| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 16.0.3006123291015625.1 |
$x^{16} - x^{15} - 3 x^{14} + 6 x^{13} + x^{12} - 10 x^{11} + 8 x^{10} + 5 x^{9} - 13 x^{8} + 5 x^{7} + 8 x^{6} - 10 x^{5} + x^{4} + 6 x^{3} - 3 x^{2} - x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 11^{4}\cdot 29^{2}$ |
$3$ |
$9.2763136443$ |
$59.72041882063591$ |
|
|
? |
$D_4^2:C_4$ (as 16T547) |
trivial |
trivial |
$10$ |
$7$ |
$35.8754367412$ |
$0$ |
$29$ |
| 16.0.3207314697265625.1 |
$x^{16} - 2 x^{15} - x^{14} + x^{13} + 11 x^{12} - 11 x^{11} - 10 x^{10} + 5 x^{9} + 22 x^{8} - 10 x^{7} - 15 x^{6} + 3 x^{5} + 11 x^{4} - 2 x^{3} - 4 x^{2} + x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 181^{2}\cdot 401$ |
$3$ |
$9.31394884654$ |
$900.8219853969824$ |
|
|
? |
$C_4^4.C_2\wr C_4$ (as 16T1771) |
trivial |
trivial |
$10$ |
$7$ |
$37.3668375913$ |
$0$ |
$401$ |
| 16.0.3692461181640625.1 |
$x^{16} - 2 x^{15} - 2 x^{14} + 9 x^{13} - 3 x^{12} - 15 x^{11} + 17 x^{10} + 8 x^{9} - 25 x^{8} + 8 x^{7} + 17 x^{6} - 15 x^{5} - 3 x^{4} + 9 x^{3} - 2 x^{2} - 2 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 3889^{2}$ |
$2$ |
$9.39630804632$ |
$208.51940394717084$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$40.8735633138$ |
$0$ |
$3889$ |
| 16.0.4186494384765625.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 6 x^{13} - 5 x^{12} + 15 x^{11} - 6 x^{10} - 17 x^{9} + 26 x^{8} - 7 x^{7} - 16 x^{6} + 17 x^{5} - 2 x^{4} - 9 x^{3} + 9 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 41^{2}\cdot 101^{2}$ |
$3$ |
$9.47034187384$ |
$215.16920661222215$ |
|
|
? |
$C_2^2\wr C_2^2.D_4$ (as 16T1720) |
trivial |
trivial |
$10$ |
$7$ |
$43.5759224128$ |
$0$ |
$101$ |
| 16.0.4919707275390625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 29 x^{13} + 50 x^{12} - 77 x^{11} + 112 x^{10} - 149 x^{9} + 176 x^{8} - 182 x^{7} + 159 x^{6} - 118 x^{5} + 73 x^{4} - 36 x^{3} + 15 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 67^{4}$ |
$2$ |
$9.56634862885$ |
$27.369376545007917$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
trivial |
$10$ |
$7$ |
$48.4508350282$ |
$0$ |
$67$ |
| 16.0.6472705322265625.1 |
$x^{16} - x^{15} + x^{14} + x^{13} + 3 x^{12} + 4 x^{11} + 4 x^{10} + 8 x^{9} + 8 x^{8} + 9 x^{7} + 6 x^{6} + 8 x^{5} + 8 x^{4} + 3 x^{3} + 4 x^{2} + 3 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 19^{2}\cdot 271^{2}$ |
$3$ |
$9.73179304548$ |
$239.93242815578742$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$56.3298547938$ |
$0$ |
$271$ |
| 16.0.6561000000000000.1 |
$x^{16} - 5 x^{15} + 15 x^{14} - 32 x^{13} + 56 x^{12} - 85 x^{11} + 114 x^{10} - 134 x^{9} + 131 x^{8} - 98 x^{7} + 42 x^{6} + 9 x^{5} - 28 x^{4} + 18 x^{3} - x^{2} - 3 x + 1$ |
$16$ |
(0, 8) |
$2^{12}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$9.74003746425$ |
$16.3807251762544$ |
|
|
? |
$C_4 \times D_4$ (as 16T19) |
trivial |
trivial |
$30$ |
$7$ |
$175.01473438$ |
$0$ |
$5$ |
| 16.0.7105708251953125.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 5 x^{13} + 3 x^{12} + 5 x^{11} - 14 x^{10} + 17 x^{9} - 12 x^{8} - 3 x^{7} + 31 x^{6} - 60 x^{5} + 68 x^{4} - 50 x^{3} + 24 x^{2} - 7 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 181\cdot 401^{2}$ |
$3$ |
$9.78870996517$ |
$900.8219853969824$ |
|
|
? |
$C_4^4.C_2\wr C_4$ (as 16T1771) |
trivial |
trivial |
$10$ |
$7$ |
$60.6835925321$ |
$0$ |
$401$ |
| 16.0.8336000000000000.1 |
$x^{16} - 4 x^{15} + 7 x^{14} - 8 x^{13} + 7 x^{12} - 2 x^{10} - 6 x^{9} + 5 x^{8} + 6 x^{7} - 2 x^{6} + 7 x^{4} + 8 x^{3} + 7 x^{2} + 4 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 521$ |
$3$ |
$9.88689351343$ |
$215.86953618122132$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1616) |
trivial |
trivial |
$10$ |
$7$ |
$68.3950390559$ |
$0$ |
$521$ |
| 16.0.10065687500000000.1 |
$x^{16} - 3 x^{15} + 4 x^{14} - 3 x^{13} + 10 x^{12} - 25 x^{11} + 35 x^{10} - 39 x^{9} + 52 x^{8} - 66 x^{7} + 72 x^{6} - 80 x^{5} + 82 x^{4} - 61 x^{3} + 29 x^{2} - 8 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 5^{12}\cdot 11^{5}$ |
$3$ |
$10.004092881$ |
$74.08038982008472$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1616) |
trivial |
trivial |
$10$ |
$7$ |
$74.4244590616$ |
$0$ |
$11$ |
| 16.0.11610062500000000.1 |
$x^{16} - 5 x^{15} + 15 x^{14} - 30 x^{13} + 43 x^{12} - 40 x^{11} + 15 x^{10} + 20 x^{9} - 36 x^{8} + 20 x^{7} + 15 x^{6} - 35 x^{5} + 27 x^{4} - 15 x^{3} + 10 x^{2} - 5 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 5^{12}\cdot 431^{2}$ |
$3$ |
$10.0937410715$ |
$110.19269431629391$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$80.5768870744$ |
$0$ |
$431$ |
| 16.0.14584336181640625.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} - 2 x^{12} + 2 x^{11} + 2 x^{10} - 12 x^{9} + 19 x^{8} - 15 x^{7} + 5 x^{6} + 6 x^{5} - 8 x^{4} + 5 x^{3} - 2 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 59^{2}\cdot 131^{2}$ |
$3$ |
$10.2386551729$ |
$293.9606214962803$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$95.2086244076$ |
$0$ |
$131$ |
| 16.0.15376000000000000.1 |
$x^{16} - 6 x^{15} + 19 x^{14} - 44 x^{13} + 81 x^{12} - 128 x^{11} + 181 x^{10} - 224 x^{9} + 246 x^{8} - 244 x^{7} + 215 x^{6} - 166 x^{5} + 107 x^{4} - 52 x^{3} + 20 x^{2} - 6 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 31^{2}$ |
$3$ |
$10.272536916$ |
$52.65666427053407$ |
|
|
? |
$D_4^2:C_4$ (as 16T547) |
trivial |
trivial |
$10$ |
$7$ |
$94.1131825689$ |
$0$ |
$31$ |
| 16.0.16965062500000000.1 |
$x^{16} - 7 x^{15} + 26 x^{14} - 69 x^{13} + 144 x^{12} - 248 x^{11} + 364 x^{10} - 463 x^{9} + 515 x^{8} - 502 x^{7} + 428 x^{6} - 314 x^{5} + 195 x^{4} - 98 x^{3} + 37 x^{2} - 9 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 5^{12}\cdot 521^{2}$ |
$3$ |
$10.3358742404$ |
$215.86953618122132$ |
|
|
✓ |
$C_2^2\wr C_2^2.C_4$ (as 16T1609) |
trivial |
trivial |
$10$ |
$7$ |
$104.291995137$ |
$0$ |
$521$ |
| 16.0.20893799072265625.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - x^{13} - 3 x^{12} + 5 x^{11} - 3 x^{10} - 2 x^{9} + 5 x^{8} - 2 x^{7} - 3 x^{6} + 5 x^{5} - 3 x^{4} - x^{3} + 3 x^{2} - 2 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 11^{2}\cdot 29^{4}$ |
$3$ |
$10.4713117223$ |
$59.72041882063591$ |
|
|
✓ |
$D_4^2:C_4$ (as 16T547) |
trivial |
trivial |
$10$ |
$7$ |
$115.980915255$ |
$0$ |
$29$ |
| 16.0.24068613525390625.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 9 x^{13} + 11 x^{12} - 16 x^{11} + 20 x^{10} - 15 x^{9} + 17 x^{8} - 10 x^{7} - 2 x^{5} - 4 x^{4} + 3 x^{3} + x^{2} + x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 9929^{2}$ |
$2$ |
$10.5642991848$ |
$333.1810239839254$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$127.826318151$ |
$0$ |
$9929$ |
| 16.0.28323838134765625.1 |
$x^{16} - 2 x^{15} - x^{14} + 5 x^{13} - 2 x^{12} - 5 x^{11} + 6 x^{10} + 2 x^{9} - 7 x^{8} + 2 x^{7} + 6 x^{6} - 5 x^{5} - 2 x^{4} + 5 x^{3} - x^{2} - 2 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 10771^{2}$ |
$2$ |
$10.6723364102$ |
$347.0208076301062$ |
|
|
✓ |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$145.46809548$ |
$0$ |
$10771$ |
| 16.0.29761640869140625.1 |
$x^{16} - 2 x^{15} - 2 x^{14} + 3 x^{13} + 6 x^{12} - 13 x^{10} - 5 x^{9} + 17 x^{8} + 5 x^{7} - 13 x^{6} + 6 x^{4} - 3 x^{3} - 2 x^{2} + 2 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 61^{2}\cdot 181^{2}$ |
$3$ |
$10.7054161565$ |
$351.3433259617662$ |
|
|
✓ |
$C_2^2\wr C_2^2.D_4$ (as 16T1720) |
trivial |
trivial |
$10$ |
$7$ |
$148.832307384$ |
$0$ |
$181$ |
| 16.0.31334531494140625.1 |
$x^{16} - 2 x^{15} + 5 x^{14} - 3 x^{13} + 4 x^{12} + 4 x^{11} + 4 x^{10} - x^{9} + 21 x^{8} - 13 x^{7} + 26 x^{6} - 7 x^{5} + 14 x^{4} + x^{3} + 5 x^{2} + x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 11329^{2}$ |
$2$ |
$10.73992999$ |
$355.89615140582174$ |
|
|
? |
$S_4^2:C_4$ (as 16T1497) |
trivial |
trivial |
$10$ |
$7$ |
$148.252775341$ |
$0$ |
$11329$ |
| 16.0.33215062500000000.1 |
$x^{16} - 4 x^{15} + 3 x^{14} + 15 x^{13} - 40 x^{12} + 33 x^{11} + 20 x^{10} - 79 x^{9} + 111 x^{8} - 125 x^{7} + 125 x^{6} - 96 x^{5} + 53 x^{4} - 24 x^{3} + 12 x^{2} - 5 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$10.7791233589$ |
$15.243982444638442$ |
|
|
? |
$C_4 \times D_4$ (as 16T19) |
trivial |
trivial |
$30$ |
$7$ |
$444.254874978$ |
$0$ |
$5$ |
| 16.0.38416000000000000.1 |
$x^{16} - 8 x^{15} + 32 x^{14} - 84 x^{13} + 164 x^{12} - 256 x^{11} + 344 x^{10} - 422 x^{9} + 478 x^{8} - 480 x^{7} + 400 x^{6} - 260 x^{5} + 127 x^{4} - 46 x^{3} + 14 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 7^{4}$ |
$3$ |
$10.8775730594$ |
$19.85995155932405$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
trivial |
$10$ |
$7$ |
$175.447877376$ |
$0$ |
$7$ |
| 16.0.45749199462890625.1 |
$x^{16} - x^{15} - x^{14} + x^{13} + 2 x^{12} - 5 x^{11} + 5 x^{9} + 3 x^{8} - 8 x^{7} + 9 x^{6} - 4 x^{5} - x^{4} - x^{3} + 2 x^{2} - 2 x + 1$ |
$16$ |
(0, 8) |
$3^{8}\cdot 5^{12}\cdot 13^{4}$ |
$3$ |
$10.9969935084$ |
$20.88140933013045$ |
|
|
|
$C_4 \times D_4$ (as 16T19) |
trivial |
trivial |
$30$ |
$7$ |
$543.59991789$ |
$0$ |
$13$ |
| 16.0.49617562500000000.1 |
$x^{16} - 5 x^{15} + 13 x^{14} - 27 x^{13} + 46 x^{12} - 57 x^{11} + 63 x^{10} - 57 x^{9} + 25 x^{8} - 11 x^{7} - 3 x^{6} + 28 x^{5} + 8 x^{4} + 13 x^{3} - 3 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2}$ |
$4$ |
$11.0529247703$ |
$54.32871920356417$ |
|
|
? |
$C_2^6:(C_2\times C_4)$ (as 16T797) |
trivial |
trivial |
$30$ |
$7$ |
$527.313974778$ |
$0$ |
$11$ |
| 16.0.58723833251953125.1 |
$x^{16} - 8 x^{15} + 35 x^{14} - 105 x^{13} + 238 x^{12} - 427 x^{11} + 624 x^{10} - 755 x^{9} + 764 x^{8} - 649 x^{7} + 463 x^{6} - 276 x^{5} + 137 x^{4} - 56 x^{3} + 18 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$3^{8}\cdot 5^{12}\cdot 61\cdot 601$ |
$4$ |
$11.1699415308$ |
$1108.8946396510341$ |
|
|
✓ |
$C_2\wr (C_2\times C_4)$ (as 16T1379) |
trivial |
trivial |
$30$ |
$7$ |
$597.570897447$ |
$0$ |
$601$ |
| 16.0.69678188720703125.1 |
$x^{16} - x^{15} + 2 x^{14} - 7 x^{13} + 12 x^{12} - 15 x^{11} + 28 x^{10} - 39 x^{9} + 45 x^{8} - 51 x^{7} + 48 x^{6} - 40 x^{5} + 27 x^{4} - 13 x^{3} + 7 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 41^{4}\cdot 101$ |
$3$ |
$11.2899898971$ |
$215.16920661222215$ |
|
|
? |
$C_2^2\wr C_2^2.D_4$ (as 16T1726) |
trivial |
trivial |
$10$ |
$7$ |
$231.831684055$ |
$0$ |
$101$ |
| 16.0.90855146728515625.1 |
$x^{16} - 6 x^{15} + 10 x^{14} + 11 x^{13} - 57 x^{12} + 53 x^{11} + 49 x^{10} - 138 x^{9} + 86 x^{8} + 39 x^{7} - 83 x^{6} + 32 x^{5} + 20 x^{4} - 26 x^{3} + 9 x^{2} + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 101^{2}\cdot 191^{2}$ |
$3$ |
$11.4788094313$ |
$464.41354068302337$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1609) |
trivial |
trivial |
$10$ |
$7$ |
$257.012765335$ |
$0$ |
$191$ |
| 16.0.104976000000000000.2 |
$x^{16} - 7 x^{14} + 21 x^{12} - 36 x^{10} + 39 x^{8} - 28 x^{6} + 14 x^{4} - 4 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{8}\cdot 5^{12}$ |
$3$ |
$11.5829218529$ |
$21.243172342434338$ |
|
|
✓ |
$(C_2^2\times D_4):C_4$ (as 16T315) |
trivial |
trivial |
$30$ |
$7$ |
$807.70772603$ |
$0$ |
$5$ |
| 16.0.110722562500000000.1 |
$x^{16} - 2 x^{15} + 7 x^{14} - 11 x^{13} + 24 x^{12} - 44 x^{11} + 54 x^{10} - 78 x^{9} + 108 x^{8} - 95 x^{7} + 95 x^{6} - 95 x^{5} + 52 x^{4} - 19 x^{3} + 14 x^{2} - x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 5^{12}\cdot 11^{6}$ |
$3$ |
$11.6215688115$ |
$31.366700656905365$ |
|
|
? |
$D_4^2:C_4$ (as 16T491) |
trivial |
trivial |
$10$ |
$7$ |
$286.663445166$ |
$0$ |
$11$ |
| 16.0.117135062500000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} + x^{12} + 2 x^{10} - 5 x^{9} + 7 x^{8} - 5 x^{7} - 3 x^{6} + 10 x^{5} - 9 x^{4} + 2 x^{3} + 3 x^{2} - 3 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 5^{12}\cdot 37^{4}$ |
$3$ |
$11.6625342481$ |
$32.28605847922135$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
trivial |
$10$ |
$7$ |
$333.853446138$ |
$0$ |
$37$ |
| 16.0.145220537353515625.1 |
$x^{16} - 6 x^{15} + 18 x^{14} - 45 x^{13} + 105 x^{12} - 208 x^{11} + 345 x^{10} - 496 x^{9} + 621 x^{8} - 645 x^{7} + 535 x^{6} - 359 x^{5} + 208 x^{4} - 106 x^{3} + 42 x^{2} - 10 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 29^{6}$ |
$2$ |
$11.8202524613$ |
$18.006383777357115$ |
|
|
? |
$C_4\wr C_2$ (as 16T28) |
trivial |
trivial |
$10$ |
$7$ |
$367.977318378$ |
$0$ |
$29$ |
| 16.0.145220537353515625.2 |
$x^{16} - 3 x^{15} + 5 x^{14} - 2 x^{13} - x^{12} + 6 x^{11} + 4 x^{10} - 9 x^{9} + 26 x^{8} - 12 x^{7} + 6 x^{6} + 12 x^{5} + 4 x^{4} - 6 x^{3} + 5 x^{2} + 4 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 29^{6}$ |
$2$ |
$11.8202524613$ |
$41.78553833475025$ |
|
|
? |
$C_4^2:C_4$ (as 16T121) |
trivial |
trivial |
$10$ |
$7$ |
$316.208668145$ |
$0$ |
$29$ |
| 16.0.148333301025390625.1 |
$x^{16} - 4 x^{15} + 14 x^{14} - 36 x^{13} + 76 x^{12} - 137 x^{11} + 211 x^{10} - 281 x^{9} + 331 x^{8} - 336 x^{7} + 305 x^{6} - 244 x^{5} + 172 x^{4} - 108 x^{3} + 60 x^{2} - 24 x + 11$ |
$16$ |
(0, 8) |
$5^{12}\cdot 157^{4}$ |
$2$ |
$11.8359307729$ |
$41.89646002154997$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
trivial |
$10$ |
$7$ |
$374.86019186$ |
$0$ |
$157$ |
| 16.0.156816000000000000.1 |
$x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} - 10 x^{12} + 31 x^{10} - 14 x^{9} - 24 x^{8} + 54 x^{7} + 31 x^{6} - 36 x^{5} + 8 x^{4} + 48 x^{3} + 21 x^{2} + 2 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{4}\cdot 5^{12}\cdot 11^{2}$ |
$4$ |
$11.8771406169$ |
$54.32871920356417$ |
|
|
? |
$C_2^6:(C_2\times C_4)$ (as 16T791) |
trivial |
trivial |
$10$ |
$7$ |
$373.617259214$ |
$0$ |
$11$ |
| 16.0.162488139892578125.1 |
$x^{16} - 8 x^{15} + 27 x^{14} - 49 x^{13} + 49 x^{12} - 21 x^{11} - 6 x^{10} + 8 x^{9} + 13 x^{8} - 45 x^{7} + 70 x^{6} - 70 x^{5} + 52 x^{4} - 31 x^{3} + 9 x^{2} + x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 29^{4}\cdot 941$ |
$3$ |
$11.9035459896$ |
$552.3588463942248$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1616) |
trivial |
trivial |
$10$ |
$7$ |
$405.254846722$ |
$0$ |
$941$ |
| 16.0.181808965087890625.1 |
$x^{16} - 7 x^{15} + 25 x^{14} - 66 x^{13} + 147 x^{12} - 282 x^{11} + 465 x^{10} - 667 x^{9} + 841 x^{8} - 923 x^{7} + 869 x^{6} - 689 x^{5} + 446 x^{4} - 218 x^{3} + 71 x^{2} - 13 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 29^{2}\cdot 941^{2}$ |
$3$ |
$11.9874264607$ |
$552.3588463942248$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1609) |
trivial |
trivial |
$10$ |
$7$ |
$445.224724121$ |
$0$ |
$941$ |
| 16.0.218103593994140625.1 |
$x^{16} - 3 x^{15} + 6 x^{14} - 8 x^{13} + 26 x^{12} - 69 x^{11} + 129 x^{10} - 183 x^{9} + 276 x^{8} - 467 x^{7} + 780 x^{6} - 1077 x^{5} + 1152 x^{4} - 901 x^{3} + 495 x^{2} - 172 x + 31$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{12}\cdot 41^{2}$ |
$3$ |
$12.1245722659$ |
$48.80455673313263$ |
|
|
|
$(C_2^3\times C_4):C_4$ (as 16T292) |
trivial |
trivial |
$30$ |
$7$ |
$1278.94388647$ |
$0$ |
$41$ |
| 16.0.234256000000000000.4 |
$x^{16} - 6 x^{15} + 14 x^{14} - 4 x^{13} - 49 x^{12} + 102 x^{11} - 39 x^{10} - 144 x^{9} + 236 x^{8} - 104 x^{7} - 80 x^{6} + 114 x^{5} - 38 x^{4} - 12 x^{3} + 15 x^{2} - 6 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 11^{4}$ |
$3$ |
$12.1788328563$ |
$31.366700656905365$ |
|
|
? |
$D_4^2:C_4$ (as 16T621) |
trivial |
trivial |
$10$ |
$7$ |
$463.76150454$ |
$0$ |
$11$ |
| 16.0.234256000000000000.5 |
$x^{16} - 5 x^{14} + 13 x^{12} - 20 x^{10} + 19 x^{8} - 10 x^{6} + 2 x^{4} + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 11^{4}$ |
$3$ |
$12.1788328563$ |
$37.301503595352386$ |
|
|
✓ |
$D_4^2:C_4$ (as 16T621) |
trivial |
trivial |
$10$ |
$7$ |
$437.481833568$ |
$0$ |
$11$ |
| 16.0.331776000000000000.1 |
$x^{16} - 6 x^{15} + 17 x^{14} - 24 x^{13} + 21 x^{12} - 17 x^{10} + 30 x^{9} - 28 x^{8} + 30 x^{7} - 17 x^{6} + 21 x^{4} - 24 x^{3} + 17 x^{2} - 6 x + 1$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{4}\cdot 5^{12}$ |
$3$ |
$12.4466595458$ |
$16.3807251762544$ |
|
|
? |
$C_4 \times D_4$ (as 16T19) |
trivial |
trivial |
$10$ |
$7$ |
$463.2717987$ |
$0$ |
$5$ |
| 16.0.331776000000000000.2 |
$x^{16} - 4 x^{15} + 16 x^{14} - 42 x^{13} + 97 x^{12} - 180 x^{11} + 288 x^{10} - 382 x^{9} + 432 x^{8} - 392 x^{7} + 290 x^{6} - 150 x^{5} + 50 x^{4} + 6 x^{3} - 4 x^{2} + 4 x + 1$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{4}\cdot 5^{12}$ |
$3$ |
$12.4466595458$ |
$21.243172342434338$ |
|
|
? |
$(C_2^2\times D_4):C_4$ (as 16T213) |
trivial |
trivial |
$10$ |
$7$ |
$572.284371891$ |
$0$ |
$5$ |
| 16.0.344862562500000000.1 |
$x^{16} - 5 x^{15} + 12 x^{14} - 21 x^{13} + 38 x^{12} - 64 x^{11} + 90 x^{10} - 155 x^{9} + 361 x^{8} - 696 x^{7} + 920 x^{6} - 808 x^{5} + 445 x^{4} - 120 x^{3} - 7 x^{2} + 9 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2}$ |
$4$ |
$12.4767903664$ |
$62.37594312593305$ |
|
|
? |
$(D_4\times C_2^3):C_4$ (as 16T469) |
trivial |
trivial |
$30$ |
$7$ |
$1465.49125851$ |
$0$ |
$29$ |
| 16.0.367709590087890625.1 |
$x^{16} - x^{15} + 2 x^{14} - 2 x^{13} + 7 x^{12} - 10 x^{11} + 8 x^{10} - 9 x^{9} + 10 x^{8} - 16 x^{7} + 18 x^{6} - 10 x^{5} + 7 x^{4} - 8 x^{3} + 7 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 197^{4}$ |
$2$ |
$12.5269129583$ |
$46.9310873285213$ |
|
|
? |
$C_2^5.D_6$ (as 16T725) |
trivial |
trivial |
$10$ |
$7$ |
$622.933299888$ |
$0$ |
$197$ |
| 16.0.394070062500000000.1 |
$x^{16} - 6 x^{15} + 23 x^{14} - 64 x^{13} + 127 x^{12} - 184 x^{11} + 198 x^{10} - 146 x^{9} + 69 x^{8} - 46 x^{6} + 22 x^{5} - 2 x^{4} + 10 x^{3} + 20 x^{2} + 8 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}$ |
$4$ |
$12.5812369041$ |
$108.46046697219393$ |
|
|
? |
$C_2^7:(C_2\times C_4)$ (as 16T1102) |
trivial |
trivial |
$30$ |
$7$ |
$1736.16637185$ |
$0$ |
$31$ |
| 16.0.394070062500000000.2 |
$x^{16} - 4 x^{15} + 7 x^{14} + 2 x^{13} - 20 x^{12} + 6 x^{11} + 123 x^{10} - 357 x^{9} + 570 x^{8} - 573 x^{7} + 389 x^{6} - 153 x^{5} + 29 x^{4} + 11 x^{3} - 4 x^{2} + 3 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}$ |
$4$ |
$12.5812369041$ |
$108.46046697219393$ |
|
|
? |
$C_2^7:(C_2\times C_4)$ (as 16T1102) |
trivial |
trivial |
$30$ |
$7$ |
$1681.80534328$ |
$0$ |
$31$ |
| 16.0.394070062500000000.3 |
$x^{16} - 4 x^{15} + 3 x^{14} + 15 x^{13} - 25 x^{12} - 17 x^{11} + 60 x^{10} + 26 x^{9} - 44 x^{8} - 45 x^{7} + 20 x^{6} + 154 x^{5} + 223 x^{4} + 171 x^{3} + 77 x^{2} + 15 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}$ |
$4$ |
$12.5812369041$ |
$64.49097950992532$ |
|
|
? |
$(D_4\times C_2^3):C_4$ (as 16T469) |
trivial |
trivial |
$30$ |
$7$ |
$1708.93994166$ |
$0$ |
$31$ |
| 16.0.394070062500000000.4 |
$x^{16} - 5 x^{15} + 15 x^{14} - 32 x^{13} + 46 x^{12} - 45 x^{11} + 64 x^{10} - 214 x^{9} + 611 x^{8} - 1228 x^{7} + 1822 x^{6} - 2061 x^{5} + 1792 x^{4} - 1182 x^{3} + 569 x^{2} - 183 x + 31$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2}$ |
$4$ |
$12.5812369041$ |
$91.20401787366178$ |
|
|
? |
$C_2^6:(C_2\times C_4)$ (as 16T797) |
trivial |
trivial |
$30$ |
$7$ |
$1624.71489814$ |
$0$ |
$31$ |
| 16.0.414595136962890625.1 |
$x^{16} - 2 x^{15} + 6 x^{14} - 9 x^{13} + 19 x^{12} - 28 x^{11} + 49 x^{10} - 68 x^{9} + 105 x^{8} - 127 x^{7} + 148 x^{6} - 139 x^{5} + 120 x^{4} - 73 x^{3} + 37 x^{2} - 9 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 7^{4}\cdot 29^{4}$ |
$3$ |
$12.6212251078$ |
$47.64041348647476$ |
|
|
|
$C_2^4.D_4$ (as 16T247) |
trivial |
trivial |
$10$ |
$7$ |
$583.750925038$ |
$0$ |
$29$ |
| 16.0.456976000000000000.1 |
$x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 110 x^{12} - 180 x^{11} + 240 x^{10} - 262 x^{9} + 237 x^{8} - 182 x^{7} + 148 x^{6} - 160 x^{5} + 192 x^{4} - 192 x^{3} + 136 x^{2} - 64 x + 16$ |
$16$ |
(0, 8) |
$2^{16}\cdot 5^{12}\cdot 13^{4}$ |
$3$ |
$12.6982343247$ |
$34.09919864600766$ |
|
|
? |
$C_2^4.D_4$ (as 16T247) |
trivial |
trivial |
$10$ |
$7$ |
$702.047210526$ |
$0$ |
$13$ |
| 16.0.495616000000000000.1 |
$x^{16} - 6 x^{15} + 24 x^{14} - 70 x^{13} + 156 x^{12} - 278 x^{11} + 390 x^{10} - 442 x^{9} + 442 x^{8} - 456 x^{7} + 530 x^{6} - 556 x^{5} + 421 x^{4} - 210 x^{3} + 66 x^{2} - 12 x + 1$ |
$16$ |
(0, 8) |
$2^{24}\cdot 5^{12}\cdot 11^{2}$ |
$3$ |
$12.762818183$ |
$37.301503595352386$ |
|
|
? |
$D_4^2:C_4$ (as 16T491) |
trivial |
trivial |
$10$ |
$7$ |
$707.754116424$ |
$0$ |
$11$ |
| 16.0.611840141845703125.1 |
$x^{16} - 2 x^{15} + 4 x^{14} + 3 x^{12} + 10 x^{11} + 11 x^{10} + 17 x^{9} + 28 x^{8} + 27 x^{7} + 31 x^{6} + 30 x^{5} + 23 x^{4} + 15 x^{3} + 9 x^{2} + 3 x + 1$ |
$16$ |
(0, 8) |
$5^{12}\cdot 61^{4}\cdot 181$ |
$3$ |
$12.9319754934$ |
$351.3433259617662$ |
|
|
? |
$C_2^2\wr C_2^2.D_4$ (as 16T1726) |
trivial |
trivial |
$10$ |
$7$ |
$821.509721837$ |
$0$ |
$181$ |
