| 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 |
| 15.11.145...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 376 x^{5} + 100 x^{4} + 130 x^{3} - 50 x^{2} - 5 x + 1$ |
$15$ |
[11,2] |
$5^{15}\cdot 7^{10}\cdot 13^{2}$ |
$3$ |
$25.7569525549$ |
|
|
|
✓ |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$12$ |
$236547.883566$ |
| 15.11.622...664.1 |
$x^{15} - 5 x^{14} - 6 x^{13} + 68 x^{12} - 58 x^{11} - 251 x^{10} + 376 x^{9} + 413 x^{8} - 851 x^{7} - 378 x^{6} + 989 x^{5} + 238 x^{4} - 605 x^{3} - 123 x^{2} + 152 x + 39$ |
$15$ |
[11,2] |
$2^{10}\cdot 3\cdot 401^{6}\cdot 487$ |
$4$ |
$28.3740345933$ |
$1215.0214864046318$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$12$ |
$901863.820503$ |
| 15.11.724...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 4 x^{10} - 275 x^{9} + 40 x^{8} + 450 x^{7} - 140 x^{6} - 372 x^{5} + 200 x^{4} + 110 x^{3} - 100 x^{2} + 15 x + 1$ |
$15$ |
[11,2] |
$5^{15}\cdot 7^{10}\cdot 29^{2}$ |
$3$ |
$28.6652079971$ |
|
|
|
✓ |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$12$ |
$576748.869975$ |
| 15.11.192...625.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 275 x^{9} + 450 x^{7} - 379 x^{5} + 145 x^{3} - 20 x - 1$ |
$15$ |
[11,2] |
$5^{15}\cdot 229^{5}$ |
$2$ |
$30.5901658632$ |
|
|
|
✓ |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$12$ |
$1558991.24486$ |
| 15.11.342...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - x^{10} - 275 x^{9} + 10 x^{8} + 450 x^{7} - 35 x^{6} - 379 x^{5} + 50 x^{4} + 145 x^{3} - 25 x^{2} - 20 x + 3$ |
$15$ |
[11,2] |
$5^{15}\cdot 257^{5}$ |
$2$ |
$31.7893058987$ |
|
|
|
✓ |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$12$ |
$1845650.46873$ |
| 15.11.461...728.1 |
$x^{15} - 18 x^{13} - 12 x^{12} + 90 x^{11} + 120 x^{10} + 13 x^{9} - 54 x^{8} - 522 x^{7} - 1304 x^{6} - 1053 x^{5} + 234 x^{4} + 984 x^{3} + 720 x^{2} + 240 x + 32$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{15}\cdot 11^{12}$ |
$3$ |
$32.42814204$ |
$133.7061122075245$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$12$ |
$1076539.51981$ |
| 15.11.105...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 378 x^{5} + 100 x^{4} + 140 x^{3} - 50 x^{2} - 15 x + 5$ |
$15$ |
[11,2] |
$5^{17}\cdot 13^{10}$ |
$2$ |
$34.26059542697078$ |
$78.18681617097855$ |
|
|
✓ |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$12$ |
$3120144.901515419$ |
| 15.11.164...264.1 |
$x^{15} - 6 x^{14} + 71 x^{12} - 147 x^{11} - 100 x^{10} + 408 x^{9} + 134 x^{8} - 138 x^{7} - 1231 x^{6} + 68 x^{5} + 2191 x^{4} - 508 x^{3} - 1128 x^{2} + 195 x + 191$ |
$15$ |
[11,2] |
$2^{10}\cdot 31^{2}\cdot 401^{7}$ |
$3$ |
$41.1467555845$ |
$724.8440151530837$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T79) |
trivial |
$2$ |
$12$ |
$21667091.8912$ |
| 15.11.198...304.1 |
$x^{15} - 15 x^{13} - 2 x^{12} + 90 x^{11} + 24 x^{10} - 330 x^{9} - 108 x^{8} + 945 x^{7} + 64 x^{6} - 1863 x^{5} + 750 x^{4} + 1492 x^{3} - 1368 x^{2} + 384 x - 32$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 43$ |
$4$ |
$41.6696606503$ |
$839.597456029411$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$12$ |
$7656491.80773$ |
| 15.11.253...272.1 |
$x^{15} - 6 x^{13} - 2 x^{12} - 27 x^{11} + 24 x^{10} + 107 x^{9} + 144 x^{8} + 249 x^{7} - 934 x^{6} - 819 x^{5} + 1164 x^{4} + 404 x^{3} - 360 x^{2} - 48 x + 32$ |
$15$ |
[11,2] |
$2^{15}\cdot 3^{13}\cdot 36497^{3}$ |
$3$ |
$42.3629813546$ |
$5304.942664400066$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$12$ |
$17100873.4823$ |
| 15.11.262...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - x^{10} - 275 x^{9} + 10 x^{8} + 450 x^{7} - 35 x^{6} - 379 x^{5} + 50 x^{4} + 145 x^{3} - 25 x^{2} - 20 x - 1$ |
$15$ |
[11,2] |
$5^{19}\cdot 13^{10}$ |
$2$ |
$42.46106736365799$ |
$88.93058087108261$ |
|
|
✓ |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$12$ |
$16611576.247190157$ |
| 15.11.350...609.1 |
$x^{15} - 3 x^{14} - 16 x^{13} + 49 x^{12} + 32 x^{11} - 38 x^{10} - 174 x^{9} - 390 x^{8} + 969 x^{7} + 348 x^{6} - 1173 x^{5} + 120 x^{4} + 333 x^{3} + 24 x^{2} - 88 x + 13$ |
$15$ |
[11,2] |
$7^{10}\cdot 2281^{2}\cdot 48859^{2}$ |
$3$ |
$43.2853906374$ |
$38630.79297259466$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$12$ |
$15546964.7594$ |
| 15.11.521...600.1 |
$x^{15} - 15 x^{13} - 10 x^{12} + 36 x^{11} + 48 x^{10} + 313 x^{9} + 594 x^{8} - 981 x^{7} - 3584 x^{6} - 2457 x^{5} + 2418 x^{4} + 5128 x^{3} + 3600 x^{2} + 1200 x + 160$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{15}\cdot 5^{2}\cdot 61^{3}\cdot 397^{3}$ |
$5$ |
$44.4455195641$ |
$9015.79878416829$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$12$ |
$13035573.9343$ |
| 15.11.578...009.1 |
$x^{15} - 15 x^{13} - 11 x^{12} + 90 x^{11} + 132 x^{10} - 578 x^{9} - 594 x^{8} + 3177 x^{7} + 1925 x^{6} - 8559 x^{5} - 5313 x^{4} + 8129 x^{3} + 6633 x^{2} + 561 x + 11$ |
$15$ |
[11,2] |
$3^{20}\cdot 11^{12}\cdot 23^{2}$ |
$3$ |
$44.7547909169$ |
$286.0485850500585$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$12$ |
$16335813.596$ |
| 15.11.578...009.2 |
$x^{15} - 27 x^{13} - 31 x^{12} + 252 x^{11} + 564 x^{10} - 664 x^{9} - 3123 x^{8} - 1641 x^{7} + 5490 x^{6} + 8388 x^{5} - 753 x^{4} - 9231 x^{3} - 3159 x^{2} + 3186 x + 659$ |
$15$ |
[11,2] |
$3^{20}\cdot 11^{12}\cdot 23^{2}$ |
$3$ |
$44.7547909169$ |
$291.26858881174$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$12$ |
$11715038.8016$ |
| 15.11.678...552.1 |
$x^{15} - 18 x^{13} - 12 x^{12} + 81 x^{11} + 108 x^{10} + 117 x^{9} + 162 x^{8} - 783 x^{7} - 2352 x^{6} - 1647 x^{5} + 1374 x^{4} + 3064 x^{3} + 2160 x^{2} + 720 x + 96$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{13}\cdot 401^{6}$ |
$3$ |
$45.2323863066$ |
$795.9932113959791$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$12$ |
$27456451.0633$ |
| 15.11.934...000.1 |
$x^{15} - 15 x^{13} - 25 x^{12} + 90 x^{11} + 300 x^{10} - 90 x^{9} - 1350 x^{8} - 1215 x^{7} + 2250 x^{6} + 4617 x^{5} + 675 x^{4} - 4455 x^{3} - 4050 x^{2} - 1215 x - 81$ |
$15$ |
[11,2] |
$2^{12}\cdot 3^{14}\cdot 5^{21}$ |
$3$ |
$46.2056595321$ |
|
|
|
? |
$C_3:S_3^4:F_5$ (as 15T85) |
trivial |
$2$ |
$12$ |
$25760883.6123$ |
| 15.11.139...000.1 |
$x^{15} - 5 x^{14} - 15 x^{13} + 55 x^{12} - 5 x^{11} - 367 x^{10} + 365 x^{9} + 1255 x^{8} - 1015 x^{7} - 1825 x^{6} + 913 x^{5} + 1105 x^{4} - 285 x^{3} - 215 x^{2} + 35 x + 5$ |
$15$ |
[11,2] |
$2^{14}\cdot 5^{15}\cdot 7^{6}\cdot 37^{2}\cdot 173$ |
$5$ |
$47.4533837885$ |
$4696.958488101504$ |
|
|
? |
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$12$ |
$57104148.2399$ |
| 15.11.168...000.1 |
$x^{15} - 5 x^{13} - 35 x^{12} - 10 x^{11} + 318 x^{10} - 1030 x^{9} + 1520 x^{8} + 6095 x^{7} - 9150 x^{6} - 11729 x^{5} + 9225 x^{4} + 7485 x^{3} - 2150 x^{2} - 1005 x + 11$ |
$15$ |
[11,2] |
$2^{12}\cdot 3^{10}\cdot 5^{21}\cdot 11^{4}$ |
$4$ |
$65.3382585515$ |
|
|
|
? |
$C_3:S_3^4:F_5$ (as 15T85) |
trivial |
$2$ |
$12$ |
$488158772.516$ |
| 15.11.303...000.1 |
$x^{15} - 30 x^{13} - 40 x^{12} + 330 x^{11} + 834 x^{10} - 1415 x^{9} - 5550 x^{8} + 795 x^{7} + 12190 x^{6} + 5259 x^{5} - 3480 x^{4} - 655 x^{3} - 390 x^{2} - 540 x + 106$ |
$15$ |
[11,2] |
$2^{20}\cdot 3^{18}\cdot 5^{16}\cdot 7^{2}$ |
$4$ |
$67.9464195612$ |
$383.2993200161381$ |
|
|
? |
$C_3:S_3^4:F_5$ (as 15T84) |
trivial |
$2$ |
$12$ |
$1953427000.27$ |
| 15.11.319...064.1 |
$x^{15} - 3 x^{14} - 28 x^{13} + 95 x^{12} - 316 x^{11} + 588 x^{10} + 533 x^{9} + 122 x^{8} + 1104 x^{7} - 9965 x^{6} - 4408 x^{5} + 12535 x^{4} - 465 x^{3} - 4676 x^{2} + 1839 x - 193$ |
$15$ |
[11,2] |
$2^{10}\cdot 37^{4}\cdot 401^{7}$ |
$3$ |
$68.182747467$ |
$815.5887830751706$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T79) |
trivial |
$2$ |
$12$ |
$1073902360.98$ |
| 15.11.502...000.1 |
$x^{15} - 45 x^{13} + 435 x^{11} - 378 x^{10} - 1365 x^{9} + 2130 x^{8} - 900 x^{7} - 420 x^{6} + 2880 x^{5} - 2520 x^{4} - 105 x^{3} + 450 x^{2} - 6$ |
$15$ |
[11,2] |
$2^{20}\cdot 3^{22}\cdot 5^{16}$ |
$3$ |
$70.2617839628$ |
$161.6708430530387$ |
|
|
? |
$C_3:S_3^4:F_5$ (as 15T84) |
trivial |
$2$ |
$12$ |
$2910142113.91$ |
| 15.11.162...656.1 |
$x^{15} - 23 x^{13} - 2 x^{12} + 179 x^{11} + 80 x^{10} - 673 x^{9} - 594 x^{8} + 1912 x^{7} - 252 x^{6} - 760 x^{5} + 880 x^{4} - 912 x^{3} - 416 x^{2} + 448 x + 128$ |
$15$ |
[11,2] |
$2^{16}\cdot 3^{12}\cdot 881^{6}$ |
$3$ |
$75.9951767082$ |
$2909.139140399604$ |
|
|
? |
$C_3:S_3^4:A_5$ (as 15T88) |
trivial |
$2$ |
$12$ |
$6336681486.91$ |
| 15.11.293...688.1 |
$x^{15} - 33 x^{13} - 22 x^{12} + 63 x^{11} + 84 x^{10} + 4618 x^{9} + 9180 x^{8} - 13401 x^{7} - 50696 x^{6} - 93123 x^{5} - 160026 x^{4} - 186376 x^{3} - 121680 x^{2} - 40560 x - 5408$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{20}\cdot 13^{2}\cdot 36497^{3}$ |
$4$ |
$79.0361088276$ |
|
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$12$ |
$1315631457.3$ |
| 15.11.824...696.1 |
$x^{15} - 17 x^{13} - 20 x^{12} - 225 x^{11} + 128 x^{10} + 2139 x^{9} - 9852 x^{8} - 15448 x^{7} + 52520 x^{6} + 34464 x^{5} - 91328 x^{4} - 20160 x^{3} + 45312 x^{2} + 7168 x - 4096$ |
$15$ |
[11,2] |
$2^{12}\cdot 3^{16}\cdot 881^{6}$ |
$3$ |
$84.6727564836$ |
|
|
|
? |
$C_3:S_3^4:A_5$ (as 15T88) |
trivial |
$2$ |
$12$ |
$9860259684.86$ |
| 15.11.110...524.1 |
$x^{15} - 33 x^{13} - 64 x^{12} - 90 x^{11} + 1248 x^{10} + 5806 x^{9} - 10512 x^{8} - 31521 x^{7} + 41392 x^{6} + 28314 x^{5} - 35190 x^{4} + 28312 x^{3} - 17136 x^{2} + 816 x + 544$ |
$15$ |
[11,2] |
$2^{2}\cdot 3^{20}\cdot 17^{2}\cdot 31^{3}\cdot 9739^{3}$ |
$5$ |
$86.3642635098$ |
$50510.97041543447$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$12$ |
$4145512912.37$ |
| 15.11.126...072.1 |
$x^{15} - 20 x^{13} - 39 x^{12} + 160 x^{11} + 624 x^{10} - 173 x^{9} - 3744 x^{8} - 4324 x^{7} + 7911 x^{6} + 21392 x^{5} + 6600 x^{4} - 26128 x^{3} - 33168 x^{2} - 15040 x - 2304$ |
$15$ |
[11,2] |
$2^{10}\cdot 881^{6}\cdot 3769\cdot 70177$ |
$4$ |
$87.1308109624$ |
$3766179.9574855454$ |
|
|
|
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$12$ |
$44248875484.8$ |
| 15.11.133...536.1 |
$x^{15} - 20 x^{13} - 18 x^{12} + 160 x^{11} + 288 x^{10} - 525 x^{9} - 1728 x^{8} - 100 x^{7} + 4286 x^{6} + 4496 x^{5} - 2032 x^{4} - 6975 x^{3} - 5152 x^{2} - 1540 x - 144$ |
$15$ |
[11,2] |
$2^{15}\cdot 53^{9}\cdot 109\cdot 11316791$ |
$4$ |
$87.4323537912$ |
$2759572.38409611$ |
|
|
? |
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$12$ |
$21273776933.5$ |
| 15.11.164...392.1 |
$x^{15} - 15 x^{13} - 7 x^{12} + 90 x^{11} + 84 x^{10} - 291 x^{9} - 378 x^{8} + 594 x^{7} + 822 x^{6} - 810 x^{5} - 963 x^{4} + 523 x^{3} + 594 x^{2} + 132 x + 8$ |
$15$ |
[11,2] |
$2^{13}\cdot 3^{16}\cdot 881^{6}$ |
$3$ |
$88.6772802283$ |
|
|
|
? |
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$12$ |
$16309663961.4$ |
| 15.11.226...000.1 |
$x^{15} - 5 x^{14} - 57 x^{13} + 289 x^{12} + 825 x^{11} - 4717 x^{10} - 3601 x^{9} + 31833 x^{8} + 1339 x^{7} - 83815 x^{6} + 2237 x^{5} + 55003 x^{4} + 36939 x^{3} + 1177 x^{2} - 4915 x + 235$ |
$15$ |
[11,2] |
$2^{12}\cdot 5^{8}\cdot 13^{10}\cdot 101323^{2}$ |
$4$ |
$105.600175278$ |
$40335.637070503304$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$12$ |
$28726471148.4$ |
| 15.11.168...456.1 |
$x^{15} - 24 x^{13} - 16 x^{12} - 207 x^{11} - 276 x^{10} + 5713 x^{9} + 11610 x^{8} + 369 x^{7} - 17936 x^{6} - 101547 x^{5} - 281706 x^{4} - 365416 x^{3} - 242640 x^{2} - 80880 x - 10784$ |
$15$ |
[11,2] |
$2^{10}\cdot 3^{20}\cdot 337^{2}\cdot 401^{6}$ |
$4$ |
$164.105601726$ |
|
|
|
? |
$C_3:S_3^4:D_5$ (as 15T80) |
trivial |
$2$ |
$12$ |
$375388468767$ |
| 15.11.312...281.1 |
$x^{15} + 9 x^{13} - 6 x^{12} - 2646 x^{11} + 3528 x^{10} + 6330 x^{9} - 15012 x^{8} + 1341405 x^{7} - 3552616 x^{6} - 7159347 x^{5} + 34121178 x^{4} - 47335848 x^{3} + 31732560 x^{2} - 10577520 x + 1410336$ |
$15$ |
[11,2] |
$3^{22}\cdot 59^{2}\cdot 83^{2}\cdot 401^{6}$ |
$4$ |
$171.011875455$ |
$74113.93320896936$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T80) |
trivial |
$2$ |
$12$ |
$571892290212$ |
| 15.11.414...704.1 |
$x^{15} - 6 x^{14} - 135 x^{13} + 333 x^{12} + 6096 x^{11} + 7464 x^{10} - 63720 x^{9} - 277812 x^{8} - 732105 x^{7} - 1606206 x^{6} - 1637631 x^{5} + 2883087 x^{4} + 11810481 x^{3} + 13866012 x^{2} + 3584043 x - 2191593$ |
$15$ |
[11,2] |
$2^{12}\cdot 3^{24}\cdot 17^{3}\cdot 37^{3}\cdot 379531^{2}$ |
$5$ |
$203.164473547$ |
$1509413.0880594563$ |
|
|
? |
$F_5\wr C_3$ (as 15T75) |
trivial |
$2$ |
$12$ |
$1771496479170$ |
| 15.11.721...896.1 |
$x^{15} - 4 x^{14} - 201 x^{13} + 121 x^{12} + 12616 x^{11} + 34020 x^{10} - 207932 x^{9} - 1372760 x^{8} - 2713681 x^{7} + 1113480 x^{6} + 16513183 x^{5} + 35754551 x^{4} + 36074673 x^{3} + 12241538 x^{2} - 11026275 x - 10525969$ |
$15$ |
[11,2] |
$2^{12}\cdot 7^{10}\cdot 13^{3}\cdot 29^{2}\cdot 97^{3}\cdot 192263^{2}$ |
$6$ |
$210.800450914$ |
$6150130.864484555$ |
|
|
? |
$F_5\wr C_3$ (as 15T75) |
trivial |
$2$ |
$12$ |
$1804860014880$ |
| 15.11.288...696.1 |
$x^{15} - 4 x^{14} - 82 x^{13} + 498 x^{12} + 4457 x^{11} - 20812 x^{10} - 97302 x^{9} + 419638 x^{8} + 726751 x^{7} - 3499132 x^{6} - 1752538 x^{5} + 12169158 x^{4} + 742731 x^{3} - 17291716 x^{2} + 715786 x + 7403218$ |
$15$ |
[11,2] |
$2^{20}\cdot 37^{5}\cdot 43^{2}\cdot 139^{2}\cdot 317^{3}\cdot 1867^{2}$ |
$6$ |
$231.207950778$ |
$5209344.109713366$ |
|
|
? |
$F_5\wr S_3$ (as 15T82) |
trivial |
$2$ |
$12$ |
$12436007749000$ |
| 15.11.296...392.1 |
$x^{15} - x^{14} - 28 x^{13} - 79 x^{12} - 1100 x^{11} + 1753 x^{10} + 15805 x^{9} + 2562 x^{8} + 38320 x^{7} - 121800 x^{6} - 728448 x^{5} + 301216 x^{4} + 1038400 x^{3} - 167680 x^{2} - 76800 x + 4096$ |
$15$ |
[11,2] |
$2^{10}\cdot 37^{5}\cdot 151^{2}\cdot 44269^{2}\cdot 305873^{2}$ |
$5$ |
$231.652119798$ |
$13806907.861533877$ |
|
|
|
$D_5\wr S_3$ (as 15T60) |
trivial |
$2$ |
$12$ |
$10419229882500$ |
| 15.11.582...961.1 |
$x^{15} - x^{14} - 186 x^{13} - 169 x^{12} + 13042 x^{11} + 34845 x^{10} - 388062 x^{9} - 1748786 x^{8} + 3122317 x^{7} + 29742540 x^{6} + 42132858 x^{5} - 69864557 x^{4} - 294637932 x^{3} - 458139413 x^{2} - 439035709 x - 204947137$ |
$15$ |
[11,2] |
$61^{4}\cdot 397^{4}\cdot 1301806921^{2}$ |
$3$ |
$242.31016572$ |
$828175124.482607$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T89) |
$[3]$ |
$2$ |
$12$ |
$1136826668480$ |
| 15.11.154...041.1 |
$x^{15} - 3 x^{14} - 126 x^{13} + 531 x^{12} + 5769 x^{11} - 34514 x^{10} - 95880 x^{9} + 1029924 x^{8} - 622189 x^{7} - 13231140 x^{6} + 37048867 x^{5} + 26547802 x^{4} - 288701374 x^{3} + 540249339 x^{2} - 423492779 x + 120987661$ |
$15$ |
[11,2] |
$61^{4}\cdot 397^{4}\cdot 28309^{2}\cdot 74821^{2}$ |
$4$ |
$258.558307376$ |
$1145661948.1962285$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T89) |
$[3]$ |
$2$ |
$12$ |
$1522175959660$ |
| 15.11.159...088.1 |
$x^{15} - 4 x^{14} - 98 x^{13} + 222 x^{12} + 2460 x^{11} - 1774 x^{10} - 6038 x^{9} - 36416 x^{8} - 276240 x^{7} + 345120 x^{6} + 980608 x^{5} + 64640 x^{4} + 3744000 x^{3} - 2539520 x^{2} + 204800 x + 32768$ |
$15$ |
[11,2] |
$2^{14}\cdot 37^{5}\cdot 252949^{2}\cdot 4682551^{2}$ |
$4$ |
$259.117832221$ |
$14861418.533932675$ |
|
|
|
$D_5\wr S_3$ (as 15T60) |
trivial |
$2$ |
$12$ |
$80704179128700$ |
| 15.11.672...424.1 |
$x^{15} - 6 x^{14} - 148 x^{13} + 391 x^{12} + 6782 x^{11} + 5664 x^{10} - 78190 x^{9} - 247562 x^{8} - 512976 x^{7} - 1563298 x^{6} - 2430874 x^{5} + 4161024 x^{4} + 21891109 x^{3} + 29908420 x^{2} + 12024364 x - 1344637$ |
$15$ |
[11,2] |
$2^{12}\cdot 13^{3}\cdot 29^{2}\cdot 53^{3}\cdot 229^{5}\cdot 97367^{2}$ |
$6$ |
$285.225033593$ |
$9672350.918008791$ |
|
|
|
$F_5\wr S_3$ (as 15T82) |
trivial |
$2$ |
$12$ |
$58551393935000$ |
| 15.11.226...000.1 |
$x^{15} - 234 x^{13} - 936 x^{12} + 10592 x^{11} + 91756 x^{10} + 318690 x^{9} + 925776 x^{8} + 2973004 x^{7} + 7361212 x^{6} + 11707090 x^{5} + 11784960 x^{4} + 7512850 x^{3} + 2948100 x^{2} + 651000 x + 62000$ |
$15$ |
[11,2] |
$2^{24}\cdot 5^{6}\cdot 23^{2}\cdot 31^{4}\cdot 37^{5}\cdot 1596629^{2}$ |
$6$ |
$490.144275072$ |
$6295084.304638134$ |
|
|
? |
$A_5\wr S_3$ (as 15T96) |
$[3]$ |
$2$ |
$12$ |
$2079637697780000$ |
| 15.11.819...000.1 |
$x^{15} - 153 x^{13} - 72 x^{12} + 5535 x^{11} + 25854 x^{10} - 75798 x^{9} - 687906 x^{8} - 542818 x^{7} + 3065428 x^{6} + 5465315 x^{5} + 600030 x^{4} - 3014275 x^{3} - 734500 x^{2} + 395500 x + 113000$ |
$15$ |
[11,2] |
$2^{12}\cdot 5^{6}\cdot 7^{12}\cdot 13^{3}\cdot 113^{4}\cdot 508087^{2}$ |
$6$ |
$534.02111607$ |
$4890828.766546343$ |
|
|
? |
$S_5\wr C_3$ (as 15T101) |
trivial |
$2$ |
$12$ |
$2090737998620000$ |
| 15.11.404...000.1 |
$x^{15} - 144 x^{13} - 936 x^{12} + 5540 x^{11} + 75392 x^{10} - 370134 x^{9} - 1459296 x^{8} + 10678864 x^{7} + 27161712 x^{6} - 73028000 x^{5} - 285963840 x^{4} - 324408800 x^{3} - 168640000 x^{2} - 41664000 x - 3968000$ |
$15$ |
[11,2] |
$2^{21}\cdot 5^{6}\cdot 31^{4}\cdot 37^{5}\cdot 1387715921^{2}$ |
$5$ |
$692.522303339$ |
$38697767.539513834$ |
|
|
|
$A_5^3:D_6$ (as 15T97) |
trivial |
$2$ |
$12$ |
$182131728633000000$ |
| 15.11.145...000.1 |
$x^{15} - 360 x^{13} - 648 x^{12} + 39784 x^{11} + 127584 x^{10} - 1599876 x^{9} - 6284088 x^{8} + 21382724 x^{7} + 72393848 x^{6} + 18576960 x^{5} - 80928000 x^{4} - 45803000 x^{3} + 21018800 x^{2} + 15736000 x + 2248000$ |
$15$ |
[11,2] |
$2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 281^{4}\cdot 44850007^{2}$ |
$5$ |
$754.129698025$ |
$19515640.66436397$ |
|
|
? |
$A_5\wr C_3$ (as 15T92) |
$[3]$ |
$2$ |
$12$ |
$8314234047450000$ |
| 15.11.448...000.1 |
$x^{15} - 432 x^{13} - 2592 x^{12} + 31528 x^{11} + 680480 x^{10} - 787680 x^{9} - 56878848 x^{8} + 112700512 x^{7} + 1181988864 x^{6} - 2781299200 x^{5} - 5558538240 x^{4} + 21733222400 x^{3} - 23532339200 x^{2} + 10637312000 x - 1736704000$ |
$15$ |
[11,2] |
$2^{28}\cdot 5^{6}\cdot 53^{4}\cdot 71^{5}\cdot 27404129^{2}$ |
$5$ |
$813.041053924$ |
$15895542.768045366$ |
|
|
|
$A_5^3:D_6$ (as 15T97) |
trivial |
$2$ |
$12$ |
$4662175235540000000$ |
| 15.11.475...505.1 |
$x^{15} - 2 x^{14} - 23 x^{13} + 42 x^{12} + 182 x^{11} - 301 x^{10} - 614 x^{9} + 885 x^{8} + 918 x^{7} - 1112 x^{6} - 525 x^{5} + 508 x^{4} + 60 x^{3} - 65 x^{2} + x + 1$ |
$15$ |
[11,2] |
$5\cdot 11\cdot 433\cdot 2879\cdot 1581889\cdot 43\!\cdots\!17$ |
$6$ |
$951.615700846$ |
$2.180027599323276e+22$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$12$ |
$424752046904000000$ |
| 15.11.132...000.1 |
$x^{15} - 378 x^{13} - 864 x^{12} + 34944 x^{11} + 273216 x^{10} + 281880 x^{9} - 18133632 x^{8} - 120731040 x^{7} - 55931904 x^{6} + 1226545920 x^{5} + 2439797760 x^{4} - 632947200 x^{3} - 2466662400 x^{2} + 651264000$ |
$15$ |
[11,2] |
$2^{15}\cdot 3^{24}\cdot 5^{6}\cdot 53^{4}\cdot 1783^{2}\cdot 603557^{2}$ |
$6$ |
$1018.75132851$ |
$48478816.93020052$ |
|
|
|
$A_5^3:C_6$ (as 15T95) |
trivial |
$2$ |
$12$ |
$476218915504000000$ |
| 15.11.158...000.1 |
$x^{15} - 684 x^{13} - 432 x^{12} + 146384 x^{11} + 86128 x^{10} - 12084336 x^{9} - 4014720 x^{8} + 382478112 x^{7} - 471272384 x^{6} - 1146538240 x^{5} + 1889210880 x^{4} + 416368000 x^{3} - 1810022400 x^{2} + 879872000 x - 125696000$ |
$15$ |
[11,2] |
$2^{22}\cdot 5^{6}\cdot 19^{2}\cdot 37^{5}\cdot 491^{4}\cdot 1307^{2}\cdot 3119^{2}$ |
$7$ |
$1031.16202269$ |
$60217945.711150266$ |
|
|
? |
$A_5\wr S_3$ (as 15T96) |
$[3]$ |
$2$ |
$12$ |
$631360478866000000$ |
| 15.11.424...000.1 |
$x^{15} - 306 x^{13} - 288 x^{12} + 24240 x^{11} + 2756 x^{10} - 112752 x^{9} + 5324544 x^{8} - 1338292 x^{7} - 40210112 x^{6} - 9352320 x^{5} + 85779360 x^{4} + 95779000 x^{3} + 41322000 x^{2} + 7952000 x + 568000$ |
$15$ |
[11,2] |
$2^{18}\cdot 5^{6}\cdot 7^{10}\cdot 71^{4}\cdot 223^{2}\cdot 1709^{2}\cdot 31541^{2}$ |
$7$ |
$1101.2381143$ |
$106292928.0058098$ |
|
|
? |
$A_5\wr C_3$ (as 15T92) |
$[3]$ |
$2$ |
$12$ |
$211856365529000000$ |
| 15.11.204...000.1 |
$x^{15} - 1026 x^{13} - 8208 x^{12} + 237732 x^{11} + 4049952 x^{10} + 11537640 x^{9} - 234539712 x^{8} - 2907652896 x^{7} - 16113845376 x^{6} - 52098560640 x^{5} - 105057976320 x^{4} - 133947814400 x^{3} - 105124300800 x^{2} - 46427136000 x - 8843264000$ |
$15$ |
[11,2] |
$2^{15}\cdot 3^{21}\cdot 5^{6}\cdot 17^{4}\cdot 127^{4}\cdot 1709^{2}\cdot 7759^{2}$ |
$7$ |
$1222.91095056$ |
|
|
|
|
$A_5^3:C_6$ (as 15T95) |
trivial |
$2$ |
$12$ |
$1866318824730000000$ |
