + 2385250 x^{14} - 9948420 x^{13} - 29032971 x^{12} + 247870758 x^{11} - 109823779 x^{10} - 2879373801 x^{9} + 7247306792 x^{8} + 9672661015 x^{7} - 71078825238 x^{6} + 89876215729 x^{5} + 141470849513 x^{4} - 604358702025 x^{3} + 843239380035 x^{2} - 569139139934 x + 156657136133$ |
$21$ |
[5,8] |
$3^{2}\cdot 73^{2}\cdot 1249^{2}\cdot 2741^{6}\cdot 3877^{2}\cdot 9811^{2}$ |
$6$ |
$166.722627619$ |
$20776771425.4863$ |
|
|
? |
$C_3^7.C_2^6:\GL(3,2)$ (as 21T145) |
$[3]$ |
$2$ |
$12$ |
$830894950455000$ |
| 21.5.176...328.1 |
$x^{21} - 7 x^{15} - 6 x^{14} - 147 x^{9} - 252 x^{8} - 108 x^{7} + 343 x^{3} + 882 x^{2} + 756 x + 216$ |
$21$ |
[5,8] |
$2^{33}\cdot 3^{18}\cdot 7^{21}\cdot 37^{7}$ |
$4$ |
$177.762504144$ |
|
|
|
? |
$S_7\wr C_3.C_2$ (as 21T162) |
trivial |
$2$ |
$12$ |
$9472324331430000$ |
| 21.5.602...141.1 |
$x^{21} - 7 x^{20} - 188 x^{19} + 778 x^{18} + 17508 x^{17} - 17843 x^{16} - 932140 x^{15} - 1542174 x^{14} + 26751880 x^{13} + 113453527 x^{12} - 285357185 x^{11} - 2903686327 x^{10} - 3836195996 x^{9} + 26214572726 x^{8} + 115945855524 x^{7} + 105703821028 x^{6} - 515904519138 x^{5} - 2086385055472 x^{4} - 3732486850641 x^{3} - 3805861147297 x^{2} - 2154688272800 x - 530346668697$ |
$21$ |
[5,8] |
$3^{10}\cdot 67^{2}\cdot 127^{2}\cdot 20731^{2}\cdot 121591^{2}\cdot 280909^{3}$ |
$6$ |
$188.462211005$ |
$708669254282.1372$ |
|
|
? |
$C_3^6.(S_3\times S_7)$ (as 21T144) |
$[3]$ |
$2$ |
$12$ |
$2553824201440000$ |
| 21.5.467...304.1 |
$x^{21} + 168 x^{15} - 144 x^{14} - 1176 x^{9} + 2016 x^{8} - 864 x^{7} - 9604 x^{3} + 24696 x^{2} - 21168 x + 6048$ |
$21$ |
[5,8] |
$2^{22}\cdot 3^{30}\cdot 7^{34}$ |
$3$ |
$231.857163974$ |
|
|
|
? |
$A_7^3.S_4$ (as 21T161) |
trivial |
$2$ |
$12$ |
$584051430826000000$ |
| 21.5.375...264.1 |
$x^{21} - 21 x^{15} - 18 x^{14} - 441 x^{9} - 756 x^{8} - 324 x^{7} - 343 x^{3} - 882 x^{2} - 756 x - 216$ |
$21$ |
[5,8] |
$2^{26}\cdot 3^{40}\cdot 7^{28}$ |
$3$ |
$256.037501636$ |
|
|
|
? |
$A_7^3.S_4$ (as 21T161) |
trivial |
$2$ |
$12$ |
$2489522045230000000$ |
| 21.5.903...176.1 |
$x^{21} + 14 x^{15} - 12 x^{14} - 196 x^{9} + 336 x^{8} - 144 x^{7} - 2058 x^{3} + 5292 x^{2} - 4536 x + 1296$ |
$21$ |
[5,8] |
$2^{36}\cdot 3^{22}\cdot 7^{22}\cdot 101^{7}$ |
$4$ |
$370.97160074$ |
|
|
|
? |
$A_7^3.S_4$ (as 21T160) |
trivial |
$2$ |
$12$ |
$50841293689700000000$ |
