| 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 |
| 15.7.297...329.1 |
$x^{15} - x^{14} - 12 x^{13} + 13 x^{12} + 52 x^{11} - 59 x^{10} - 97 x^{9} + 105 x^{8} + 80 x^{7} - 53 x^{6} - 50 x^{5} + 4 x^{4} + 9 x^{3} + 3 x^{2} + 3 x + 1$ |
$15$ |
[7,4] |
$3^{6}\cdot 7993^{4}$ |
$2$ |
$17.0439840331$ |
$154.85154180698365$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
$2$ |
$10$ |
$3449.59973544$ |
| 15.7.306...241.1 |
$x^{15} - 6 x^{14} + 13 x^{13} - 10 x^{12} - 9 x^{11} + 30 x^{10} - 38 x^{9} + 45 x^{8} - 19 x^{7} - 48 x^{6} + 47 x^{5} - 38 x^{4} + 34 x^{3} + 5 x^{2} - 7 x + 1$ |
$15$ |
[7,4] |
$11^{12}\cdot 23^{2}\cdot 43^{2}$ |
$3$ |
$17.0794410507$ |
$400.82706302115287$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$10$ |
$3397.28173407$ |
| 15.7.141...881.1 |
$x^{15} - x^{14} + 12 x^{12} - 13 x^{11} + 2 x^{10} + 20 x^{9} - 22 x^{8} + x^{7} - 80 x^{6} + 90 x^{5} - x^{4} + x^{3} - 10 x^{2} + 1$ |
$15$ |
[7,4] |
$11^{6}\cdot 41^{8}$ |
$2$ |
$18.9107374166$ |
$39.43533916948872$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
$2$ |
$10$ |
$8426.46622965$ |
| 15.7.134...208.1 |
$x^{15} - 15 x^{13} - 10 x^{12} + 72 x^{11} + 96 x^{10} - 103 x^{9} - 270 x^{8} - 99 x^{7} + 176 x^{6} + 459 x^{5} + 906 x^{4} + 1096 x^{3} + 720 x^{2} + 240 x + 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 13^{3}\cdot 347^{3}$ |
$4$ |
$25.6249179762$ |
$1262.8714687961035$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$10$ |
$90574.4782003$ |
| 15.7.173...136.1 |
$x^{15} - 6 x^{13} - 6 x^{12} + 27 x^{11} + 12 x^{10} - 88 x^{9} + 54 x^{8} - 72 x^{7} + 408 x^{6} - 297 x^{5} - 474 x^{4} + 616 x^{3} - 72 x^{2} - 144 x + 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 4903^{3}$ |
$3$ |
$26.0555531277$ |
|
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$10$ |
$96504.3069418$ |
| 15.7.575...744.1 |
$x^{15} - 6 x^{14} + 8 x^{13} + 30 x^{12} - 122 x^{11} + 90 x^{10} + 325 x^{9} - 728 x^{8} + 58 x^{7} + 1440 x^{6} - 1327 x^{5} - 904 x^{4} + 1775 x^{3} - 218 x^{2} - 716 x + 296$ |
$15$ |
[7,4] |
$2^{14}\cdot 29^{4}\cdot 89^{6}$ |
$3$ |
$28.2286514516$ |
$670.5229726961478$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T89) |
trivial |
$2$ |
$10$ |
$364659.378308$ |
| 15.7.133...872.1 |
$x^{15} - 2 x^{14} - 12 x^{13} + 21 x^{12} + 59 x^{11} - 84 x^{10} - 150 x^{9} + 160 x^{8} + 204 x^{7} - 150 x^{6} - 140 x^{5} + 67 x^{4} + 44 x^{3} - 13 x^{2} - 4 x + 1$ |
$15$ |
[7,4] |
$2^{3}\cdot 4373\cdot 411967\cdot 924989228549$ |
$4$ |
$29.8532238808$ |
$115460726104.23566$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$10$ |
$625563.074557$ |
| 15.7.278...224.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 11 x^{12} - 30 x^{11} + 122 x^{9} - 174 x^{8} + 126 x^{7} + 282 x^{6} - 476 x^{5} - 4 x^{4} + 72 x^{3} - 216 x^{2} + 112 x + 16$ |
$15$ |
[7,4] |
$2^{14}\cdot 43^{4}\cdot 89^{6}$ |
$3$ |
$31.3551526973$ |
$871.8878657445434$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T89) |
trivial |
$2$ |
$10$ |
$811563.21016$ |
| 15.7.334...489.1 |
$x^{15} - 6 x^{14} + 14 x^{13} - 2 x^{12} - 81 x^{11} + 267 x^{10} - 478 x^{9} + 345 x^{8} + 603 x^{7} - 1896 x^{6} + 2450 x^{5} - 2082 x^{4} + 445 x^{3} + 2020 x^{2} - 2460 x + 859$ |
$15$ |
[7,4] |
$11^{12}\cdot 23^{2}\cdot 67^{4}$ |
$3$ |
$31.7417699914$ |
$538.7177286092511$ |
|
|
? |
$C_3:S_3^4:C_5$ (as 15T71) |
trivial |
$2$ |
$10$ |
$316012.234645$ |
| 15.7.353...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 383 x^{5} + 100 x^{4} + 165 x^{3} - 50 x^{2} - 40 x + 8$ |
$15$ |
[7,4] |
$2^{12}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$31.8561064713$ |
|
|
|
? |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$10$ |
$526115.053709$ |
| 15.7.353...000.2 |
$x^{15} - 15 x^{13} + 90 x^{11} - 14 x^{10} - 275 x^{9} + 140 x^{8} + 450 x^{7} - 490 x^{6} - 375 x^{5} + 700 x^{4} + 125 x^{3} - 350 x^{2} + 56$ |
$15$ |
[7,4] |
$2^{12}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$31.8561064713$ |
|
|
|
? |
$D_5^3.C_6$ (as 15T59) |
trivial |
$2$ |
$10$ |
$535760.760837$ |
| 15.7.398...552.1 |
$x^{15} - 4 x^{14} - 6 x^{13} + 63 x^{12} - 113 x^{11} - 102 x^{10} + 732 x^{9} - 1232 x^{8} + 734 x^{7} + 453 x^{6} - 804 x^{5} + 183 x^{4} - 46 x^{3} + 218 x^{2} - 53 x + 3$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{8}\cdot 331^{3}\cdot 547^{3}$ |
$4$ |
$32.1154784907$ |
$8109.998688954744$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$10$ |
$1327578.57871$ |
| 15.7.838...192.1 |
$x^{15} - 9 x^{13} - 6 x^{12} - 36 x^{11} - 48 x^{10} + 119 x^{9} + 270 x^{8} + 261 x^{7} + 256 x^{6} - 27 x^{5} - 714 x^{4} - 1064 x^{3} - 720 x^{2} - 240 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{9}\cdot 401^{6}$ |
$3$ |
$33.745600879$ |
$352.7655870204816$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$10$ |
$1870953.74415$ |
| 15.7.208...384.1 |
$x^{15} + 9 x^{13} - 6 x^{12} - 9 x^{11} + 12 x^{10} - 139 x^{9} + 270 x^{8} - 180 x^{7} + 40 x^{6} + 243 x^{5} - 810 x^{4} + 1080 x^{3} - 720 x^{2} + 240 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 61^{3}\cdot 397^{3}$ |
$4$ |
$35.8617919631$ |
$3083.359812200957$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$10$ |
$971559.572188$ |
| 15.7.307...424.1 |
$x^{15} - x^{14} - 11 x^{13} + 8 x^{12} + 48 x^{11} - 21 x^{10} - 108 x^{9} + 17 x^{8} + 137 x^{7} + 6 x^{6} - 99 x^{5} - 8 x^{4} + 38 x^{3} - 6 x + 1$ |
$15$ |
[7,4] |
$2^{11}\cdot 11\cdot 13667278608949991783$ |
$3$ |
$36.8038833618$ |
$82484026761.95607$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$10$ |
$3782469.74424$ |
| 15.7.522...529.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 25 x^{12} - 39 x^{11} + 325 x^{10} - 886 x^{9} + 1475 x^{8} - 714 x^{7} - 3448 x^{6} + 9908 x^{5} - 13758 x^{4} + 11749 x^{3} - 6069 x^{2} + 1604 x - 131$ |
$15$ |
[7,4] |
$11^{12}\cdot 23\cdot 38281\cdot 189223$ |
$4$ |
$38.1264600294$ |
$2779435.915025367$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$10$ |
$1332210.24405$ |
| 15.7.554...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 387 x^{5} + 100 x^{4} + 185 x^{3} - 50 x^{2} - 60 x + 8$ |
$15$ |
[7,4] |
$2^{18}\cdot 5^{15}\cdot 37^{5}$ |
$3$ |
$38.2771775947$ |
|
|
|
? |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$10$ |
$5557858.58989$ |
| 15.7.936...125.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 380 x^{5} + 100 x^{4} + 150 x^{3} - 50 x^{2} - 25 x + 9$ |
$15$ |
[7,4] |
$3^{7}\cdot 5^{15}\cdot 107^{5}$ |
$3$ |
$39.6358201495$ |
|
|
|
✓ |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$10$ |
$5809572.07467$ |
| 15.7.104...920.1 |
$x^{15} - 15 x^{13} - 10 x^{12} + 90 x^{11} + 120 x^{10} - 250 x^{9} - 540 x^{8} + 225 x^{7} + 1128 x^{6} + 297 x^{5} - 1098 x^{4} - 684 x^{3} + 432 x^{2} + 432 x + 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 5\cdot 61^{3}\cdot 397^{3}$ |
$5$ |
$39.9236267929$ |
$6832.541620349856$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$10$ |
$2888406.53521$ |
| 15.7.106...744.1 |
$x^{15} - 15 x^{13} - 6 x^{12} + 90 x^{11} + 72 x^{10} - 282 x^{9} - 324 x^{8} + 513 x^{7} + 768 x^{6} - 567 x^{5} - 1206 x^{4} + 164 x^{3} + 1080 x^{2} + 480 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{15}\cdot 11^{12}\cdot 23$ |
$4$ |
$39.9672182762$ |
$614.0458551912413$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$10$ |
$2211657.27405$ |
| 15.7.214...792.1 |
$x^{15} - 3 x^{13} - 2 x^{12} - 54 x^{11} - 72 x^{10} - 51 x^{9} - 54 x^{8} + 207 x^{7} + 640 x^{6} + 891 x^{5} + 1098 x^{4} + 1128 x^{3} + 720 x^{2} + 240 x + 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{16}\cdot 36497^{3}$ |
$3$ |
$41.8858598896$ |
$5227.796383881872$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$10$ |
$3912057.26194$ |
| 15.7.226...184.1 |
$x^{15} + 12 x^{13} - 8 x^{12} + 9 x^{11} - 12 x^{10} - 185 x^{9} + 378 x^{8} - 495 x^{7} + 704 x^{6} - 405 x^{5} - 522 x^{4} + 1032 x^{3} - 720 x^{2} + 240 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{12}\cdot 401^{6}$ |
$3$ |
$42.0379390909$ |
$528.5116573022199$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T80) |
trivial |
$2$ |
$10$ |
$7043298.15376$ |
| 15.7.112...664.1 |
$x^{15} - 3 x^{14} - 20 x^{13} + 54 x^{12} + 104 x^{11} - 221 x^{10} - 155 x^{9} - 112 x^{8} + 165 x^{7} + 554 x^{6} + 1088 x^{5} + 572 x^{4} - 1059 x^{3} - 1770 x^{2} - 1234 x - 277$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{8}\cdot 401^{7}$ |
$3$ |
$46.7683491417$ |
$517.8678999789855$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T79) |
trivial |
$2$ |
$10$ |
$17663529.5702$ |
| 15.7.117...136.1 |
$x^{15} - 2 x^{14} + 23 x^{13} - 29 x^{12} + 78 x^{11} + 108 x^{10} - 353 x^{9} + 913 x^{8} - 585 x^{7} - 345 x^{6} + 2379 x^{5} - 2442 x^{4} + 342 x^{3} + 480 x^{2} - 188 x + 17$ |
$15$ |
[7,4] |
$2^{10}\cdot 83^{2}\cdot 401^{7}$ |
$3$ |
$46.9206964718$ |
$1397.6190870339008$ |
|
|
? |
$C_3:S_3^4:D_5$ (as 15T79) |
trivial |
$2$ |
$10$ |
$15705215.5584$ |
| 15.7.140...625.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 27 x^{10} - 275 x^{9} + 270 x^{8} + 450 x^{7} - 945 x^{6} - 270 x^{5} + 1350 x^{4} - 400 x^{3} - 675 x^{2} + 525 x - 106$ |
$15$ |
[7,4] |
$3^{6}\cdot 5^{15}\cdot 229^{5}$ |
$3$ |
$47.47121350011743$ |
|
|
|
? |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$10$ |
$17829545.169436164$ |
| 15.7.140...625.2 |
$x^{15} - 15 x^{13} + 90 x^{11} - 15 x^{10} - 275 x^{9} + 150 x^{8} + 450 x^{7} - 525 x^{6} - 348 x^{5} + 750 x^{4} - 10 x^{3} - 375 x^{2} + 135 x + 14$ |
$15$ |
[7,4] |
$3^{6}\cdot 5^{15}\cdot 229^{5}$ |
$3$ |
$47.47121350011743$ |
|
|
|
? |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$10$ |
$23195233.06962111$ |
| 15.7.444...952.1 |
$x^{15} - 15 x^{13} - 4 x^{12} + 90 x^{11} + 48 x^{10} - 306 x^{9} - 216 x^{8} + 729 x^{7} + 656 x^{6} - 1215 x^{5} - 1668 x^{4} + 620 x^{3} + 2016 x^{2} + 1056 x + 96$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{11}\cdot 59\cdot 401^{6}$ |
$4$ |
$51.2731658554$ |
$2594.763877379148$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$10$ |
$28810259.5858$ |
| 15.7.448...625.1 |
$x^{15} - x^{14} - 4 x^{13} - 35 x^{12} - 24 x^{11} - 71 x^{10} + 899 x^{9} + 1896 x^{8} - 6905 x^{7} - 1614 x^{6} + 18939 x^{5} - 416 x^{4} - 14084 x^{3} - 28970 x^{2} + 3401 x - 97$ |
$15$ |
[7,4] |
$3^{8}\cdot 5^{14}\cdot 257^{5}$ |
$3$ |
$51.3035850556$ |
$404.72475773505266$ |
|
|
? |
$D_5\wr S_3$ (as 15T60) |
trivial |
$2$ |
$10$ |
$36339727.7705$ |
| 15.7.144...000.1 |
$x^{15} - 20 x^{11} - 16 x^{10} + 75 x^{7} + 120 x^{6} + 48 x^{5} + 125 x^{3} + 300 x^{2} + 240 x + 64$ |
$15$ |
[7,4] |
$2^{24}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$55.4647028661$ |
|
|
|
? |
$S_5\wr C_3$ (as 15T101) |
trivial |
$2$ |
$10$ |
$30653623.648$ |
| 15.7.144...000.2 |
$x^{15} - 20 x^{11} - 128 x^{10} - 800 x^{7} + 3200 x^{6} + 3072 x^{5} + 8000 x^{3} - 25600 x^{2} - 20480 x + 32768$ |
$15$ |
[7,4] |
$2^{24}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$55.4647028661$ |
|
|
|
? |
$S_5\wr C_3$ (as 15T101) |
trivial |
$2$ |
$10$ |
$40554373.5781$ |
| 15.7.183...904.1 |
$x^{15} + 9 x^{13} - 6 x^{12} - 36 x^{11} + 48 x^{10} - 151 x^{9} + 270 x^{8} - 99 x^{7} - 176 x^{6} + 459 x^{5} - 906 x^{4} + 1096 x^{3} - 720 x^{2} + 240 x - 32$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{16}\cdot 401^{6}$ |
$3$ |
$56.3473830948$ |
|
|
|
? |
$C_3:S_3^4:D_5$ (as 15T80) |
trivial |
$2$ |
$10$ |
$47060734.5622$ |
| 15.7.109...024.1 |
$x^{15} - 15 x^{13} - 6 x^{12} + 90 x^{11} + 72 x^{10} - 406 x^{9} - 324 x^{8} + 1629 x^{7} + 1016 x^{6} - 3915 x^{5} - 2694 x^{4} + 5992 x^{3} + 3312 x^{2} - 6960 x - 864$ |
$15$ |
[7,4] |
$2^{8}\cdot 3^{14}\cdot 11^{6}\cdot 131^{6}$ |
$4$ |
$74.0164232301$ |
$2117.432444378886$ |
|
|
|
$C_3:S_3^4:A_5$ (as 15T88) |
$[3]$ |
$2$ |
$10$ |
$2171299929.11$ |
| 15.7.308...125.1 |
$x^{15} - 4 x^{14} + 11 x^{13} - 38 x^{12} + 139 x^{11} - 206 x^{10} - 2038 x^{9} + 7767 x^{8} - 9664 x^{7} - 5430 x^{6} + 20708 x^{5} + 7092 x^{4} - 3218 x^{3} - 4097 x^{2} - 3552 x - 188$ |
$15$ |
[7,4] |
$5^{6}\cdot 11^{12}\cdot 229^{5}$ |
$3$ |
$79.3074483979$ |
$230.41825932701707$ |
|
|
? |
$D_5\wr S_3$ (as 15T60) |
$[5]$ |
$2$ |
$10$ |
$140830601.101$ |
| 15.7.461...416.1 |
$x^{15} - 6 x^{14} - 15 x^{13} + 195 x^{12} - 177 x^{11} - 1944 x^{10} + 125 x^{9} + 17799 x^{8} + 6408 x^{7} - 65914 x^{6} - 5610 x^{5} + 101934 x^{4} - 28655 x^{3} - 49518 x^{2} + 36987 x - 10313$ |
$15$ |
[7,4] |
$2^{12}\cdot 3^{20}\cdot 17^{2}\cdot 3343733^{2}$ |
$4$ |
$81.4597496787$ |
$92267.1110657069$ |
|
|
|
$D_5\wr C_3$ (as 15T50) |
trivial |
$2$ |
$10$ |
$574507211.585$ |
| 15.7.651...624.1 |
$x^{15} - 15 x^{13} - 22 x^{12} + 90 x^{11} + 264 x^{10} - 806 x^{9} - 1188 x^{8} + 5229 x^{7} + 14104 x^{6} - 14715 x^{5} - 72150 x^{4} - 6696 x^{3} + 105552 x^{2} + 63504 x - 27616$ |
$15$ |
[7,4] |
$2^{18}\cdot 3^{12}\cdot 881^{6}$ |
$3$ |
$83.3534081498$ |
|
|
|
|
$C_3:S_3^4:A_5$ (as 15T88) |
trivial |
$2$ |
$10$ |
$6482329993.06$ |
| 15.7.148...368.1 |
$x^{15} - 15 x^{13} - 10 x^{12} + 90 x^{11} + 120 x^{10} - 374 x^{9} - 540 x^{8} + 1341 x^{7} + 1608 x^{6} - 3051 x^{5} - 3978 x^{4} + 6536 x^{3} + 4752 x^{2} - 11184 x + 3680$ |
$15$ |
[7,4] |
$2^{20}\cdot 3^{16}\cdot 53^{9}$ |
$3$ |
$88.0781507249$ |
$828.9736568118362$ |
|
|
|
$C_3:S_3^4:F_5$ (as 15T85) |
trivial |
$2$ |
$10$ |
$7414055979.85$ |
| 15.7.156...536.1 |
$x^{15} - x^{14} - 37 x^{13} + 81 x^{12} + 394 x^{11} - 906 x^{10} - 1650 x^{9} + 3878 x^{8} + 1548 x^{7} - 3724 x^{6} + 28484 x^{5} + 42844 x^{4} - 18504 x^{3} - 59864 x^{2} - 36216 x - 7288$ |
$15$ |
[7,4] |
$2^{26}\cdot 137^{10}$ |
$2$ |
$88.3620339208$ |
$130.11902033846712$ |
|
|
? |
$A_8$ (as 15T72) |
trivial |
$2$ |
$10$ |
$12284484047.2$ |
| 15.7.156...536.2 |
$x^{15} - 4 x^{14} - 30 x^{13} + 32 x^{12} + 421 x^{11} + 132 x^{10} - 3322 x^{9} - 112 x^{8} + 11245 x^{7} - 816 x^{6} - 22856 x^{5} + 7348 x^{4} + 20212 x^{3} - 4272 x^{2} - 8528 x - 1648$ |
$15$ |
[7,4] |
$2^{26}\cdot 137^{10}$ |
$2$ |
$88.3620339208$ |
|
|
|
? |
$A_8$ (as 15T72) |
trivial |
$2$ |
$10$ |
$12284484047.2$ |
| 15.7.233...000.1 |
$x^{15} - 20 x^{13} - 30 x^{12} + 140 x^{11} + 500 x^{10} - 1200 x^{9} - 2200 x^{8} + 5300 x^{7} + 20400 x^{6} - 12600 x^{5} - 29000 x^{4} + 110500 x^{3} + 8000 x^{2} - 39500 x + 500$ |
$15$ |
[7,4] |
$2^{14}\cdot 5^{15}\cdot 7^{6}\cdot 3968023429$ |
$4$ |
$90.7560317016$ |
|
|
|
? |
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$10$ |
$2273239934.77$ |
| 15.7.267...000.1 |
$x^{15} - 5 x^{14} - 5 x^{13} - 35 x^{12} - 10 x^{11} + 950 x^{10} + 2005 x^{9} + 165 x^{8} - 11050 x^{7} - 28850 x^{6} - 1575 x^{5} + 95325 x^{4} + 21125 x^{3} - 82925 x^{2} + 14750 x - 2060$ |
$15$ |
[7,4] |
$2^{8}\cdot 3^{5}\cdot 5^{22}\cdot 71^{5}$ |
$4$ |
$91.5865862928$ |
|
|
|
|
$C_5^3:S_4$ (as 15T51) |
trivial |
$2$ |
$10$ |
$10696303528.2$ |
| 15.7.471...000.1 |
$x^{15} - 15 x^{13} - 10 x^{12} + 90 x^{11} + 120 x^{10} - 470 x^{9} - 540 x^{8} + 2205 x^{7} + 2440 x^{6} - 5643 x^{5} - 8970 x^{4} + 14120 x^{3} + 12240 x^{2} - 26160 x - 17056$ |
$15$ |
[7,4] |
$2^{10}\cdot 3^{4}\cdot 5^{15}\cdot 239^{6}$ |
$4$ |
$95.1148140254$ |
|
|
|
? |
$C_3:S_3^4:F_5$ (as 15T85) |
trivial |
$2$ |
$10$ |
$13673892773.3$ |
| 15.7.479...608.1 |
$x^{15} + 15 x^{13} - 10 x^{12} - 9 x^{11} + 12 x^{10} - 760 x^{9} + 1512 x^{8} - 2628 x^{7} + 4544 x^{6} - 1404 x^{5} - 7800 x^{4} + 12640 x^{3} - 8640 x^{2} + 2880 x - 384$ |
$15$ |
[7,4] |
$2^{8}\cdot 3^{17}\cdot 31\cdot 881^{6}$ |
$4$ |
$95.2140918169$ |
|
|
|
? |
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$10$ |
$14077541060.8$ |
| 15.7.879...424.1 |
$x^{15} - 15 x^{13} - 2 x^{12} + 90 x^{11} + 24 x^{10} - 330 x^{9} - 108 x^{8} + 945 x^{7} + 160 x^{6} - 1863 x^{5} + 174 x^{4} + 2036 x^{3} - 504 x^{2} - 1248 x + 384$ |
$15$ |
[7,4] |
$2^{17}\cdot 3^{15}\cdot 881^{6}$ |
$3$ |
$99.1468558756$ |
|
|
|
|
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$10$ |
$21229954529.5$ |
| 15.7.172...528.1 |
$x^{15} - 20 x^{13} - 23 x^{12} + 160 x^{11} + 368 x^{10} - 455 x^{9} - 2208 x^{8} - 940 x^{7} + 5251 x^{6} + 7856 x^{5} - 792 x^{4} - 10957 x^{3} - 10192 x^{2} - 3532 x - 289$ |
$15$ |
[7,4] |
$2^{12}\cdot 23\cdot 53^{9}\cdot 5540509427$ |
$4$ |
$103.691069491$ |
$14024121.476561375$ |
|
|
? |
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$10$ |
$7182211989.47$ |
| 15.7.207...528.1 |
$x^{15} - 6 x^{14} - 45 x^{13} + 237 x^{12} + 927 x^{11} - 3972 x^{10} - 15815 x^{9} - 1359 x^{8} + 32784 x^{7} + 13036 x^{6} - 44982 x^{5} - 205428 x^{4} - 402517 x^{3} - 219972 x^{2} + 103137 x + 90953$ |
$15$ |
[7,4] |
$2^{24}\cdot 3^{20}\cdot 19^{2}\cdot 73^{3}\cdot 503^{2}$ |
$5$ |
$104.998666343$ |
$65165.59270379993$ |
|
|
? |
$F_5\wr C_3$ (as 15T75) |
trivial |
$2$ |
$10$ |
$3797541389.82$ |
| 15.7.324...000.1 |
$x^{15} - 15 x^{13} - 30 x^{12} + 90 x^{11} + 360 x^{10} - 70 x^{9} - 1620 x^{8} - 1395 x^{7} + 3960 x^{6} + 5157 x^{5} - 6750 x^{4} - 11080 x^{3} + 6480 x^{2} + 17040 x - 8032$ |
$15$ |
[7,4] |
$2^{22}\cdot 3^{16}\cdot 5^{16}\cdot 7^{6}$ |
$4$ |
$108.155153819$ |
$802.3772411911064$ |
|
|
? |
$C_3:S_3^4:F_5$ (as 15T84) |
trivial |
$2$ |
$10$ |
$32145104433.7$ |
| 15.7.960...000.1 |
$x^{15} - 50 x^{13} - 5 x^{12} + 330 x^{11} + 266 x^{10} + 9150 x^{9} - 12230 x^{8} - 55090 x^{7} + 142500 x^{6} - 156072 x^{5} + 136600 x^{4} - 150040 x^{3} + 126420 x^{2} - 48320 x + 1024$ |
$15$ |
[7,4] |
$2^{8}\cdot 5^{24}\cdot 229^{5}$ |
$3$ |
$116.282180079$ |
|
|
|
|
$C_5^3:S_4$ (as 15T51) |
trivial |
$2$ |
$10$ |
$27870703200.4$ |
| 15.7.252...016.1 |
$x^{15} - 3 x^{14} - 34 x^{13} + 131 x^{12} + 140 x^{11} + 6 x^{10} - 844 x^{9} - 23534 x^{8} + 34798 x^{7} - 338826 x^{6} + 697817 x^{5} + 1734863 x^{4} - 384987 x^{3} + 1185332 x^{2} - 3097360 x - 1985369$ |
$15$ |
[7,4] |
$2^{12}\cdot 7^{10}\cdot 181^{3}\cdot 1918013^{2}$ |
$4$ |
$124.014350867$ |
$841174.0960404088$ |
|
|
? |
$F_5\wr C_3$ (as 15T75) |
trivial |
$2$ |
$10$ |
$14904443382.7$ |
| 15.7.147...672.1 |
$x^{15} - 4 x^{14} + 16 x^{13} + 88 x^{12} - 1028 x^{11} + 2372 x^{10} + 7436 x^{9} - 57504 x^{8} + 79584 x^{7} + 298192 x^{6} - 1051888 x^{5} + 622192 x^{4} + 1351424 x^{3} - 1648576 x^{2} + 2016 x + 349664$ |
$15$ |
[7,4] |
$2^{10}\cdot 109^{8}\cdot 373^{5}$ |
$3$ |
$139.4923550768799$ |
$1307.6221785596658$ |
|
|
? |
$C_5^3:S_4$ (as 15T51) |
trivial |
$2$ |
$10$ |
$45912631980.879456$ |
| 15.7.449...288.1 |
$x^{15} - x^{14} - 45 x^{13} - 187 x^{12} - 215 x^{11} + 1683 x^{10} + 6975 x^{9} + 12185 x^{8} - 14857 x^{7} - 41575 x^{6} + 142641 x^{5} + 821871 x^{4} + 1562899 x^{3} + 1035129 x^{2} + 89497 x - 69121$ |
$15$ |
[7,4] |
$2^{20}\cdot 13^{4}\cdot 37^{5}\cdot 61^{3}\cdot 30893^{2}$ |
$5$ |
$150.270168866$ |
$287126.9166909081$ |
|
|
? |
$F_5\wr S_3$ (as 15T82) |
trivial |
$2$ |
$10$ |
$202085653591$ |
