| 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 |
| 15.3.1788527348449625.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 9 x^{12} + 13 x^{11} - 15 x^{10} + 18 x^{9} - 23 x^{8} + 33 x^{7} - 44 x^{6} + 48 x^{5} - 44 x^{4} + 30 x^{3} - 16 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$5^{3}\cdot 7^{10}\cdot 37^{3}$ |
$3$ |
$10.3952045383$ |
$49.77193869732466$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$26.5068203244$ |
| 15.3.2164169497031757.1 |
$x^{15} - 7 x^{14} + 23 x^{13} - 45 x^{12} + 54 x^{11} - 32 x^{10} - 14 x^{9} + 55 x^{8} - 72 x^{7} + 69 x^{6} - 57 x^{5} + 39 x^{4} - 21 x^{3} + 9 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$3^{3}\cdot 69593\cdot 1151759887$ |
$3$ |
$10.5281666665$ |
$15506878.391474314$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$29.6657425505$ |
| 15.3.2354315214908549.1 |
$x^{15} - x^{14} + x^{13} - x^{12} - x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - x^{6} + 2 x^{3} - x^{2} + 2 x - 1$ |
$15$ |
[3,6] |
$27765763\cdot 84792023$ |
$2$ |
$10.5874402875$ |
$48521286.204186186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$31.1653663197$ |
| 15.3.2432060458605625.1 |
$x^{15} - x^{14} - 2 x^{13} + x^{12} + 2 x^{11} - 4 x^{10} - 4 x^{9} + 3 x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 5 x^{4} + 5 x^{3} - x^{2} - 4 x - 1$ |
$15$ |
[3,6] |
$5^{4}\cdot 19^{2}\cdot 47^{6}$ |
$3$ |
$10.6103967712$ |
$142.7352803864651$ |
|
|
? |
$C_3\wr D_5$ (as 15T46) |
trivial |
$2$ |
$8$ |
$32.0155843928$ |
| 15.3.3276367268581097.1 |
$x^{15} - 6 x^{13} - x^{12} + 16 x^{11} + 8 x^{10} - 20 x^{9} - 24 x^{8} + 4 x^{7} + 31 x^{6} + 15 x^{5} - 15 x^{4} - 14 x^{3} + x^{2} + 4 x + 1$ |
$15$ |
[3,6] |
$3276367268581097$ |
$1$ |
$10.8232952365$ |
$57239560.34580539$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$37.7909873347$ |
| 15.3.4864965285308625.1 |
$x^{15} - 3 x^{14} + 6 x^{13} - 12 x^{12} + 14 x^{11} - 17 x^{10} + 24 x^{9} - 28 x^{8} + 31 x^{7} - 21 x^{6} + 18 x^{5} - 15 x^{4} + 16 x^{3} - 11 x^{2} + 5 x - 1$ |
$15$ |
[3,6] |
$3^{9}\cdot 5^{3}\cdot 7^{11}$ |
$3$ |
$11.1123347675$ |
$40.77320330425099$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
$2$ |
$8$ |
$50.4138149085$ |
| 15.3.6114596477365737.1 |
$x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} - 8 x^{11} + 18 x^{10} - 18 x^{9} + 20 x^{7} - 27 x^{6} + 15 x^{5} + 3 x^{4} - 11 x^{3} + 10 x^{2} - 5 x + 1$ |
$15$ |
[3,6] |
$3^{4}\cdot 15601\cdot 4838718377$ |
$3$ |
$11.2829982327$ |
$15048805.141895186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$53.4601866446$ |
| 15.3.10544075126076649.1 |
$x^{15} - 6 x^{14} + 11 x^{13} - x^{12} - 10 x^{11} - 13 x^{10} + 18 x^{9} + 40 x^{8} - 30 x^{7} - 64 x^{6} + 42 x^{5} + 47 x^{4} - 27 x^{3} - 19 x^{2} + 9 x + 1$ |
$15$ |
[3,6] |
$37^{2}\cdot 43^{2}\cdot 1609^{3}$ |
$3$ |
$11.7003961458$ |
$5466.694549893152$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
$2$ |
$8$ |
$73.2403388939$ |
| 15.3.11354350039657729.1 |
$x^{15} - 4 x^{14} + 5 x^{13} + x^{12} - 7 x^{11} + x^{10} + 7 x^{9} - 2 x^{8} - 8 x^{7} + 22 x^{6} - 37 x^{5} + 35 x^{4} - 20 x^{3} + 11 x^{2} - 7 x + 1$ |
$15$ |
[3,6] |
$13^{2}\cdot 127^{2}\cdot 1609^{3}$ |
$3$ |
$11.7582895867$ |
$5603.285322545042$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
$2$ |
$8$ |
$79.4890458165$ |
| 15.3.12853809661090929.1 |
$x^{15} - x^{14} - x^{13} + 3 x^{12} - x^{10} - 4 x^{9} + 4 x^{8} + 2 x^{7} - 7 x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x + 1$ |
$15$ |
[3,6] |
$3\cdot 4284603220363643$ |
$2$ |
$11.855925391$ |
$113374642.9369942$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$108.091851993$ |
| 15.3.15315650494266781.1 |
$x^{15} - 2 x^{14} + x^{13} - x^{12} + 7 x^{11} - 5 x^{10} - 10 x^{9} + 7 x^{8} + 16 x^{7} - 15 x^{6} - 19 x^{5} + 27 x^{4} - 2 x^{3} - 11 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$127^{2}\cdot 9829^{3}$ |
$2$ |
$11.9952424328$ |
$2504.9005119012204$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
$2$ |
$8$ |
$87.5727798613$ |
| 15.3.16680932154277329.1 |
$x^{15} - 2 x^{14} + 6 x^{13} - 14 x^{12} + 23 x^{11} - 35 x^{10} + 44 x^{9} - 41 x^{8} + 25 x^{7} - 4 x^{6} - 20 x^{5} + 34 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$ |
$15$ |
[3,6] |
$3\cdot 47\cdot 103\cdot 11057\cdot 103878739$ |
$5$ |
$12.063722938$ |
$129154683.05205712$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$124.641970008$ |
| 15.3.19664802801826816.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 23 x^{12} + 19 x^{11} + 7 x^{10} - 41 x^{9} + 47 x^{8} - 10 x^{7} - 39 x^{6} + 50 x^{5} - 18 x^{4} - 16 x^{3} + 21 x^{2} - 9 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 79^{7}$ |
$2$ |
$12.1968019833$ |
$17.776388834631177$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$103.698212623$ |
| 15.3.21643467887730481.1 |
$x^{15} - x^{14} - x^{13} + x^{12} - 7 x^{11} - 2 x^{10} + 18 x^{9} + 12 x^{8} - 17 x^{7} + 7 x^{6} - 11 x^{5} - 21 x^{4} + 22 x^{3} - 11 x^{2} - 2 x - 1$ |
$15$ |
[3,6] |
$13^{2}\cdot 47^{6}\cdot 109^{2}$ |
$3$ |
$12.2750081706$ |
$864.8925624711881$ |
|
|
? |
$C_3\wr D_5$ (as 15T46) |
trivial |
$2$ |
$8$ |
$116.633322592$ |
| 15.3.23713122135310336.1 |
$x^{15} - 5 x^{14} + 10 x^{13} - 5 x^{12} - 15 x^{11} + 29 x^{10} - 8 x^{9} - 31 x^{8} + 36 x^{7} - 24 x^{5} + 12 x^{4} + 9 x^{3} - 9 x^{2} + 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 67^{6}$ |
$2$ |
$12.3499703768$ |
$23.15167380558045$ |
|
|
? |
$A_5$ (as 15T5) |
trivial |
$2$ |
$8$ |
$133.707274982$ |
| 15.3.31123779291971584.1 |
$x^{15} + x^{13} - x^{12} - 5 x^{11} - 4 x^{10} - 5 x^{9} - x^{8} + 4 x^{7} + 2 x^{6} - 2 x^{5} - 4 x^{4} - 5 x^{3} - 4 x^{2} - 3 x - 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 587^{4}$ |
$2$ |
$12.5759119634$ |
$81.49323216626063$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$152.23669177$ |
| 15.3.39671359416303616.1 |
$x^{15} - 7 x^{14} + 24 x^{13} - 47 x^{12} + 46 x^{11} + 18 x^{10} - 150 x^{9} + 296 x^{8} - 383 x^{7} + 371 x^{6} - 282 x^{5} + 171 x^{4} - 83 x^{3} + 31 x^{2} - 8 x + 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 73^{6}$ |
$2$ |
$12.7810089465$ |
$24.166091947189145$ |
|
|
? |
$A_5$ (as 15T5) |
trivial |
$2$ |
$8$ |
$170.85154758$ |
| 15.3.47090024679574321.1 |
$x^{15} - x^{12} - x^{11} - x^{8} - 2 x^{7} + 2 x^{5} + 3 x^{4} + 2 x^{3} - x - 1$ |
$15$ |
[3,6] |
$14731^{4}$ |
$1$ |
$12.9279181717$ |
$121.37133104650373$ |
|
|
✓ |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$175.688399353$ |
| 15.3.57352136505929721.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 10 x^{12} + 22 x^{11} - 33 x^{10} + 40 x^{9} - 63 x^{8} + 81 x^{7} - 81 x^{6} + 63 x^{5} - 69 x^{4} + 57 x^{3} - 24 x^{2} + 3$ |
$15$ |
[3,6] |
$3^{18}\cdot 23^{6}$ |
$2$ |
$13.0989546953$ |
$58.192859749017636$ |
|
|
? |
$C_3^4:A_5$ (as 15T53) |
trivial |
$2$ |
$8$ |
$279.393832589$ |
| 15.3.59463924292145152.1 |
$x^{15} - x^{14} - 6 x^{13} + 15 x^{12} - 9 x^{11} - 13 x^{10} + 30 x^{9} - 31 x^{8} + 24 x^{7} - 14 x^{6} + 10 x^{5} - 18 x^{4} + 27 x^{3} - 21 x^{2} + 8 x - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 37^{2}$ |
$3$ |
$13.1305697532$ |
$132.357735064494$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$8$ |
$226.669584518$ |
| 15.3.69184806150882304.1 |
$x^{15} + x^{13} - 3 x^{12} - 3 x^{11} - 5 x^{10} - 2 x^{9} + 3 x^{8} + 7 x^{7} + 4 x^{6} + x^{5} + x^{4} + 3 x^{3} + x^{2} - 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 47^{4}\cdot 61^{4}$ |
$3$ |
$13.2637822009$ |
$84.99639580651171$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$273.665310463$ |
| 15.3.98765528526263521.1 |
$x^{15} - 3 x^{14} + 7 x^{13} - 12 x^{12} + 8 x^{11} - 2 x^{10} - 17 x^{9} + 36 x^{8} - 49 x^{7} + 54 x^{6} - 41 x^{5} + 30 x^{4} - 17 x^{3} + 8 x^{2} - 5 x + 3$ |
$15$ |
[3,6] |
$13^{3}\cdot 31^{6}\cdot 37^{3}$ |
$3$ |
$13.5823116986$ |
$122.11060560000512$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$8$ |
$363.728980494$ |
| 15.3.126064044311049216.1 |
$x^{15} - 4 x^{14} + 3 x^{13} + 15 x^{12} - 40 x^{11} + 23 x^{10} + 52 x^{9} - 111 x^{8} + 83 x^{7} - 67 x^{5} + 86 x^{4} - 62 x^{3} + 26 x^{2} - 7 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 3^{5}\cdot 47^{7}$ |
$3$ |
$13.8050955127$ |
$18.849343120394256$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$8$ |
$280.863045663$ |
| 15.3.137631064560062464.1 |
$x^{15} - x^{14} - 2 x^{13} + 3 x^{12} + 11 x^{11} - 5 x^{10} - 14 x^{9} - 5 x^{8} - 10 x^{7} + 22 x^{6} + 14 x^{5} + 2 x^{4} - 13 x^{3} - 5 x^{2} + 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 23^{6}\cdot 61^{3}$ |
$3$ |
$13.8861258816$ |
$65.21580088926439$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$8$ |
$381.090214491$ |
| 15.3.146928604515779584.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 9 x^{12} - x^{11} - 5 x^{10} + 4 x^{9} - x^{8} + x^{7} - x^{5} - x^{4} + 7 x^{3} - x^{2} + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 3461^{4}$ |
$2$ |
$13.9467737903$ |
$93.38722346966051$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
$2$ |
$8$ |
$470.017972215$ |
| 15.3.274502366303440896.1 |
$x^{15} - x^{14} - x^{13} - 5 x^{12} + 5 x^{11} - 5 x^{10} - x^{9} + 3 x^{8} + 7 x^{7} + x^{6} - 3 x^{5} + x^{4} - 13 x^{3} + 5 x^{2} - 3 x + 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{9}\cdot 23^{7}$ |
$3$ |
$14.540178547115914$ |
$30.08357041040144$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$8$ |
$525.2779714178208$ |
| 15.3.334095024862954369.1 |
$x^{15} - 2 x^{14} + 3 x^{13} - 5 x^{12} + x^{11} - 19 x^{10} + 16 x^{9} - 26 x^{8} + 55 x^{7} - 78 x^{6} + 88 x^{5} - 54 x^{4} + 39 x^{3} - 52 x^{2} + 21 x - 1$ |
$15$ |
[3,6] |
$7^{12}\cdot 17^{6}$ |
$2$ |
$14.731874164$ |
$20.867615567973587$ |
|
|
? |
$D_5\times C_3$ (as 15T3) |
trivial |
$2$ |
$8$ |
$678.185779099$ |
| 15.3.351730374981194881.1 |
$x^{15} - 2 x^{14} + x^{12} - 6 x^{11} + 27 x^{9} - 37 x^{8} + 44 x^{7} - 34 x^{6} + 14 x^{5} - 15 x^{4} - 8 x^{3} + 9 x - 1$ |
$15$ |
[3,6] |
$7^{12}\cdot 71^{4}$ |
$2$ |
$14.7824808479$ |
$153.19868787917656$ |
|
|
? |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$8$ |
$694.485336338$ |
| 15.3.872411699045053489.1 |
$x^{15} - x^{14} - 10 x^{12} + 17 x^{11} - 6 x^{10} - 17 x^{9} + 35 x^{8} - 10 x^{7} - 19 x^{6} + 23 x^{5} - 16 x^{4} - 5 x^{3} + 10 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$7^{8}\cdot 73^{6}$ |
$2$ |
$15.7053673385$ |
$31.265121691698095$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$8$ |
$1080.93773334$ |
| 15.3.872411699045053489.2 |
$x^{15} - 4 x^{14} + 10 x^{13} - 12 x^{12} + 5 x^{11} + 9 x^{10} - 5 x^{9} - 17 x^{8} + 21 x^{7} + 4 x^{6} - 27 x^{5} + 17 x^{4} - 10 x^{3} + 7 x^{2} - x + 1$ |
$15$ |
[3,6] |
$7^{8}\cdot 73^{6}$ |
$2$ |
$15.7053673385$ |
$31.265121691698095$ |
|
|
? |
$\GL(2,4)$ (as 15T15) |
trivial |
$2$ |
$8$ |
$1080.93773334$ |
| 15.3.124...288.1 |
$x^{15} - 5 x^{14} + 16 x^{13} - 39 x^{12} + 65 x^{11} - 91 x^{10} + 78 x^{9} - 39 x^{8} - 26 x^{7} + 78 x^{6} - 78 x^{5} + 52 x^{4} - 13 x^{3} - 9 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{13}$ |
$2$ |
$16.0783533395$ |
$18.278423529398573$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$8$ |
$1735.38854006$ |
| 15.3.131...717.1 |
$x^{15} - 5 x^{12} + 9 x^{9} - 5 x^{6} - 2 x^{3} + 1$ |
$15$ |
[3,6] |
$3^{15}\cdot 13^{3}\cdot 347^{3}$ |
$3$ |
$16.14268678$ |
$344.29277552112063$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
$2$ |
$8$ |
$1071.54789688$ |
| 15.3.131...717.2 |
$x^{15} - x^{9} - 2 x^{6} + 1$ |
$15$ |
[3,6] |
$3^{15}\cdot 13^{3}\cdot 347^{3}$ |
$3$ |
$16.14268678$ |
$344.29277552112063$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
$2$ |
$8$ |
$1193.14375265$ |
| 15.3.132...125.1 |
$x^{15} - 14 x^{10} + 35 x^{5} + 7$ |
$15$ |
[3,6] |
$5^{9}\cdot 7^{14}$ |
$2$ |
$16.1487969276$ |
$20.558227794588174$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$8$ |
$1272.85837366$ |
| 15.3.148...624.1 |
$x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} + 3 x^{11} + 11 x^{10} + x^{9} + 22 x^{8} + 13 x^{7} + 9 x^{6} + 5 x^{5} - 12 x^{4} - 14 x^{3} - 12 x^{2} - 8 x - 2$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{6}\cdot 89^{6}$ |
$3$ |
$16.2715341149$ |
$28.44982682753188$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$2917.47210187$ |
| 15.3.185...944.1 |
$x^{15} - 2 x^{14} + 13 x^{12} - 18 x^{11} + 38 x^{9} - 58 x^{8} + 38 x^{7} - 12 x^{6} - 58 x^{5} + 110 x^{4} - 77 x^{3} + 22 x^{2} - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 277^{6}$ |
$2$ |
$16.5126168606$ |
$28.97769793904893$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$2752.96294871$ |
| 15.3.188...625.1 |
$x^{15} - 3 x^{13} - 5 x^{12} - 5 x^{11} + 23 x^{10} - 9 x^{9} + 6 x^{8} + 19 x^{7} - 147 x^{6} + 180 x^{5} + 41 x^{4} - 193 x^{3} + 113 x^{2} - 27 x + 5$ |
$15$ |
[3,6] |
$5^{4}\cdot 23^{4}\cdot 47^{6}$ |
$3$ |
$16.5332627337$ |
$162.12406677777543$ |
|
|
? |
$C_3^4:D_5$ (as 15T34) |
trivial |
$2$ |
$8$ |
$1994.644882$ |
| 15.3.193...968.1 |
$x^{15} - 4 x^{14} + 7 x^{13} - 15 x^{12} + 18 x^{11} - 24 x^{10} + 36 x^{9} - 16 x^{8} + 71 x^{7} + 69 x^{5} + 67 x^{4} + 17 x^{3} + 48 x^{2} + 27 x + 5$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 211^{2}$ |
$3$ |
$16.5612966065$ |
$422.4770749541333$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$8$ |
$2104.10568096$ |
| 15.3.205...129.1 |
$x^{15} - 2 x^{14} + 3 x^{13} - 10 x^{12} + 35 x^{11} - 124 x^{10} + 208 x^{9} - 195 x^{8} + 86 x^{7} + 81 x^{6} - 88 x^{5} + 50 x^{4} + 24 x^{3} - 8 x^{2} - 3 x + 1$ |
$15$ |
[3,6] |
$149^{4}\cdot 1609^{3}$ |
$2$ |
$16.6275226102$ |
$1127.3762141541706$ |
|
|
? |
$C_3^4:S_5$ (as 15T63) |
trivial |
$2$ |
$8$ |
$1397.2218196$ |
| 15.3.222...000.1 |
$x^{15} - 5 x^{14} + 9 x^{13} - 11 x^{12} + 17 x^{11} - 17 x^{10} - 3 x^{9} + 13 x^{8} - x^{7} + 21 x^{6} - 25 x^{5} - 5 x^{4} - 13 x^{3} - 3 x^{2} - x - 1$ |
$15$ |
[3,6] |
$2^{28}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$16.7188986112$ |
$24.1776264427508$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$6480.35807094$ |
| 15.3.304...921.1 |
$x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{11} + 12 x^{10} + 37 x^{9} + 2 x^{8} + 37 x^{7} - 37 x^{6} - 39 x^{5} + 47 x^{4} - 22 x^{3} + 6 x^{2} - 1$ |
$15$ |
[3,6] |
$7^{10}\cdot 47^{6}$ |
$2$ |
$17.0701696183$ |
$25.086936025192795$ |
|
|
? |
$D_5\times C_3$ (as 15T3) |
trivial |
$2$ |
$8$ |
$1650.39003052$ |
| 15.3.349...136.1 |
$x^{15} - 3 x^{14} + x^{13} - x^{12} + 6 x^{11} - 14 x^{9} + 42 x^{8} - 17 x^{7} - 17 x^{6} + 51 x^{5} - 15 x^{4} - 2 x^{3} - 8 x^{2} - 10 x + 2$ |
$15$ |
[3,6] |
$2^{20}\cdot 17^{6}\cdot 37^{2}\cdot 101$ |
$4$ |
$17.2293099633$ |
$2342.3103816165226$ |
|
|
? |
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$8$ |
$7111.13069013$ |
| 15.3.447...896.1 |
$x^{15} + 5 x^{13} - 10 x^{12} + 9 x^{11} - 36 x^{10} + 41 x^{9} - 30 x^{8} + 58 x^{7} - 24 x^{6} - 49 x^{5} + 74 x^{4} - 72 x^{3} + 80 x^{2} - 80 x + 32$ |
$15$ |
[3,6] |
$2^{10}\cdot 13^{3}\cdot 347^{3}\cdot 47609$ |
$4$ |
$17.5140734414$ |
$56134.07361930721$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$8$ |
$1965.65204624$ |
| 15.3.476...625.1 |
$x^{15} - 3 x^{14} - 8 x^{13} + 32 x^{12} + 16 x^{11} - 134 x^{10} + 43 x^{9} + 244 x^{8} - 211 x^{7} - 98 x^{6} + 134 x^{5} + 49 x^{4} - 110 x^{3} + 55 x^{2} - 12 x + 1$ |
$15$ |
[3,6] |
$5^{4}\cdot 29^{4}\cdot 47^{6}$ |
$3$ |
$17.5874932503$ |
$189.21733892812023$ |
|
|
? |
$C_3^4:D_5$ (as 15T34) |
trivial |
$2$ |
$8$ |
$1960.65116687$ |
| 15.3.615...000.1 |
$x^{15} - 7 x^{10} + 9 x^{5} + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 5^{9}\cdot 79^{5}$ |
$3$ |
$17.8900284058$ |
$59.438938453253584$ |
|
|
? |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$8$ |
$8138.95877003$ |
| 15.3.665...153.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 6 x^{12} + 7 x^{11} - 7 x^{10} + 5 x^{9} - 3 x^{8} - x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} - 3 x^{3} + x - 1$ |
$15$ |
[3,6] |
$33479\cdot 37871\cdot 69401\cdot 75617$ |
$4$ |
$17.9833651002$ |
$2579480273.582714$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$5504.77056814$ |
| 15.3.708...136.1 |
$x^{15} - 5 x^{14} + 15 x^{13} - 32 x^{12} + 49 x^{11} - 60 x^{10} + 51 x^{9} - 22 x^{8} - 15 x^{7} + 40 x^{6} - 49 x^{5} + 38 x^{4} - 15 x^{3} + 10 x^{2} + 4 x + 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 59^{2}\cdot 89^{6}$ |
$3$ |
$18.0589959558$ |
$604.2147753071621$ |
|
|
|
$C_3^5:S_5$ (as 15T77) |
trivial |
$2$ |
$8$ |
$3192.16334039$ |
| 15.3.726...941.1 |
$x^{15} + 3 x^{13} - 5 x^{12} + 9 x^{11} - 15 x^{10} - 20 x^{9} + 45 x^{8} - 165 x^{7} + 216 x^{6} - 351 x^{5} + 336 x^{4} - 242 x^{3} + 81 x^{2} - 15 x + 1$ |
$15$ |
[3,6] |
$3^{15}\cdot 47^{7}$ |
$2$ |
$18.0897926306$ |
$35.143128879205776$ |
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$8$ |
$2590.79097197$ |
| 15.3.726...941.2 |
$x^{15} + 6 x^{13} - 4 x^{12} + 9 x^{11} + 3 x^{10} - 18 x^{9} + 45 x^{8} - 126 x^{7} + 216 x^{6} - 324 x^{5} + 243 x^{4} - 205 x^{3} + 90 x^{2} - 30 x + 11$ |
$15$ |
[3,6] |
$3^{15}\cdot 47^{7}$ |
$2$ |
$18.0897926306$ |
$35.143128879205776$ |
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$8$ |
$2652.22907153$ |
| 15.3.774...572.1 |
$x^{15} - 2 x^{14} + 5 x^{12} - 8 x^{11} + 2 x^{10} + 9 x^{9} - 10 x^{8} + 11 x^{6} - 7 x^{5} - 3 x^{4} + 7 x^{3} - 2 x^{2} - 2 x + 1$ |
$15$ |
[3,6] |
$2^{2}\cdot 62896103\cdot 30801208681$ |
$3$ |
$18.1670090503$ |
|
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$8$ |
$4178.0205499$ |
