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 |
21.9.252...441.1 |
$x^{21} - 9 x^{19} + 3 x^{17} + 66 x^{15} - 75 x^{14} - 90 x^{13} + 198 x^{12} - 21 x^{11} + 63 x^{9} - 177 x^{8} + 54 x^{7} + 45 x^{6} - 51 x^{5} + 18 x^{4} - 8 x^{3} - 3 x^{2} + 3$ |
$21$ |
[9,6] |
$3^{34}\cdot 73^{6}$ |
$2$ |
$20.1771578454$ |
|
|
|
? |
$C_3\times A_7$ (as 21T44) |
trivial |
$2$ |
$14$ |
$823613.327719$ |
21.9.332...609.1 |
$x^{21} - 6 x^{20} + 12 x^{19} - 2 x^{18} - 27 x^{17} + 36 x^{16} - 39 x^{15} + 180 x^{14} - 396 x^{13} + 183 x^{12} + 558 x^{11} - 738 x^{10} - 339 x^{9} + 1035 x^{8} + 27 x^{7} - 936 x^{6} + 27 x^{5} + 621 x^{4} + 99 x^{3} - 189 x^{2} - 81 x - 9$ |
$21$ |
[9,6] |
$3^{36}\cdot 53^{6}$ |
$2$ |
$20.4443072604$ |
|
|
|
? |
$C_3\times A_7$ (as 21T44) |
trivial |
$2$ |
$14$ |
$967276.035305$ |
21.9.184...873.1 |
$x^{21} - 2 x^{20} - 2 x^{19} + 12 x^{18} - 25 x^{17} + x^{16} + 48 x^{15} - 91 x^{14} + 103 x^{13} - 12 x^{12} - 110 x^{11} + 272 x^{10} - 277 x^{9} - 78 x^{8} + 278 x^{7} - 46 x^{6} + 11 x^{5} - 114 x^{4} + 3 x^{3} + 93 x^{2} - 19 x - 23$ |
$21$ |
[9,6] |
$71^{3}\cdot 8623^{3}\cdot 283573^{2}$ |
$3$ |
$22.1821586762$ |
$3377289.469795227$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$1614740.57391$ |
21.9.778...553.1 |
$x^{21} - 8 x^{20} + 15 x^{19} + 42 x^{18} - 181 x^{17} + 43 x^{16} + 664 x^{15} - 785 x^{14} - 999 x^{13} + 2386 x^{12} - 12 x^{11} - 3337 x^{10} + 2186 x^{9} + 1818 x^{8} - 2845 x^{7} + 445 x^{6} + 1349 x^{5} - 754 x^{4} - 347 x^{3} + 279 x^{2} + 76 x + 1$ |
$21$ |
[9,6] |
$71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3}$ |
$4$ |
$23.7555403331$ |
$5456272.155977658$ |
|
|
? |
$C_3^7.S_7$ (as 21T139) |
trivial |
$2$ |
$14$ |
$3400600.48543$ |
21.9.155...113.1 |
$x^{21} - x^{20} + 3 x^{19} - 8 x^{17} + 11 x^{16} - 38 x^{15} - 57 x^{14} - 99 x^{13} - 54 x^{12} + 84 x^{11} + 86 x^{10} + 362 x^{9} - 80 x^{8} - 244 x^{7} + 140 x^{6} - 71 x^{5} + 3 x^{4} + 9 x^{3} - 7 x^{2} + 2 x + 1$ |
$21$ |
[9,6] |
$7^{14}\cdot 71^{3}\cdot 8623^{3}$ |
$3$ |
$24.5528032693$ |
$2863.2354387573537$ |
|
|
? |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$14$ |
$4976307.00235$ |
21.9.155...641.1 |
$x^{21} - 15 x^{19} - 4 x^{18} + 93 x^{17} + 12 x^{16} - 281 x^{15} + 63 x^{14} + 375 x^{13} - 266 x^{12} - 23 x^{11} + 432 x^{10} - 39 x^{9} - 220 x^{8} - 298 x^{7} + 36 x^{6} + 171 x^{5} + 26 x^{4} - 33 x^{3} - 1$ |
$21$ |
[9,6] |
$7^{14}\cdot 593^{3}\cdot 1033^{3}$ |
$3$ |
$24.5547277939$ |
$2864.0210180614768$ |
|
|
? |
$C_3\times S_7$ (as 21T56) |
trivial |
$2$ |
$14$ |
$4936254.92703$ |
21.9.426...529.1 |
$x^{21} - 12 x^{19} - 6 x^{18} + 3 x^{17} - 129 x^{16} - 144 x^{15} + 111 x^{14} - 273 x^{13} - 611 x^{12} + 93 x^{11} + 426 x^{10} + 1596 x^{9} + 1509 x^{8} - 1977 x^{7} - 1134 x^{6} + 1617 x^{5} + 435 x^{4} - 254 x^{3} - 39 x^{2} + 18 x + 3$ |
$21$ |
[9,6] |
$3^{34}\cdot 13^{2}\cdot 73^{6}$ |
$3$ |
$25.7602358284$ |
|
|
|
? |
$C_3^7.A_7$ (as 21T132) |
trivial |
$2$ |
$14$ |
$13046035.51$ |
21.9.111...281.1 |
$x^{21} - 2 x^{20} - 10 x^{19} + 31 x^{18} - 24 x^{17} - 152 x^{16} + 288 x^{15} + 7 x^{14} - 127 x^{13} + 465 x^{12} - 466 x^{11} + 1998 x^{10} + 1430 x^{9} + 2635 x^{8} + 613 x^{7} - 570 x^{6} - 1087 x^{5} - 669 x^{4} + 195 x^{3} + 193 x^{2} + 93 x - 53$ |
$21$ |
[9,6] |
$13^{16}\cdot 109^{6}$ |
$2$ |
$26.9674946452$ |
$88.51143378673154$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$14$ |
$12045126.3727$ |
21.9.111...281.2 |
$x^{21} - x^{20} - 12 x^{19} + 8 x^{18} + 49 x^{17} - 14 x^{16} - 94 x^{15} + 123 x^{14} - 7 x^{13} - 1078 x^{12} + 1150 x^{11} + 1019 x^{10} - 4414 x^{9} + 6562 x^{8} + 4203 x^{7} - 14456 x^{6} + 3035 x^{5} + 9936 x^{4} - 5649 x^{3} - 1996 x^{2} + 1631 x - 79$ |
$21$ |
[9,6] |
$13^{16}\cdot 109^{6}$ |
$2$ |
$26.9674946452$ |
$88.51143378673154$ |
|
|
? |
$C_3\times \GL(3,2)$ (as 21T22) |
trivial |
$2$ |
$14$ |
$12045126.3727$ |
21.9.524...857.1 |
$x^{21} - 12 x^{19} - 12 x^{18} + 63 x^{17} + 63 x^{16} - 167 x^{15} - 18 x^{14} + 249 x^{13} + 133 x^{12} - 180 x^{11} - 1605 x^{10} - 24 x^{9} + 2187 x^{8} + 498 x^{7} + 232 x^{6} - 1215 x^{5} - 1710 x^{4} + 929 x^{3} + 765 x^{2} - 321 x - 173$ |
$21$ |
[9,6] |
$3^{28}\cdot 71^{3}\cdot 8623^{3}$ |
$3$ |
$29.0311382304$ |
|
|
|
? |
$C_3^6.S_7$ (as 21T130) |
trivial |
$2$ |
$14$ |
$32106686.5651$ |
21.9.136...489.1 |
$x^{21} - 7 x^{20} + 7 x^{19} + 55 x^{18} - 132 x^{17} - 112 x^{16} + 589 x^{15} - 188 x^{14} - 1078 x^{13} + 1042 x^{12} + 579 x^{11} - 1297 x^{10} + 411 x^{9} + 431 x^{8} - 127 x^{7} - 455 x^{6} - 126 x^{5} + 888 x^{4} - 460 x^{3} - 146 x^{2} + 127 x - 1$ |
$21$ |
[9,6] |
$17^{10}\cdot 19^{2}\cdot 61^{2}\cdot 131^{6}$ |
$4$ |
$30.3864653$ |
$30172.450876657273$ |
|
|
? |
$C_3^7.A_7$ (as 21T132) |
trivial |
$2$ |
$14$ |
$39718417.9458$ |
21.9.161...921.1 |
$x^{21} - 9 x^{20} + 20 x^{19} + 49 x^{18} - 258 x^{17} + 121 x^{16} + 953 x^{15} - 1378 x^{14} - 1194 x^{13} + 3586 x^{12} - 572 x^{11} - 3807 x^{10} + 2407 x^{9} + 1581 x^{8} - 1937 x^{7} + 33 x^{6} + 644 x^{5} - 231 x^{4} - 49 x^{3} + 50 x^{2} - 12 x + 1$ |
$21$ |
[9,6] |
$13^{8}\cdot 109^{6}\cdot 181^{2}\cdot 601^{2}$ |
$4$ |
$30.6304197023$ |
$201697.9142158035$ |
|
|
✓ |
$C_3^7.\GL(3,2)$ (as 21T115) |
trivial |
$2$ |
$14$ |
$74775557.941$ |
21.9.193...976.1 |
$x^{21} - 5 x^{20} + 20 x^{19} - 76 x^{18} + 244 x^{17} - 536 x^{16} + 482 x^{15} + 655 x^{14} - 2970 x^{13} + 3601 x^{12} + 274 x^{11} - 4051 x^{10} + 4053 x^{9} + 428 x^{8} - 4459 x^{7} + 1158 x^{6} + 825 x^{5} + 130 x^{4} + 898 x^{3} - 516 x^{2} - 260 x + 73$ |
$21$ |
[9,6] |
$2^{14}\cdot 79^{8}\cdot 9199^{3}$ |
$3$ |
$30.8916341043$ |
|
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$14$ |
$55415325.3394$ |
21.9.273...241.1 |
$x^{21} - 8 x^{20} + 11 x^{19} + 69 x^{18} - 212 x^{17} - 125 x^{16} + 1107 x^{15} - 639 x^{14} - 2429 x^{13} + 3139 x^{12} + 1803 x^{11} - 4950 x^{10} + 904 x^{9} + 3274 x^{8} - 2054 x^{7} - 553 x^{6} + 924 x^{5} - 224 x^{4} - 88 x^{3} + 61 x^{2} - 13 x + 1$ |
$21$ |
[9,6] |
$13^{6}\cdot 19^{2}\cdot 109^{6}\cdot 96757^{2}$ |
$4$ |
$31.4054006135$ |
$564905.2210786343$ |
|
|
✓ |
$C_3^7.\GL(3,2)$ (as 21T115) |
trivial |
$2$ |
$14$ |
$110042286.853$ |
21.9.101...752.1 |
$x^{21} - 4 x^{20} + 8 x^{19} - 4 x^{18} - 36 x^{17} + 48 x^{16} - 52 x^{15} + 114 x^{14} - 216 x^{12} + 584 x^{11} - 404 x^{10} - 140 x^{9} + 160 x^{8} - 208 x^{7} + 204 x^{6} - 192 x^{5} + 144 x^{4} - 4 x^{3} - 32 x^{2} + 16 x - 4$ |
$21$ |
[9,6] |
$2^{20}\cdot 37^{7}\cdot 317^{6}$ |
$3$ |
$33.4208508784$ |
$209.56836594522878$ |
|
|
? |
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$14$ |
$241328139.391$ |
21.9.101...752.2 |
$x^{21} - 2 x^{20} - 2 x^{19} + 16 x^{18} - 8 x^{17} - 68 x^{16} - 150 x^{15} + 164 x^{14} + 240 x^{13} - 62 x^{12} - 256 x^{11} + 30 x^{10} + 512 x^{9} - 436 x^{8} - 114 x^{7} + 216 x^{6} - 44 x^{5} - 44 x^{4} - 2 x^{3} + 20 x^{2} + 4 x - 2$ |
$21$ |
[9,6] |
$2^{20}\cdot 37^{7}\cdot 317^{6}$ |
$3$ |
$33.4208508784$ |
$209.56836594522878$ |
|
|
? |
$S_3\times \GL(3,2)$ (as 21T27) |
trivial |
$2$ |
$14$ |
$241328139.391$ |
21.9.356...264.1 |
$x^{21} - x^{20} + 4 x^{19} + x^{18} - 17 x^{17} + 24 x^{16} - 107 x^{15} - 238 x^{14} - 467 x^{13} - 355 x^{12} + 497 x^{11} + 812 x^{10} + 3209 x^{9} - 222 x^{8} - 3450 x^{7} + 1169 x^{6} - 373 x^{5} + 2 x^{4} + 32 x^{3} - 12 x^{2} + 3 x + 1$ |
$21$ |
[9,6] |
$2^{14}\cdot 37^{7}\cdot 71^{3}\cdot 8623^{3}$ |
$4$ |
$35.4913862335$ |
$7555.198744333686$ |
|
|
? |
$S_3\times S_7$ (as 21T74) |
trivial |
$2$ |
$14$ |
$257019918.368$ |
21.9.177...088.1 |
$x^{21} - 2 x^{20} - 10 x^{19} + 18 x^{18} + 68 x^{17} - 28 x^{16} - 376 x^{15} - 352 x^{14} + 648 x^{13} + 856 x^{12} - 848 x^{11} - 912 x^{10} + 1240 x^{9} + 432 x^{8} - 1144 x^{7} + 120 x^{6} + 448 x^{5} - 144 x^{3} - 64 x^{2} + 32 x + 16$ |
$21$ |
[9,6] |
$2^{20}\cdot 7^{6}\cdot 37^{7}\cdot 73^{6}$ |
$4$ |
$38.3057248571$ |
$543.9517221720648$ |
|
|
? |
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$14$ |
$1075461154.98$ |
21.9.210...648.1 |
$x^{21} - 27 x^{17} - 36 x^{16} - 39 x^{15} - 54 x^{14} + 45 x^{13} + 208 x^{12} + 945 x^{11} + 2526 x^{10} + 3985 x^{9} + 5076 x^{8} + 3393 x^{7} - 5790 x^{6} - 18252 x^{5} - 22104 x^{4} - 15056 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3}$ |
$4$ |
$38.619258655$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$572421980.598$ |
21.9.227...336.1 |
$x^{21} - 3 x^{19} - 2 x^{18} - 45 x^{17} + 6 x^{16} + 57 x^{15} - 18 x^{14} + 384 x^{13} - 82 x^{12} - 369 x^{11} - 114 x^{10} - 235 x^{9} + 1422 x^{8} + 3867 x^{7} + 1160 x^{6} - 3312 x^{5} - 1512 x^{4} + 112 x^{3} + 288 x^{2} + 384 x - 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 23^{3}\cdot 239^{3}\cdot 431^{3}$ |
$5$ |
$38.7672942778$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$673571318.196$ |
21.9.391...561.1 |
$x^{21} - 6 x^{20} + 12 x^{19} + 5 x^{18} - 66 x^{17} + 108 x^{16} + 4 x^{15} - 261 x^{14} + 351 x^{13} - 15 x^{12} - 459 x^{11} + 486 x^{10} - 27 x^{9} - 342 x^{8} + 279 x^{7} - 17 x^{6} - 108 x^{5} + 69 x^{4} - 6 x^{3} - 12 x^{2} + 6 x - 1$ |
$21$ |
[9,6] |
$3^{18}\cdot 7^{14}\cdot 13^{2}\cdot 296773^{2}$ |
$4$ |
$39.7770789053$ |
|
|
|
? |
$A_7\wr C_3$ (as 21T153) |
trivial |
$2$ |
$14$ |
$1145269176.62$ |
21.9.558...057.1 |
$x^{21} - 2 x^{20} - 29 x^{19} + 68 x^{18} + 307 x^{17} - 748 x^{16} - 1496 x^{15} + 3371 x^{14} + 3691 x^{13} - 7180 x^{12} - 6204 x^{11} + 7336 x^{10} + 7843 x^{9} - 91 x^{8} - 4359 x^{7} - 3432 x^{6} + 52 x^{5} + 951 x^{4} + 433 x^{3} + 29 x^{2} - 27 x - 5$ |
$21$ |
[9,6] |
$11^{13}\cdot 29^{6}\cdot 43^{7}$ |
$3$ |
$40.4565781335$ |
$456.5553791528178$ |
|
|
? |
$S_3\times A_7$ (as 21T57) |
trivial |
$2$ |
$14$ |
$1630641508.19$ |
21.9.130...848.1 |
$x^{21} - 30 x^{19} - 34 x^{18} + 387 x^{17} + 954 x^{16} - 2237 x^{15} - 10944 x^{14} - 525 x^{13} + 63996 x^{12} + 83790 x^{11} - 181800 x^{10} - 495124 x^{9} + 82314 x^{8} + 1330701 x^{7} + 810842 x^{6} - 1778580 x^{5} - 1822800 x^{4} + 1114720 x^{3} + 1473696 x^{2} - 332928 x - 341632$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 17^{2}\cdot 59^{3}\cdot 10859^{3}$ |
$5$ |
$42.1224665026$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$1452098719.54$ |
21.9.430...321.1 |
$x^{21} - 6 x^{20} + 12 x^{19} + 4 x^{18} - 63 x^{17} + 108 x^{16} - 9 x^{15} - 243 x^{14} + 360 x^{13} - 57 x^{12} - 432 x^{11} + 513 x^{10} - 69 x^{9} - 333 x^{8} + 297 x^{7} - 30 x^{6} - 108 x^{5} + 72 x^{4} - 7 x^{3} - 12 x^{2} + 6 x - 1$ |
$21$ |
[9,6] |
$3^{44}\cdot 181^{2}\cdot 36541^{2}$ |
$3$ |
$44.5913019751$ |
|
|
|
? |
$A_7\wr C_3$ (as 21T153) |
trivial |
$2$ |
$14$ |
$10314709459.0$ |
21.9.455...872.1 |
$x^{21} - 18 x^{19} - 24 x^{18} + 90 x^{17} + 252 x^{16} - 256 x^{15} - 1368 x^{14} - 102 x^{13} + 4096 x^{12} + 2556 x^{11} - 6780 x^{10} - 3112 x^{9} + 12384 x^{8} + 6666 x^{7} - 11436 x^{6} - 8712 x^{5} + 6192 x^{4} + 4576 x^{3} - 2880 x^{2} - 384 x + 256$ |
$21$ |
[9,6] |
$2^{32}\cdot 3^{21}\cdot 317^{6}$ |
$3$ |
$44.7117830875$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$14$ |
$12412580355.9$ |
21.9.135...073.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 7 x^{14} + 2940 x^{13} + 98 x^{12} - 5733 x^{11} - 539 x^{10} + 7007 x^{9} + 1470 x^{8} - 5131 x^{7} - 2058 x^{6} + 1960 x^{5} + 1372 x^{4} - 147 x^{3} - 343 x^{2} - 98 x - 7$ |
$21$ |
[9,6] |
$7^{35}\cdot 71^{3}$ |
$2$ |
$47.0936348126$ |
|
|
|
✓ |
$D_7\wr C_3$ (as 21T45) |
trivial |
$2$ |
$14$ |
$4675153182.69$ |
21.9.285...453.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 8 x^{14} + 2940 x^{13} + 112 x^{12} - 5733 x^{11} - 616 x^{10} + 7007 x^{9} + 1680 x^{8} - 5126 x^{7} - 2352 x^{6} + 1925 x^{5} + 1568 x^{4} - 77 x^{3} - 392 x^{2} - 133 x - 13$ |
$21$ |
[9,6] |
$7^{38}\cdot 13^{3}$ |
$2$ |
$48.7932548339$ |
|
|
|
✓ |
$D_7\wr C_3$ (as 21T45) |
trivial |
$2$ |
$14$ |
$13141879201.5$ |
21.9.797...949.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 6 x^{14} + 2940 x^{13} + 84 x^{12} - 5733 x^{11} - 462 x^{10} + 7007 x^{9} + 1260 x^{8} - 5137 x^{7} - 1764 x^{6} + 2002 x^{5} + 1176 x^{4} - 231 x^{3} - 294 x^{2} - 56 x + 1$ |
$21$ |
[9,6] |
$7^{17}\cdot 47^{3}\cdot 229^{7}$ |
$3$ |
$51.2400960052$ |
|
|
|
? |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$14$ |
$33047121628.3$ |
21.9.971...632.1 |
$x^{21} - 42 x^{19} - 28 x^{18} + 756 x^{17} + 1008 x^{16} - 7305 x^{15} - 15282 x^{14} + 37035 x^{13} + 123664 x^{12} - 52677 x^{11} - 539382 x^{10} - 405392 x^{9} + 987120 x^{8} + 2007441 x^{7} + 620538 x^{6} - 2081484 x^{5} - 3261240 x^{4} - 2340560 x^{3} - 949536 x^{2} - 211008 x - 20096$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 157^{2}\cdot 593^{3}\cdot 1033^{3}$ |
$5$ |
$51.722278619$ |
|
|
|
? |
$C_3^6.(S_3\times S_7)$ (as 21T144) |
trivial |
$2$ |
$14$ |
$11718147093.4$ |
21.9.169...277.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 6 x^{14} + 2940 x^{13} + 84 x^{12} - 5733 x^{11} - 462 x^{10} + 7007 x^{9} + 1260 x^{8} - 5136 x^{7} - 1764 x^{6} + 1995 x^{5} + 1176 x^{4} - 217 x^{3} - 294 x^{2} - 63 x - 1$ |
$21$ |
[9,6] |
$3^{31}\cdot 7^{21}\cdot 17^{3}$ |
$3$ |
$53.1126914501$ |
|
|
|
✓ |
$D_7^3:C_3^2$ (as 21T70) |
trivial |
$2$ |
$14$ |
$33345384563.4$ |
21.9.175...304.1 |
$x^{21} - 15 x^{19} - 22 x^{18} + 27 x^{17} + 168 x^{16} + 105 x^{15} - 54 x^{14} - 1014 x^{13} + 1890 x^{12} + 13563 x^{11} - 25146 x^{10} + 13781 x^{9} + 77688 x^{8} - 265965 x^{7} - 246390 x^{6} + 126756 x^{5} - 76728 x^{4} - 22336 x^{3} + 60768 x^{2} - 40512 x + 27008$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 211^{2}\cdot 8623^{3}$ |
$5$ |
$53.1949669038$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$14948518010.9$ |
21.9.346...744.1 |
$x^{21} - x^{20} - 27 x^{19} + 39 x^{18} + 380 x^{17} - 662 x^{16} - 3120 x^{15} + 3546 x^{14} + 9982 x^{13} + 3246 x^{12} - 10664 x^{11} - 20884 x^{10} - 15180 x^{9} - 7396 x^{8} - 7696 x^{7} - 3296 x^{6} + 1440 x^{5} + 520 x^{4} + 136 x^{3} + 656 x^{2} + 312 x + 24$ |
$21$ |
[9,6] |
$2^{26}\cdot 3^{9}\cdot 47^{7}\cdot 2276293^{2}$ |
$4$ |
$54.9541627715$ |
|
|
|
? |
$\PSL(2,7)\wr S_3$ (as 21T146) |
trivial |
$2$ |
$14$ |
$153154579102$ |
21.9.346...744.2 |
$x^{21} - 6 x^{20} + 13 x^{19} - 25 x^{18} + 29 x^{17} + 34 x^{16} + 10 x^{15} + 77 x^{14} - 179 x^{13} - 279 x^{12} - 692 x^{11} - 1196 x^{10} - 1314 x^{9} - 2334 x^{8} - 3096 x^{7} - 3644 x^{6} - 4884 x^{5} - 4772 x^{4} - 3472 x^{3} - 2304 x^{2} - 1080 x - 216$ |
$21$ |
[9,6] |
$2^{26}\cdot 3^{9}\cdot 47^{7}\cdot 2276293^{2}$ |
$4$ |
$54.9541627715$ |
$83417.38046821809$ |
|
|
? |
$\PSL(2,7)\wr S_3$ (as 21T146) |
trivial |
$2$ |
$14$ |
$153154579102$ |
21.9.529...149.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5150 x^{7} - 588 x^{6} + 2093 x^{5} + 392 x^{4} - 413 x^{3} - 98 x^{2} + 35 x + 9$ |
$21$ |
[9,6] |
$3^{10}\cdot 7^{21}\cdot 107^{7}$ |
$3$ |
$56.0737881777$ |
|
|
|
✓ |
$C_7^3:(C_6\times S_4)$ (as 21T87) |
trivial |
$2$ |
$14$ |
$96727720212.8$ |
21.9.799...800.1 |
$x^{21} - 21 x^{19} - 14 x^{18} + 171 x^{17} + 228 x^{16} - 707 x^{15} - 1566 x^{14} + 1629 x^{13} + 6896 x^{12} + 81 x^{11} - 20322 x^{10} - 19128 x^{9} + 25776 x^{8} + 59865 x^{7} + 17162 x^{6} - 67500 x^{5} - 104184 x^{4} - 74576 x^{3} - 30240 x^{2} - 6720 x - 640$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 5^{2}\cdot 11^{12}\cdot 29^{6}$ |
$5$ |
$57.185513353$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$14$ |
$59128196036.7$ |
21.9.819...208.1 |
$x^{21} + 15 x^{19} - 10 x^{18} + 36 x^{17} - 48 x^{16} - 281 x^{15} + 594 x^{14} - 1368 x^{13} + 2680 x^{12} - 1134 x^{11} - 3708 x^{10} + 9933 x^{9} - 18900 x^{8} + 23553 x^{7} - 11586 x^{6} - 9612 x^{5} + 19800 x^{4} - 14800 x^{3} + 6048 x^{2} - 1344 x + 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{25}\cdot 8388019^{3}$ |
$3$ |
$57.250905271$ |
|
|
|
? |
$C_3^7.(C_2^6.S_7)$ (as 21T149) |
trivial |
$2$ |
$14$ |
$46235467385.5$ |
21.9.979...448.1 |
$x^{21} + 18 x^{19} - 12 x^{18} + 81 x^{17} - 108 x^{16} - 99 x^{15} + 270 x^{14} - 1557 x^{13} + 3712 x^{12} - 4887 x^{11} + 5682 x^{10} - 3485 x^{9} - 5148 x^{8} + 15567 x^{7} - 23006 x^{6} + 26892 x^{5} - 24408 x^{4} + 15312 x^{3} - 6048 x^{2} + 1344 x - 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 7\cdot 71^{3}\cdot 283583^{3}$ |
$5$ |
$57.739161665$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$42868486262.7$ |
21.9.174...737.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 9 x^{14} + 2940 x^{13} + 126 x^{12} - 5733 x^{11} - 693 x^{10} + 7007 x^{9} + 1890 x^{8} - 5121 x^{7} - 2646 x^{6} + 1890 x^{5} + 1764 x^{4} - 7 x^{3} - 441 x^{2} - 168 x - 19$ |
$21$ |
[9,6] |
$3^{31}\cdot 7^{21}\cdot 37^{3}$ |
$3$ |
$59.3538247351$ |
|
|
|
✓ |
$D_7^3:C_3^2$ (as 21T70) |
trivial |
$2$ |
$14$ |
$87006042013.7$ |
21.9.177...472.1 |
$x^{21} - 45 x^{19} - 30 x^{18} + 837 x^{17} + 1116 x^{16} - 7971 x^{15} - 16686 x^{14} + 37152 x^{13} + 126264 x^{12} - 34803 x^{11} - 487914 x^{10} - 411853 x^{9} + 737244 x^{8} + 1627689 x^{7} + 635266 x^{6} - 1401516 x^{5} - 2321496 x^{4} - 1681744 x^{3} - 683424 x^{2} - 151872 x - 14464$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6}\cdot 113^{2}$ |
$5$ |
$59.3923602701$ |
|
|
|
? |
$C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) |
trivial |
$2$ |
$14$ |
$44718695480.2$ |
21.9.231...736.1 |
$x^{21} - 6 x^{20} + 12 x^{19} + 4 x^{18} - 63 x^{17} + 108 x^{16} - 10 x^{15} - 243 x^{14} + 363 x^{13} - 59 x^{12} - 435 x^{11} + 519 x^{10} - 66 x^{9} - 336 x^{8} + 297 x^{7} - 29 x^{6} - 108 x^{5} + 72 x^{4} - 7 x^{3} - 12 x^{2} + 6 x - 1$ |
$21$ |
[9,6] |
$2^{8}\cdot 3^{18}\cdot 229^{7}\cdot 241^{2}\cdot 349^{2}$ |
$5$ |
$60.1566457561$ |
|
|
|
? |
$A_7\wr S_3$ (as 21T156) |
trivial |
$2$ |
$14$ |
$86978759036.2$ |
21.9.293...281.1 |
$x^{21} - 63 x^{19} - 4 x^{18} + 1683 x^{17} + 216 x^{16} - 24877 x^{15} - 5346 x^{14} + 221076 x^{13} + 76086 x^{12} - 1185372 x^{11} - 647136 x^{10} + 3493272 x^{9} + 3080592 x^{8} - 3545727 x^{7} - 6328004 x^{6} - 4869576 x^{5} - 126336 x^{4} + 2790672 x^{3} + 1272384 x^{2} - 282752$ |
$21$ |
[9,6] |
$3^{28}\cdot 47^{4}\cdot 59^{3}\cdot 10859^{3}$ |
$4$ |
$60.8382574825$ |
|
|
|
? |
$C_3^6.S_7$ (as 21T130) |
trivial |
$2$ |
$14$ |
$64859089096.9$ |
21.9.348...776.1 |
$x^{21} - 18 x^{19} - 2 x^{18} + 45 x^{17} + 174 x^{16} - 214 x^{15} - 1116 x^{14} + 9906 x^{13} - 15026 x^{12} - 34911 x^{11} + 106704 x^{10} - 73813 x^{9} - 33354 x^{8} + 29901 x^{7} + 53194 x^{6} - 62604 x^{5} + 14064 x^{4} + 5872 x^{3} - 1440 x^{2} - 576 x + 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6}\cdot 1667$ |
$5$ |
$61.3373365692$ |
|
|
|
? |
$C_3^7.(C_2^7.A_7)$ (as 21T151) |
trivial |
$2$ |
$14$ |
$90193315521.5$ |
21.9.517...264.1 |
$x^{21} - 3 x^{20} + 15 x^{19} - 42 x^{18} + 18 x^{17} - 279 x^{16} - 292 x^{15} - 894 x^{14} + 1677 x^{13} + 5757 x^{12} + 30555 x^{11} + 59316 x^{10} + 103482 x^{9} + 110757 x^{8} - 119745 x^{7} - 505489 x^{6} - 1236021 x^{5} - 1853052 x^{4} - 1402417 x^{3} - 526482 x^{2} - 91392 x - 5491$ |
$21$ |
[9,6] |
$2^{18}\cdot 3^{30}\cdot 17^{2}\cdot 57605311^{2}$ |
$4$ |
$62.5035642659$ |
|
|
|
? |
$\PSL(2,7)\wr C_3$ (as 21T143) |
trivial |
$2$ |
$14$ |
$223805105406$ |
21.9.517...264.2 |
$x^{21} - 6 x^{20} + 6 x^{19} + 10 x^{18} + 15 x^{17} - 36 x^{16} - 58 x^{15} + 15 x^{14} + 27 x^{13} - 21 x^{12} - 204 x^{11} - 144 x^{10} + 82 x^{9} - 114 x^{8} - 588 x^{7} - 776 x^{6} + 72 x^{5} + 576 x^{4} - 784 x^{3} - 1800 x^{2} - 1080 x - 216$ |
$21$ |
[9,6] |
$2^{18}\cdot 3^{30}\cdot 17^{2}\cdot 57605311^{2}$ |
$4$ |
$62.5035642659$ |
$622849.6463391684$ |
|
|
? |
$\PSL(2,7)\wr C_3$ (as 21T143) |
trivial |
$2$ |
$14$ |
$223805105406$ |
21.9.672...041.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 7 x^{14} + 2940 x^{13} + 98 x^{12} - 5733 x^{11} - 539 x^{10} + 7007 x^{9} + 1470 x^{8} - 5133 x^{7} - 2058 x^{6} + 1974 x^{5} + 1372 x^{4} - 175 x^{3} - 343 x^{2} - 84 x - 3$ |
$21$ |
[9,6] |
$3^{7}\cdot 7^{24}\cdot 107^{7}$ |
$3$ |
$63.2889672504$ |
$398.6243489559687$ |
|
|
? |
$C_7^3:(C_3\times S_4)$ (as 21T69) |
trivial |
$2$ |
$14$ |
$292306857193$ |
21.9.117...000.1 |
$x^{21} - 6 x^{20} + 12 x^{19} + 5 x^{18} - 66 x^{17} + 108 x^{16} + 3 x^{15} - 261 x^{14} + 354 x^{13} - 17 x^{12} - 462 x^{11} + 492 x^{10} - 24 x^{9} - 345 x^{8} + 279 x^{7} - 16 x^{6} - 108 x^{5} + 69 x^{4} - 6 x^{3} - 12 x^{2} + 6 x - 1$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{18}\cdot 5^{4}\cdot 37^{7}\cdot 559081^{2}$ |
$5$ |
$64.9976024134$ |
|
|
|
? |
$A_7\wr S_3$ (as 21T156) |
trivial |
$2$ |
$14$ |
$193208058283$ |
21.9.144...592.1 |
$x^{21} - 21 x^{19} - 20 x^{18} + 189 x^{17} + 360 x^{16} - 809 x^{15} - 2700 x^{14} + 795 x^{13} + 10496 x^{12} + 7137 x^{11} - 20652 x^{10} - 32065 x^{9} + 12744 x^{8} + 56925 x^{7} + 21196 x^{6} - 45144 x^{5} - 42288 x^{4} + 8320 x^{3} + 26496 x^{2} + 11328 x + 896$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 103\cdot 283583^{3}$ |
$5$ |
$65.626176432$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$140273626122$ |
21.9.153...521.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - x^{14} + 2940 x^{13} + 14 x^{12} - 5733 x^{11} - 77 x^{10} + 7007 x^{9} + 210 x^{8} - 5151 x^{7} - 294 x^{6} + 2100 x^{5} + 196 x^{4} - 427 x^{3} - 49 x^{2} + 42 x + 7$ |
$21$ |
[9,6] |
$7^{24}\cdot 19^{14}$ |
$2$ |
$65.8155829111$ |
$156.6339939639929$ |
|
|
✓ |
$C_4\times C_4^4.C_2$ (as 21T53) |
trivial |
$2$ |
$14$ |
$256728120726$ |
21.9.733...448.1 |
$x^{21} - 69 x^{19} - 46 x^{18} + 2043 x^{17} + 2724 x^{16} - 32707 x^{15} - 67230 x^{14} + 286632 x^{13} + 873912 x^{12} - 1070820 x^{11} - 6122808 x^{10} - 2253504 x^{9} + 19682496 x^{8} + 31706229 x^{7} - 3678686 x^{6} - 63451836 x^{5} - 86436504 x^{4} - 60419856 x^{3} - 24391584 x^{2} - 5420352 x - 516224$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 37^{2}\cdot 59^{3}\cdot 109^{2}\cdot 10859^{3}$ |
$6$ |
$70.9122631536$ |
|
|
|
? |
$C_3^6.(S_3\times S_7)$ (as 21T144) |
trivial |
$2$ |
$14$ |
$293150961077$ |
21.9.956...989.1 |
$x^{21} - 21 x^{19} + 189 x^{17} - 952 x^{15} - 2 x^{14} + 2940 x^{13} + 28 x^{12} - 5733 x^{11} - 154 x^{10} + 7007 x^{9} + 420 x^{8} - 5151 x^{7} - 588 x^{6} + 2100 x^{5} + 392 x^{4} - 427 x^{3} - 98 x^{2} + 42 x + 11$ |
$21$ |
[9,6] |
$7^{31}\cdot 67^{7}$ |
$2$ |
$71.8153496062$ |
$330.56548797385983$ |
|
|
✓ |
$C_7^3:(C_3\times S_4)$ (as 21T69) |
trivial |
$2$ |
$14$ |
$1331305157360$ |