| 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 |
| 16.8.252...625.1 |
$x^{16} - 5 x^{15} + 6 x^{14} + 17 x^{13} - 68 x^{12} + 84 x^{11} + 22 x^{10} - 225 x^{9} + 352 x^{8} - 237 x^{7} - 82 x^{6} + 347 x^{5} - 379 x^{4} + 251 x^{3} - 92 x^{2} + 8 x + 1$ |
$16$ |
[8,4] |
$5^{12}\cdot 11^{4}\cdot 29^{4}$ |
$3$ |
$14.1310741091$ |
$59.72041882063591$ |
|
|
? |
$C_2\wr D_4$ (as 16T388) |
trivial |
$2$ |
$11$ |
$1156.04018319$ |
| 16.8.262...000.1 |
$x^{16} - 8 x^{15} + 29 x^{14} - 58 x^{13} + 48 x^{12} + 62 x^{11} - 234 x^{10} + 306 x^{9} - 172 x^{8} - 68 x^{7} + 239 x^{6} - 314 x^{5} + 313 x^{4} - 206 x^{3} + 76 x^{2} - 14 x + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{8}\cdot 5^{14}$ |
$3$ |
$14.1641128029$ |
$14.164112802887677$ |
|
|
? |
$(C_8:C_2):C_2$ (as 16T16) |
trivial |
$2$ |
$11$ |
$1176.18765647$ |
| 16.8.307...625.1 |
$x^{16} - 5 x^{14} + 4 x^{12} + 15 x^{10} - 49 x^{8} + 60 x^{6} - 26 x^{4} + 1$ |
$16$ |
[8,4] |
$5^{12}\cdot 11^{2}\cdot 101^{4}$ |
$3$ |
$14.3048046828$ |
$111.45114452086767$ |
|
|
? |
$C_2^7.D_4$ (as 16T1174) |
trivial |
$2$ |
$11$ |
$1288.86099323$ |
| 16.8.326...296.1 |
$x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 20 x^{12} - 22 x^{11} + 7 x^{10} + 18 x^{9} - 53 x^{8} + 86 x^{7} - 119 x^{6} + 58 x^{5} + 68 x^{4} - 42 x^{3} - 16 x^{2} + 4 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 41^{7}$ |
$2$ |
$14.3594541351$ |
$72.90056061712143$ |
|
|
? |
$C_8\wr C_2$ (as 16T289) |
trivial |
$2$ |
$11$ |
$1313.4530654$ |
| 16.8.340...625.1 |
$x^{16} - x^{15} - 9 x^{14} - 4 x^{13} + 17 x^{12} + 28 x^{11} + 14 x^{10} - 23 x^{9} - 45 x^{8} - 23 x^{7} + 14 x^{6} + 28 x^{5} + 17 x^{4} - 4 x^{3} - 9 x^{2} - x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{4}\cdot 29^{6}$ |
$3$ |
$14.3956879045$ |
$92.67868075981409$ |
|
|
? |
$C_4^2:D_4$ (as 16T211) |
trivial |
$2$ |
$11$ |
$1363.52251312$ |
| 16.8.457...225.1 |
$x^{16} - 20 x^{12} + 46 x^{10} - 10 x^{8} - 76 x^{6} + 93 x^{4} - 34 x^{2} + 1$ |
$16$ |
[8,4] |
$3^{10}\cdot 5^{2}\cdot 1327^{4}$ |
$3$ |
$14.6652599486$ |
$185.6784083426463$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$1681.65919709$ |
| 16.8.463...000.1 |
$x^{16} - 2 x^{15} - 2 x^{14} - 4 x^{13} + 35 x^{12} - 44 x^{11} - 22 x^{10} + 174 x^{9} - 331 x^{8} + 302 x^{7} - 62 x^{6} - 188 x^{5} + 259 x^{4} - 150 x^{3} + 34 x^{2} + 2 x - 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{8}\cdot 29^{4}$ |
$3$ |
$14.6767364317$ |
$44.16876366153594$ |
|
|
? |
$C_2\wr D_4$ (as 16T388) |
trivial |
$2$ |
$11$ |
$1661.41008992$ |
| 16.8.463...000.2 |
$x^{16} - 2 x^{15} - 8 x^{14} + 26 x^{13} - 19 x^{12} - 4 x^{11} + 4 x^{10} - 16 x^{9} + 53 x^{8} - 56 x^{7} + 6 x^{6} + 54 x^{5} - 53 x^{4} + 6 x^{3} + 16 x^{2} - 8 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{8}\cdot 29^{4}$ |
$3$ |
$14.6767364317$ |
$44.16876366153594$ |
|
|
? |
$C_2^6:D_4$ (as 16T969) |
trivial |
$2$ |
$11$ |
$1635.12490583$ |
| 16.8.463...000.3 |
$x^{16} - 6 x^{15} + 14 x^{14} - 14 x^{13} - 17 x^{12} + 94 x^{11} - 184 x^{10} + 222 x^{9} - 167 x^{8} + 34 x^{7} + 74 x^{6} - 112 x^{5} + 135 x^{4} - 116 x^{3} + 54 x^{2} - 12 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{8}\cdot 29^{4}$ |
$3$ |
$14.6767364317$ |
$44.16876366153594$ |
|
|
? |
$C_2^6:D_4$ (as 16T969) |
trivial |
$2$ |
$11$ |
$1637.4644759$ |
| 16.8.471...689.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 18 x^{13} - 45 x^{12} + 10 x^{11} + 102 x^{10} - 112 x^{9} - 64 x^{8} + 156 x^{7} - 16 x^{6} - 89 x^{5} + 31 x^{4} + 24 x^{3} - 11 x^{2} - 3 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$ |
$4$ |
$14.692496258$ |
$202.7239502377556$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$1706.05390163$ |
| 16.8.488...625.1 |
$x^{16} - 2 x^{15} - 3 x^{14} + 3 x^{13} + x^{12} + 5 x^{11} - 31 x^{10} + 6 x^{9} + 89 x^{8} + 6 x^{7} - 31 x^{6} + 5 x^{5} + x^{4} + 3 x^{3} - 3 x^{2} - 2 x + 1$ |
$16$ |
[8,4] |
$5^{10}\cdot 29^{8}$ |
$2$ |
$14.7249982437$ |
$18.006383777357115$ |
|
|
? |
$C_4\wr C_2$ (as 16T42) |
trivial |
$2$ |
$11$ |
$1652.33200457$ |
| 16.8.569...125.1 |
$x^{16} - 4 x^{15} + 4 x^{14} - x^{13} - 3 x^{12} + 30 x^{11} - 40 x^{10} - 25 x^{9} + 63 x^{8} - 32 x^{7} + 4 x^{6} + 34 x^{5} - 46 x^{4} + 6 x^{3} + 17 x^{2} - 8 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 5^{12}\cdot 59^{2}\cdot 1021$ |
$4$ |
$14.866500197$ |
$1421.4350085210183$ |
|
|
? |
$C_4^4.C_2\wr C_4$ (as 16T1771) |
trivial |
$2$ |
$11$ |
$1829.05182822$ |
| 16.8.581...088.1 |
$x^{16} - 2 x^{15} - 3 x^{14} + 2 x^{13} + x^{12} + 14 x^{11} - 6 x^{10} + 4 x^{9} - 23 x^{8} + 4 x^{7} - 6 x^{6} + 14 x^{5} + x^{4} + 2 x^{3} - 3 x^{2} - 2 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 41^{6}\cdot 73$ |
$3$ |
$14.8866376851$ |
|
|
|
? |
$C_2\wr D_4.C_4$ (as 16T1722) |
trivial |
$2$ |
$11$ |
$1808.95372769$ |
| 16.8.611...625.1 |
$x^{16} - 7 x^{14} - x^{13} + 9 x^{12} + 15 x^{11} - x^{10} - 8 x^{9} - 17 x^{8} - 8 x^{7} - x^{6} + 15 x^{5} + 9 x^{4} - x^{3} - 7 x^{2} + 1$ |
$16$ |
[8,4] |
$5^{10}\cdot 29^{4}\cdot 941^{2}$ |
$3$ |
$14.9332541042$ |
$552.3588463942248$ |
|
|
? |
$C_2^2\wr C_2^2.C_4$ (as 16T1559) |
trivial |
$2$ |
$11$ |
$1930.1753716$ |
| 16.8.641...125.1 |
$x^{16} - x^{15} - 8 x^{14} + 13 x^{13} + 12 x^{12} - 39 x^{11} + 14 x^{10} + 24 x^{9} + 14 x^{8} - 67 x^{7} + 46 x^{6} + 13 x^{5} - 48 x^{4} + 36 x^{3} - 7 x^{2} - 3 x + 1$ |
$16$ |
[8,4] |
$5^{10}\cdot 29^{5}\cdot 179^{2}$ |
$3$ |
$14.9782907265$ |
$559.0524012045329$ |
|
|
? |
$C_2\wr D_4.C_4$ (as 16T1702) |
trivial |
$2$ |
$11$ |
$1959.9073218$ |
| 16.8.663...625.1 |
$x^{16} - 5 x^{15} + 6 x^{14} + 13 x^{13} - 43 x^{12} + 36 x^{11} - 19 x^{10} + 123 x^{9} - 266 x^{8} + 72 x^{7} + 421 x^{6} - 556 x^{5} + 197 x^{4} + 52 x^{3} - 34 x^{2} + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 13^{4}\cdot 29^{6}$ |
$3$ |
$15.0096335531$ |
$100.75234816841015$ |
|
|
? |
$C_2^5.D_4$ (as 16T500) |
trivial |
$2$ |
$11$ |
$1999.78008385$ |
| 16.8.677...461.1 |
$x^{16} - x^{15} - 8 x^{14} + 3 x^{13} + 12 x^{12} - 8 x^{11} + 6 x^{10} + 13 x^{9} - 7 x^{8} + 13 x^{7} + 6 x^{6} - 8 x^{5} + 12 x^{4} + 3 x^{3} - 8 x^{2} - x + 1$ |
$16$ |
[8,4] |
$29\cdot 483345053^{2}$ |
$2$ |
$15.0290674867$ |
$118393.43958598381$ |
|
|
? |
$C_2^8.S_8$ (as 16T1948) |
trivial |
$2$ |
$11$ |
$1992.28334493$ |
| 16.8.677...461.2 |
$x^{16} - x^{15} - 8 x^{14} + 11 x^{13} + 12 x^{12} - 19 x^{11} - 5 x^{10} + 2 x^{9} + 15 x^{8} + 2 x^{7} - 5 x^{6} - 19 x^{5} + 12 x^{4} + 11 x^{3} - 8 x^{2} - x + 1$ |
$16$ |
[8,4] |
$29\cdot 483345053^{2}$ |
$2$ |
$15.0290674867$ |
$118393.43958598381$ |
|
|
? |
$C_2^8.S_8$ (as 16T1948) |
trivial |
$2$ |
$11$ |
$2139.18562841$ |
| 16.8.687...000.1 |
$x^{16} - 4 x^{14} - 4 x^{12} - 36 x^{10} + 118 x^{8} - 188 x^{6} + 124 x^{4} - 28 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{44}\cdot 5^{8}$ |
$2$ |
$15.0424123723$ |
$20.371270394561137$ |
|
|
? |
$C_2\wr C_2^2$ (as 16T149) |
trivial |
$2$ |
$11$ |
$2407.72188364$ |
| 16.8.709...984.1 |
$x^{16} - 8 x^{15} + 34 x^{14} - 98 x^{13} + 203 x^{12} - 308 x^{11} + 331 x^{10} - 214 x^{9} + 9 x^{8} + 148 x^{7} - 159 x^{6} + 64 x^{5} + 16 x^{4} - 30 x^{3} + 9 x^{2} + 2 x - 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 41^{6}\cdot 89$ |
$3$ |
$15.0721710852$ |
|
|
|
✓ |
$C_2\wr D_4.C_4$ (as 16T1722) |
trivial |
$2$ |
$11$ |
$2032.05179408$ |
| 16.8.744...625.1 |
$x^{16} - 5 x^{15} + 4 x^{14} + 21 x^{13} - 48 x^{12} - 3 x^{11} + 118 x^{10} - 110 x^{9} - 81 x^{8} + 191 x^{7} - 51 x^{6} - 105 x^{5} + 79 x^{4} + 9 x^{3} - 23 x^{2} + x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 29^{6}\cdot 179^{2}$ |
$3$ |
$15.11787953$ |
$161.1055554597668$ |
|
|
? |
$C_2\wr D_4$ (as 16T1445) |
trivial |
$2$ |
$11$ |
$2154.78681157$ |
| 16.8.744...625.2 |
$x^{16} - 3 x^{15} + 5 x^{13} - 6 x^{12} - 12 x^{11} + 20 x^{10} + 27 x^{9} - 36 x^{8} + 24 x^{7} + 72 x^{6} - 58 x^{5} - 87 x^{4} - 13 x^{3} + 11 x^{2} + 5 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 29^{6}\cdot 179^{2}$ |
$3$ |
$15.11787953$ |
$373.8608732793204$ |
|
|
? |
$C_2^6.D_4$ (as 16T876) |
trivial |
$2$ |
$11$ |
$2096.64115716$ |
| 16.8.747...489.1 |
$x^{16} - 8 x^{15} + 20 x^{14} - 71 x^{12} + 62 x^{11} + 102 x^{10} - 125 x^{9} - 102 x^{8} + 124 x^{7} + 82 x^{6} - 67 x^{5} - 44 x^{4} + 14 x^{3} + 13 x^{2} - x - 1$ |
$16$ |
[8,4] |
$59\cdot 419\cdot 17383253^{2}$ |
$3$ |
$15.1210868748$ |
$655539.0128840541$ |
|
|
✓ |
$C_2^8.S_8$ (as 16T1948) |
trivial |
$2$ |
$11$ |
$2135.82187731$ |
| 16.8.776...625.1 |
$x^{16} - 5 x^{15} + 6 x^{14} + 4 x^{13} - 10 x^{12} + 7 x^{11} - 30 x^{10} + 46 x^{9} + 32 x^{8} - 112 x^{7} + 29 x^{6} + 85 x^{5} - 37 x^{4} - 29 x^{3} + 10 x^{2} + 3 x - 1$ |
$16$ |
[8,4] |
$3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}$ |
$5$ |
$15.1575575967$ |
$506.17684656649396$ |
|
|
? |
$C_2^6.D_4^2$ (as 16T1553) |
trivial |
$2$ |
$11$ |
$2143.71845256$ |
| 16.8.776...625.2 |
$x^{16} - x^{15} - 3 x^{14} + 3 x^{13} + 7 x^{12} + 12 x^{11} - 17 x^{10} - 40 x^{9} - 12 x^{8} + 21 x^{7} + 58 x^{6} + 26 x^{5} - 45 x^{4} - 25 x^{3} + 12 x^{2} + 5 x - 1$ |
$16$ |
[8,4] |
$3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}$ |
$5$ |
$15.1575575967$ |
$506.17684656649396$ |
|
|
? |
$C_2^6.D_4^2$ (as 16T1553) |
trivial |
$2$ |
$11$ |
$2165.24499918$ |
| 16.8.777...000.1 |
$x^{16} - 4 x^{15} + 4 x^{14} + 12 x^{13} - 53 x^{12} + 72 x^{11} - 174 x^{9} + 253 x^{8} - 62 x^{7} - 226 x^{6} + 274 x^{5} - 57 x^{4} - 90 x^{3} + 62 x^{2} - 14 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 11^{4}$ |
$4$ |
$15.1585786227$ |
$43.20604011399894$ |
|
|
? |
$C_2^5:D_4$ (as 16T573) |
trivial |
$2$ |
$11$ |
$2214.31517556$ |
| 16.8.797...625.1 |
$x^{16} - 2 x^{15} - 9 x^{14} + 23 x^{13} + 18 x^{12} - 82 x^{11} + 7 x^{10} + 140 x^{9} - 64 x^{8} - 130 x^{7} + 78 x^{6} + 76 x^{5} - 37 x^{4} - 31 x^{3} + 4 x^{2} + 6 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 29^{4}\cdot 41^{2}\cdot 131^{2}$ |
$4$ |
$15.1824337841$ |
$882.4936260393046$ |
|
|
? |
$C_2^2\wr D_4$ (as 16T1340) |
trivial |
$2$ |
$11$ |
$2146.72182502$ |
| 16.8.829...704.1 |
$x^{16} - x^{14} - 11 x^{12} + 12 x^{10} + 25 x^{8} - 40 x^{6} + 18 x^{4} - 4 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{8}\cdot 19^{4}\cdot 47^{2}\cdot 103^{4}$ |
$4$ |
$15.2203604125$ |
$1020.1095990275355$ |
|
|
? |
$C_2\wr C_2^3.S_4$ (as 16T1852) |
trivial |
$2$ |
$11$ |
$2259.70969555$ |
| 16.8.831...125.1 |
$x^{16} - x^{15} - 7 x^{14} + 14 x^{13} + 15 x^{12} - 48 x^{11} + 3 x^{10} + 73 x^{9} - 28 x^{8} - 110 x^{7} + 88 x^{6} + 99 x^{5} - 187 x^{4} + 105 x^{3} - 12 x^{2} - 7 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{6}\cdot 229^{3}$ |
$3$ |
$15.2221645406$ |
$795.071393273073$ |
|
|
? |
$C_4\wr D_4$ (as 16T1432) |
trivial |
$2$ |
$11$ |
$2271.42947924$ |
| 16.8.831...125.2 |
$x^{16} - 5 x^{15} + 5 x^{14} + 13 x^{13} - 28 x^{12} + 2 x^{11} + 36 x^{10} - 27 x^{9} - 29 x^{8} + 27 x^{7} + 36 x^{6} - 2 x^{5} - 28 x^{4} - 13 x^{3} + 5 x^{2} + 5 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{6}\cdot 229^{3}$ |
$3$ |
$15.2221645406$ |
$112.22744762311936$ |
|
|
? |
$C_2^2.C_2\wr D_4$ (as 16T1741) |
trivial |
$2$ |
$11$ |
$2277.6910102$ |
| 16.8.850...000.1 |
$x^{16} - 8 x^{15} + 22 x^{14} - 14 x^{13} - 46 x^{12} + 94 x^{11} - 56 x^{10} + 38 x^{9} - 92 x^{8} + 30 x^{7} + 100 x^{6} - 60 x^{5} - 23 x^{4} + 4 x^{3} + 4 x^{2} + 6 x + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{12}\cdot 5^{12}$ |
$3$ |
$15.2439824446$ |
$15.243982444638442$ |
|
|
? |
$C_4 \times D_4$ (as 16T19) |
trivial |
$2$ |
$11$ |
$2324.12805322$ |
| 16.8.856...129.1 |
$x^{16} - x^{15} + 5 x^{13} - 12 x^{12} - 4 x^{11} + 9 x^{10} - 24 x^{9} + 6 x^{8} + 40 x^{7} + 30 x^{6} + 20 x^{5} - 18 x^{4} - 26 x^{3} - x^{2} + 5 x + 1$ |
$16$ |
[8,4] |
$3^{8}\cdot 19^{4}\cdot 89\cdot 103^{4}$ |
$4$ |
$15.2508907211$ |
$722.8547571953857$ |
|
|
? |
$C_4^4.C_2\wr S_4$ (as 16T1879) |
trivial |
$2$ |
$11$ |
$2394.20098432$ |
| 16.8.879...625.1 |
$x^{16} - 5 x^{15} + 2 x^{14} + 32 x^{13} - 58 x^{12} - 51 x^{11} + 221 x^{10} - 70 x^{9} - 337 x^{8} + 302 x^{7} + 183 x^{6} - 327 x^{5} + 40 x^{4} + 117 x^{3} - 53 x^{2} + 3 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{4}\cdot 19^{4}\cdot 11801$ |
$4$ |
$15.2762409332$ |
$3511.7011547112033$ |
|
|
? |
$C_2^2.C_2^2\wr D_4$ (as 16T1719) |
trivial |
$2$ |
$11$ |
$2336.43467249$ |
| 16.8.900...328.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 12 x^{13} - 21 x^{12} + 52 x^{10} - 116 x^{9} + 160 x^{8} - 140 x^{7} + 38 x^{6} + 100 x^{5} - 170 x^{4} + 108 x^{3} - 18 x^{2} - 4 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 41^{6}\cdot 113$ |
$3$ |
$15.2987639037$ |
$487.1605451349802$ |
|
|
? |
$C_2\wr D_4.C_4$ (as 16T1722) |
trivial |
$2$ |
$11$ |
$2393.3966558$ |
| 16.8.934...456.1 |
$x^{16} - 4 x^{15} - 2 x^{14} + 20 x^{13} - 5 x^{12} - 36 x^{11} + 28 x^{10} + 20 x^{9} - 62 x^{8} + 12 x^{7} + 78 x^{6} - 8 x^{5} - 54 x^{4} - 12 x^{3} + 16 x^{2} + 8 x + 1$ |
$16$ |
[8,4] |
$2^{44}\cdot 3^{12}$ |
$2$ |
$15.3346345019$ |
$24.23672593327708$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$11$ |
$2452.93509651$ |
| 16.8.968...125.1 |
$x^{16} - 2 x^{15} - 3 x^{14} + 4 x^{13} + 15 x^{12} + 7 x^{11} - 59 x^{10} - 48 x^{9} + 99 x^{8} + 100 x^{7} - 63 x^{6} - 89 x^{5} + 3 x^{4} + 31 x^{3} + 7 x^{2} - 3 x - 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101$ |
$5$ |
$15.3680582987$ |
$2936.989104508221$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$11$ |
$2441.74607361$ |
| 16.8.968...125.2 |
$x^{16} - 4 x^{15} + 4 x^{14} + 6 x^{13} - 33 x^{12} + 38 x^{11} + 10 x^{10} - 84 x^{9} + 103 x^{8} + 14 x^{7} - 80 x^{6} + 22 x^{5} + 3 x^{4} - 7 x^{3} + 9 x^{2} - 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 101$ |
$5$ |
$15.3680582987$ |
$2936.989104508221$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$11$ |
$2412.1613156$ |
| 16.8.983...000.1 |
$x^{16} - 4 x^{15} + 14 x^{13} - 2 x^{12} - 18 x^{11} - 26 x^{10} + 18 x^{9} + 81 x^{8} - 14 x^{7} - 98 x^{6} - 2 x^{5} + 60 x^{4} + 6 x^{3} - 16 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 5^{12}\cdot 7^{4}$ |
$3$ |
$15.3832113463$ |
$26.50985484327206$ |
|
|
? |
$C_4\times S_4$ (as 16T181) |
trivial |
$2$ |
$11$ |
$2954.91741119$ |
| 16.8.985...625.1 |
$x^{16} - x^{15} - 5 x^{14} + 3 x^{13} + 6 x^{12} + 4 x^{11} - 3 x^{10} - 6 x^{9} + x^{8} - 6 x^{7} - 3 x^{6} + 4 x^{5} + 6 x^{4} + 3 x^{3} - 5 x^{2} - x + 1$ |
$16$ |
[8,4] |
$3^{12}\cdot 5^{8}\cdot 83^{4}$ |
$3$ |
$15.3849279352$ |
$73.39483731910693$ |
|
|
? |
$(C_2^2\times C_4):S_4$ (as 16T763) |
trivial |
$2$ |
$11$ |
$2543.46413175$ |
| 16.8.104...125.1 |
$x^{16} - 2 x^{15} - 4 x^{14} + 10 x^{13} - x^{12} + 2 x^{10} - 51 x^{9} + 37 x^{8} + 75 x^{7} - 59 x^{6} - 38 x^{5} + 25 x^{4} + x^{3} - x^{2} + 5 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}\cdot 109$ |
$5$ |
$15.441449648$ |
$3051.0891497955286$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$11$ |
$2540.02214256$ |
| 16.8.106...536.1 |
$x^{16} - 10 x^{14} + 31 x^{12} - 32 x^{10} + 21 x^{8} - 32 x^{6} + 31 x^{4} - 10 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{32}\cdot 223^{4}$ |
$2$ |
$15.4573915124$ |
$71.0345971379243$ |
|
|
? |
$C_2^4:S_4$ (as 16T747) |
trivial |
$2$ |
$11$ |
$2876.67071425$ |
| 16.8.108...896.1 |
$x^{16} - 12 x^{14} + 58 x^{12} - 152 x^{10} + 215 x^{8} - 128 x^{6} + 14 x^{4} + 4 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{52}\cdot 7^{4}$ |
$2$ |
$15.4746913621$ |
$27.44891961566663$ |
|
|
? |
$C_2^4:C_4$ (as 16T79) |
trivial |
$2$ |
$11$ |
$3118.63701026$ |
| 16.8.109...672.1 |
$x^{16} - 2 x^{15} - 3 x^{14} + 8 x^{13} - 6 x^{12} + 2 x^{11} + 4 x^{10} - 2 x^{9} + 32 x^{8} - 62 x^{7} + 23 x^{6} - 8 x^{5} + 8 x^{4} + 6 x^{3} - 3 x^{2} + 2 x + 1$ |
$16$ |
[8,4] |
$2^{24}\cdot 41^{6}\cdot 137$ |
$3$ |
$15.4840289706$ |
|
|
|
? |
$C_2\wr D_4.C_4$ (as 16T1722) |
trivial |
$2$ |
$11$ |
$2547.76407174$ |
| 16.8.110...000.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 8 x^{13} - 19 x^{12} + 8 x^{11} - 4 x^{10} + 76 x^{9} + 48 x^{8} - 120 x^{7} + 8 x^{6} + 68 x^{5} - 8 x^{4} - 12 x^{3} - 4 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{32}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$15.4919333848$ |
$15.491933384829668$ |
|
|
? |
$C_2 \times (C_4\times C_2):C_2$ (as 16T18) |
trivial |
$2$ |
$11$ |
$2650.06185113$ |
| 16.8.111...000.1 |
$x^{16} - 6 x^{14} + x^{12} + 25 x^{10} - 70 x^{8} + 75 x^{6} - 29 x^{4} + x^{2} + 1$ |
$16$ |
[8,4] |
$2^{12}\cdot 5^{8}\cdot 17^{8}$ |
$3$ |
$15.5053637688$ |
$26.076809620810597$ |
|
|
? |
$C_2\wr C_2^2$ (as 16T149) |
trivial |
$2$ |
$11$ |
$3279.68638925$ |
| 16.8.112...625.1 |
$x^{16} - 4 x^{15} + x^{14} + 4 x^{13} + 8 x^{12} - 4 x^{11} - x^{10} - 23 x^{9} + 13 x^{8} + 61 x^{7} - 139 x^{6} + 62 x^{5} + 53 x^{4} - 23 x^{3} - 11 x^{2} + 2 x + 1$ |
$16$ |
[8,4] |
$3^{12}\cdot 5^{14}\cdot 59^{2}$ |
$3$ |
$15.5165868385$ |
$71.59219873631896$ |
|
|
? |
$C_2^4:\OD_{16}$ (as 16T554) |
trivial |
$2$ |
$11$ |
$2676.39256757$ |
| 16.8.113...625.1 |
$x^{16} - 4 x^{15} + 3 x^{14} + x^{13} - 14 x^{12} + 32 x^{11} + 15 x^{10} + x^{9} + 51 x^{8} + x^{7} + 15 x^{6} + 32 x^{5} - 14 x^{4} + x^{3} + 3 x^{2} - 4 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131^{2}$ |
$4$ |
$15.5245107926$ |
$364.64366167534024$ |
|
|
? |
$C_2^7:D_4$ (as 16T1116) |
trivial |
$2$ |
$11$ |
$2576.53705678$ |
| 16.8.115...625.1 |
$x^{16} - 3 x^{15} - 2 x^{14} + 5 x^{13} + 8 x^{12} + 7 x^{10} - 33 x^{9} - 43 x^{8} + 49 x^{7} + 73 x^{6} - 9 x^{5} - 109 x^{4} + 55 x^{3} + 10 x^{2} - 9 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}$ |
$5$ |
$15.5425759814$ |
$969.2548684427642$ |
|
|
? |
$C_2^2\wr D_4$ (as 16T1340) |
trivial |
$2$ |
$11$ |
$2749.61894204$ |
| 16.8.115...625.2 |
$x^{16} - 2 x^{15} - 6 x^{14} + 13 x^{13} + 7 x^{12} - 9 x^{11} + 7 x^{10} - 72 x^{9} + 2 x^{8} + 83 x^{7} - 15 x^{6} + 72 x^{5} - 58 x^{4} - 54 x^{3} + 41 x^{2} - 10 x + 1$ |
$16$ |
[8,4] |
$5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2}$ |
$5$ |
$15.5425759814$ |
$969.2548684427642$ |
|
|
? |
$C_2^2\wr D_4$ (as 16T1340) |
trivial |
$2$ |
$11$ |
$2729.38505244$ |
| 16.8.119...609.1 |
$x^{16} - 4 x^{15} - x^{14} + 13 x^{13} + 2 x^{12} - 8 x^{11} - 13 x^{10} + x^{9} + 27 x^{8} + x^{7} - 13 x^{6} - 8 x^{5} + 2 x^{4} + 13 x^{3} - x^{2} - 4 x + 1$ |
$16$ |
[8,4] |
$3^{2}\cdot 7^{2}\cdot 19^{4}\cdot 43^{2}\cdot 103^{4}$ |
$5$ |
$15.5725120357$ |
$1329.34984108774$ |
|
|
? |
$C_2^8.S_4$ (as 16T1664) |
trivial |
$2$ |
$11$ |
$2853.11388035$ |
