| 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 $p$ |
| 16.0.3243658447265625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 30 x^{13} + 57 x^{12} - 100 x^{11} + 157 x^{10} - 215 x^{9} + 250 x^{8} - 240 x^{7} + 183 x^{6} - 110 x^{5} + 57 x^{4} - 30 x^{3} + 16 x^{2} - 5 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{14}$ |
$2$ |
$9.3205103882$ |
$9.320510388204081$ |
|
✓ |
? |
$C_8: C_2$ (as 16T6) |
trivial |
trivial |
$30$ |
$7$ |
$112.874368042$ |
$0$ |
$5$ |
| 16.0.13334825747498256.1 |
$x^{16} - 6 x^{15} + 15 x^{14} - 17 x^{13} - x^{12} + 24 x^{11} - 9 x^{10} - 54 x^{9} + 108 x^{8} - 95 x^{7} + 42 x^{6} - 21 x^{5} + 36 x^{4} - 43 x^{3} + 27 x^{2} - 7 x + 1$ |
$16$ |
(0, 8) |
$2^{4}\cdot 3^{12}\cdot 199^{4}$ |
$3$ |
$10.1814986745$ |
$64.3128084324925$ |
|
|
? |
$C_2^5:S_4$ (as 16T1045) |
trivial |
trivial |
$6$ |
$7$ |
$60.5270597073$ |
$0$ |
$199$ |
| 16.0.13548885344059392.1 |
$x^{16} - 4 x^{15} + 6 x^{14} - 10 x^{12} + 47 x^{10} - 82 x^{9} + 42 x^{8} + 40 x^{7} - 67 x^{6} + 18 x^{5} + 38 x^{4} - 48 x^{3} + 27 x^{2} - 8 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 73^{3}$ |
$3$ |
$10.191637614$ |
$38.95223366419873$ |
|
|
? |
$D_4^2:C_2^2$ (as 16T665) |
trivial |
trivial |
$12$ |
$7$ |
$106.415606097$ |
$0$ |
$73$ |
| 16.0.13852994719059873.1 |
$x^{16} + x^{14} - 3 x^{13} - 7 x^{12} - 9 x^{11} - 5 x^{10} + 18 x^{9} + 49 x^{8} + 87 x^{7} + 113 x^{6} + 105 x^{5} + 77 x^{4} + 45 x^{3} + 20 x^{2} + 6 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 13^{4}\cdot 97^{3}$ |
$3$ |
$10.20578651$ |
$254.03374921302205$ |
|
|
? |
$C_4\wr D_4$ (as 16T1432) |
trivial |
trivial |
$6$ |
$7$ |
$53.4955230971$ |
$0$ |
$97$ |
| 16.0.19656580065400629.1 |
$x^{16} - x^{15} - x^{14} + 3 x^{12} + x^{11} - 2 x^{10} - x^{9} - 2 x^{8} + 15 x^{7} - 21 x^{6} + 2 x^{5} + 27 x^{4} - 33 x^{3} + 16 x^{2} - 4 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 13^{4}\cdot 109^{3}$ |
$3$ |
$10.4314395934$ |
$85.80762193986789$ |
|
|
? |
$D_8\wr C_2$ (as 16T972) |
trivial |
trivial |
$6$ |
$7$ |
$63.340105233$ |
$0$ |
$109$ |
| 16.0.36560480908034304.1 |
$x^{16} - 7 x^{15} + 29 x^{14} - 87 x^{13} + 204 x^{12} - 389 x^{11} + 628 x^{10} - 871 x^{9} + 1039 x^{8} - 1062 x^{7} + 927 x^{6} - 676 x^{5} + 393 x^{4} - 171 x^{3} + 52 x^{2} - 10 x + 1$ |
$16$ |
(0, 8) |
$2^{8}\cdot 3^{12}\cdot 13^{4}\cdot 97^{2}$ |
$4$ |
$10.8439684096$ |
$272.2707431502513$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
trivial |
$6$ |
$7$ |
$92.1043893828$ |
$0$ |
$97$ |
| 16.0.96489516623265792.1 |
$x^{16} - 4 x^{15} + 9 x^{14} - 10 x^{13} - 9 x^{12} + 30 x^{11} - 24 x^{10} - 2 x^{9} + 45 x^{8} - 36 x^{7} - 24 x^{6} + 30 x^{5} - 4 x^{4} - 14 x^{3} + 6 x^{2} + 6 x + 1$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 13^{4}\cdot 97$ |
$4$ |
$11.522056703$ |
$272.2707431502513$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1778) |
trivial |
trivial |
$6$ |
$7$ |
$180.928677519$ |
$0$ |
$97$ |
| 16.0.139314069504000000.1 |
$x^{16} - 2 x^{15} - 5 x^{14} + 16 x^{13} - 4 x^{12} - 38 x^{11} + 58 x^{10} + 2 x^{9} - 80 x^{8} + 66 x^{7} + 19 x^{6} - 54 x^{5} + 19 x^{4} + 10 x^{3} - 8 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$11.7896167128$ |
$21.558246717785053$ |
|
|
? |
$D_8:C_4$ (as 16T114) |
trivial |
trivial |
$6$ |
$7$ |
$164.264328049$ |
$0$ |
$5$ |
| 16.0.164812863625282197.1 |
$x^{16} - x^{15} - 5 x^{14} + 5 x^{13} + 2 x^{12} + 5 x^{11} + 7 x^{10} - 41 x^{9} + 25 x^{8} + 21 x^{7} - 26 x^{6} + 3 x^{5} + 10 x^{4} - 7 x^{3} - 2 x^{2} + 3 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 13^{3}\cdot 109^{4}$ |
$3$ |
$11.914119288$ |
$85.80762193986789$ |
|
|
? |
$D_8\wr C_2$ (as 16T972) |
trivial |
trivial |
$6$ |
$7$ |
$250.805825535$ |
$0$ |
$109$ |
| 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 |
$30$ |
$7$ |
$1278.94388647$ |
$0$ |
$41$ |
| 16.0.840675741330898944.1 |
$x^{16} - 2 x^{15} - 3 x^{14} + 18 x^{13} - 22 x^{12} - 30 x^{11} + 113 x^{10} - 74 x^{9} - 126 x^{8} + 230 x^{7} - 67 x^{6} - 138 x^{5} + 161 x^{4} - 84 x^{3} + 36 x^{2} - 16 x + 4$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 17^{6}$ |
$3$ |
$13.1913511783$ |
$18.7972967403308$ |
|
|
|
$D_8:C_2$ (as 16T45) |
trivial |
trivial |
$12$ |
$7$ |
$2148.56458558$ |
$0$ |
$17$ |
| 16.4.989068630116335616.1 |
$x^{16} - 4 x^{15} + 3 x^{14} + 8 x^{13} - 18 x^{12} + 12 x^{11} + 3 x^{10} + 10 x^{9} - 36 x^{8} + 12 x^{7} + 21 x^{6} - 18 x^{5} + 8 x^{4} - 8 x^{3} + 12 x^{2} - 6 x + 1$ |
$16$ |
(4, 6) |
$2^{16}\cdot 3^{12}\cdot 73^{4}$ |
$3$ |
$13.3260565451$ |
$38.95223366419873$ |
|
|
? |
$D_4^2:C_2^2$ (as 16T696) |
trivial |
$[2]$ |
$2$ |
$9$ |
$390.937838278$ |
$3$ |
$73$ |
| 16.0.241...997.1 |
$x^{16} - 3 x^{15} + 3 x^{14} + 8 x^{13} - 19 x^{12} + 3 x^{11} + 54 x^{10} - 99 x^{9} + 42 x^{8} + 56 x^{7} - 102 x^{6} + 24 x^{5} + 51 x^{4} - 38 x^{3} + 9 x^{2} + 40 x + 13$ |
$16$ |
(0, 8) |
$3^{12}\cdot 16573^{3}$ |
$2$ |
$14.0921952889$ |
$293.4549950188564$ |
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1872) |
trivial |
trivial |
$6$ |
$7$ |
$908.740495594$ |
$0$ |
$16573$ |
| 16.4.272...625.1 |
$x^{16} - 6 x^{15} + 19 x^{14} - 36 x^{13} + 41 x^{12} - 18 x^{11} - 29 x^{10} + 87 x^{9} - 143 x^{8} + 168 x^{7} - 154 x^{6} + 123 x^{5} - 79 x^{4} + 21 x^{3} + 14 x^{2} - 9 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{14}\cdot 29^{2}$ |
$3$ |
$14.1984012271$ |
$50.19248452708817$ |
|
|
? |
$C_2^4:\OD_{16}$ (as 16T554) |
trivial |
$[2]$ |
$2$ |
$9$ |
$634.084590186$ |
$3$ |
$29$ |
| 16.0.587...777.1 |
$x^{16} + 7 x^{14} - 7 x^{13} + 25 x^{12} - 33 x^{11} + 97 x^{10} - 87 x^{9} + 205 x^{8} - 233 x^{7} + 283 x^{6} - 241 x^{5} + 185 x^{4} - 109 x^{3} + 43 x^{2} - 10 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 73^{7}$ |
$2$ |
$14.8951435265$ |
$97.3303855314655$ |
|
|
|
$C_8\wr C_2$ (as 16T289) |
trivial |
trivial |
$6$ |
$7$ |
$1279.51275205$ |
$0$ |
$73$ |
| 16.0.950...509.1 |
$x^{16} - 6 x^{15} + 19 x^{14} - 48 x^{13} + 95 x^{12} - 156 x^{11} + 220 x^{10} - 240 x^{9} + 250 x^{8} - 216 x^{7} + 128 x^{6} - 144 x^{5} + 86 x^{4} - 69 x^{3} + 113 x^{2} - 21 x + 49$ |
$16$ |
(0, 8) |
$3^{12}\cdot 79^{3}\cdot 331^{3}$ |
$3$ |
$15.3501904976$ |
$1098.943226177253$ |
|
|
? |
$Q_8^2.S_4\wr C_2$ (as 16T1871) |
trivial |
trivial |
$6$ |
$7$ |
$1994.62365846$ |
$0$ |
$331$ |
| 16.0.976...625.1 |
$x^{16} - 6 x^{15} + 14 x^{14} - 12 x^{13} - 7 x^{12} + 15 x^{11} + 8 x^{10} - 15 x^{9} - 14 x^{8} + 15 x^{7} + 7 x^{6} + 8 x^{4} + 6 x^{3} + x^{2} - 3 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{8}\cdot 19^{6}$ |
$3$ |
$15.3765372111$ |
$22.21788649167895$ |
|
|
? |
$D_8:C_2$ (as 16T38) |
trivial |
trivial |
$6$ |
$7$ |
$2145.51048665$ |
$0$ |
$19$ |
| 16.4.112...625.1 |
$x^{16} - 5 x^{15} + 12 x^{14} - 15 x^{13} - 7 x^{12} + 60 x^{11} - 91 x^{10} + 25 x^{9} + 105 x^{8} - 160 x^{7} + 59 x^{6} + 75 x^{5} - 97 x^{4} + 30 x^{3} + 12 x^{2} - 10 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{14}\cdot 59^{2}$ |
$3$ |
$15.5165868385$ |
$71.59219873631896$ |
|
|
? |
$C_2^6:\OD_{16}$ (as 16T1162) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1767.679048$ |
$3$ |
$59$ |
| 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 |
$[2]$ |
$2$ |
$11$ |
$2676.39256757$ |
$7$ |
$59$ |
| 16.4.112...625.4 |
$x^{16} - 4 x^{14} + 2 x^{12} - 22 x^{10} - 5 x^{8} - 38 x^{6} - 13 x^{4} - 11 x^{2} + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{14}\cdot 59^{2}$ |
$3$ |
$15.5165868385$ |
$71.59219873631896$ |
|
|
? |
$C_2^4:\OD_{16}$ (as 16T554) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1241.14563886$ |
$3$ |
$59$ |
| 16.4.120...625.1 |
$x^{16} - x^{15} + 3 x^{14} + 3 x^{13} - 4 x^{12} + 9 x^{11} + 5 x^{10} - 16 x^{9} - 21 x^{8} + 28 x^{7} + 5 x^{6} - 63 x^{5} + 26 x^{4} + 36 x^{3} - 18 x^{2} + 7 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{14}\cdot 61^{2}$ |
$3$ |
$15.5813801759$ |
$72.79551323875552$ |
|
|
? |
$C_2^7:\OD_{16}$ (as 16T1428) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1850.92480095$ |
$3$ |
$61$ |
| 16.4.120...625.2 |
$x^{16} - x^{15} + x^{14} + x^{13} - 7 x^{12} + 14 x^{11} - 16 x^{10} + 28 x^{9} - 77 x^{8} + 154 x^{7} - 184 x^{6} + 128 x^{5} - 37 x^{4} - 17 x^{3} + 19 x^{2} - 7 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{14}\cdot 61^{2}$ |
$3$ |
$15.5813801759$ |
$72.79551323875552$ |
|
|
? |
$C_2^7:\OD_{16}$ (as 16T1428) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1366.69985808$ |
$3$ |
$61$ |
| 16.0.151...176.1 |
$x^{16} - x^{15} - x^{14} + 8 x^{12} - 8 x^{11} + 7 x^{10} - 3 x^{9} + 25 x^{8} - 24 x^{7} + 16 x^{6} + 20 x^{5} + 20 x^{4} - 48 x^{3} + 32 x^{2} + 16 x + 16$ |
$16$ |
(0, 8) |
$2^{12}\cdot 3^{12}\cdot 17^{8}$ |
$3$ |
$15.8065794454$ |
$18.7972967403308$ |
|
|
|
$D_8:C_2$ (as 16T38) |
trivial |
trivial |
$6$ |
$7$ |
$6834.88091231$ |
$0$ |
$17$ |
| 16.0.356...000.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 44 x^{12} - 104 x^{11} + 124 x^{10} - 276 x^{9} + 475 x^{8} - 444 x^{7} + 604 x^{6} - 796 x^{5} + 284 x^{4} + 120 x^{3} + 2 x^{2} + 4 x + 1$ |
$16$ |
(0, 8) |
$2^{32}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$16.6730358504$ |
$20.38853093816547$ |
|
|
? |
$D_8:C_2$ (as 16T38) |
$[2]$ |
$[2]$ |
$12$ |
$7$ |
$5042.1967116$ |
$0$ |
$5$ |
| 16.0.411...000.1 |
$x^{16} - 6 x^{15} + 22 x^{14} - 70 x^{13} + 211 x^{12} - 540 x^{11} + 1159 x^{10} - 2046 x^{9} + 3007 x^{8} - 3680 x^{7} + 3748 x^{6} - 3172 x^{5} + 2192 x^{4} - 1204 x^{3} + 505 x^{2} - 142 x + 19$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 11^{2}$ |
$4$ |
$16.8229159474$ |
$71.50061550080385$ |
|
|
|
$(C_2\times D_4^2):C_4$ (as 16T799) |
trivial |
trivial |
$6$ |
$7$ |
$5861.5743076$ |
$0$ |
$11$ |
| 16.0.474...625.1 |
$x^{16} - 19 x^{14} + 167 x^{12} - 862 x^{10} + 2725 x^{8} - 5153 x^{6} + 5747 x^{4} - 4526 x^{2} + 3721$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{14}\cdot 11^{4}$ |
$3$ |
$16.9741433721$ |
$30.912635812282684$ |
✓ |
|
? |
$C_2 \times (C_8:C_2)$ (as 16T15) |
$[2]$ |
$[2]$ |
$30$ |
$7$ |
$10344.1260394$ |
$0$ |
$11$ |
| 16.8.474...625.2 |
$x^{16} - 5 x^{15} + 7 x^{14} + 10 x^{13} - 52 x^{12} + 100 x^{11} - 161 x^{10} + 275 x^{9} - 350 x^{8} + 135 x^{7} + 304 x^{6} - 435 x^{5} + 133 x^{4} + 70 x^{3} - 38 x^{2} + 1$ |
$16$ |
(8, 4) |
$3^{12}\cdot 5^{14}\cdot 11^{4}$ |
$3$ |
$16.9741433721$ |
$30.912635812282684$ |
|
|
? |
$C_2^2:\OD_{16}$ (as 16T95) |
trivial |
$[2]$ |
$2$ |
$11$ |
$7638.00708459$ |
$7$ |
$11$ |
| 16.0.474...625.3 |
$x^{16} - 5 x^{15} + 12 x^{14} - 15 x^{13} + 8 x^{12} + 29 x^{10} - 80 x^{9} + 45 x^{8} + 80 x^{7} + 29 x^{6} + 8 x^{4} + 15 x^{3} + 12 x^{2} + 5 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{14}\cdot 11^{4}$ |
$3$ |
$16.9741433721$ |
$30.912635812282684$ |
|
|
? |
$C_2^2:\OD_{16}$ (as 16T95) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$881.214818634$ |
$0$ |
$11$ |
| 16.0.722...968.2 |
$x^{16} - 6 x^{15} + 15 x^{14} - 32 x^{13} + 92 x^{12} - 222 x^{11} + 327 x^{10} - 276 x^{9} + 303 x^{8} - 704 x^{7} + 675 x^{6} + 330 x^{5} - 609 x^{4} - 586 x^{3} + 1494 x^{2} + 62 x + 61$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 73^{5}$ |
$3$ |
$17.424460108214074$ |
$38.95223366419873$ |
|
|
? |
$D_4^2:C_2^2$ (as 16T659) |
$[2]$ |
$[2]$ |
$12$ |
$7$ |
$4804.709907487032$ |
$0$ |
$73$ |
| 16.0.870...000.1 |
$x^{16} - 2 x^{15} + 13 x^{14} - 30 x^{13} + 93 x^{12} - 194 x^{11} + 432 x^{10} - 792 x^{9} + 1405 x^{8} - 2132 x^{7} + 2836 x^{6} - 3154 x^{5} + 2877 x^{4} - 2094 x^{3} + 1079 x^{2} - 338 x + 49$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{12}\cdot 5^{10}$ |
$3$ |
$17.6295889825$ |
$21.558246717785053$ |
|
|
|
$D_8:C_4$ (as 16T114) |
$[2]$ |
$[2]$ |
$6$ |
$7$ |
$5789.2337068$ |
$0$ |
$5$ |
| 16.0.103...625.1 |
$x^{16} - x^{15} + 13 x^{14} + 3 x^{13} + 66 x^{12} + 74 x^{11} + 210 x^{10} + 294 x^{9} + 409 x^{8} + 413 x^{7} + 370 x^{6} + 247 x^{5} + 141 x^{4} + 51 x^{3} + 17 x^{2} + 2 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{14}\cdot 179^{2}$ |
$3$ |
$17.8256889373$ |
$124.6999301823983$ |
|
|
? |
$C_2^4:\OD_{16}$ (as 16T554) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$1297.9805353$ |
$0$ |
$179$ |
| 16.0.141...625.1 |
$x^{16} - 5 x^{15} + 5 x^{14} + 27 x^{13} - 94 x^{12} + 110 x^{11} + 40 x^{10} - 378 x^{9} + 805 x^{8} - 1131 x^{7} + 1165 x^{6} - 887 x^{5} + 497 x^{4} - 201 x^{3} + 56 x^{2} - 10 x + 1$ |
$16$ |
(0, 8) |
$3^{12}\cdot 5^{6}\cdot 19^{8}$ |
$3$ |
$18.1690195885$ |
$22.21788649167895$ |
|
|
? |
$D_8:C_2$ (as 16T45) |
$[2]$ |
$[2]$ |
$6$ |
$7$ |
$6365.05426835$ |
$0$ |
$19$ |
| 16.0.149...296.17 |
$x^{16} - 6 x^{12} + 45 x^{8} - 108 x^{4} + 81$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.2360564556$ |
$28.12384367863563$ |
|
|
? |
$D_8:C_4$ (as 16T113) |
trivial |
trivial |
$12$ |
$7$ |
$18650.6290394$ |
$0$ |
$3$ |
| 16.0.149...296.34 |
$x^{16} - 12 x^{14} + 84 x^{12} - 396 x^{10} + 1197 x^{8} - 2052 x^{6} + 1782 x^{4} - 648 x^{2} + 81$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.23605645563822$ |
$28.12384367863563$ |
|
|
? |
$D_8:C_4$ (as 16T114) |
trivial |
trivial |
$12$ |
$7$ |
$25544.612875827956$ |
$0$ |
$3$ |
| 16.0.149...296.35 |
$x^{16} - 12 x^{14} + 54 x^{12} - 108 x^{10} + 90 x^{8} - 108 x^{6} + 378 x^{4} - 324 x^{2} + 81$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.23605645563822$ |
$25.789678363765006$ |
|
|
? |
$C_8.D_4$ (as 16T133) |
trivial |
trivial |
$12$ |
$7$ |
$18519.908961261197$ |
$0$ |
$3$ |
| 16.0.149...296.38 |
$x^{16} - 12 x^{14} + 78 x^{12} - 324 x^{10} + 738 x^{8} - 756 x^{6} + 162 x^{4} + 324 x^{2} + 81$ |
$16$ |
(0, 8) |
$2^{48}\cdot 3^{12}$ |
$2$ |
$18.23605645563822$ |
$28.12384367863563$ |
|
|
? |
$D_8:C_4$ (as 16T114) |
trivial |
trivial |
$12$ |
$7$ |
$10409.609584098896$ |
$0$ |
$3$ |
| 16.0.153...209.1 |
$x^{16} - 6 x^{15} + 8 x^{14} + 15 x^{13} - 31 x^{12} - 30 x^{11} + 83 x^{10} - 257 x^{8} + 312 x^{7} + 673 x^{6} - 1044 x^{5} - 547 x^{4} + 978 x^{3} + 259 x^{2} - 960 x + 619$ |
$16$ |
(0, 8) |
$3^{12}\cdot 257^{6}$ |
$2$ |
$18.2627368892$ |
$36.543278077309985$ |
|
|
? |
$\GL(2,3):C_2$ (as 16T190) |
trivial |
trivial |
$6$ |
$7$ |
$5696.51156378$ |
$0$ |
$257$ |
| 16.0.153...209.2 |
$x^{16} - 4 x^{15} + 20 x^{14} - 60 x^{13} + 173 x^{12} - 422 x^{11} + 928 x^{10} - 1779 x^{9} + 2977 x^{8} - 4335 x^{7} + 5371 x^{6} - 5659 x^{5} + 5018 x^{4} - 3393 x^{3} + 1916 x^{2} - 554 x + 79$ |
$16$ |
(0, 8) |
$3^{12}\cdot 257^{6}$ |
$2$ |
$18.2627368892$ |
$146.31565086210927$ |
|
|
? |
$Q_8.(C_2\times S_4)$ (as 16T739) |
trivial |
trivial |
$6$ |
$7$ |
$6195.24506493$ |
$0$ |
$257$ |
| 16.8.212...000.1 |
$x^{16} - 4 x^{14} + 2 x^{12} + 8 x^{10} - 5 x^{8} - 23 x^{6} + 32 x^{4} - 11 x^{2} + 1$ |
$16$ |
(8, 4) |
$2^{16}\cdot 3^{12}\cdot 5^{14}$ |
$3$ |
$18.6410207764$ |
$18.641020776408162$ |
|
|
? |
$C_2 \times (C_8:C_2)$ (as 16T15) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$12627.3718467$ |
$6$ |
$5$ |
| 16.0.212...000.2 |
$x^{16} + 15 x^{14} + 135 x^{12} + 765 x^{10} + 2790 x^{8} + 6075 x^{6} + 7425 x^{4} + 4050 x^{2} + 2025$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 5^{14}$ |
$3$ |
$18.6410207764$ |
$18.641020776408162$ |
|
✓ |
? |
$C_8: C_2$ (as 16T6) |
$[2, 2]$ |
$[2, 2]$ |
$30$ |
$7$ |
$12903.7195286$ |
$0$ |
$5$ |
| 16.0.212...000.3 |
$x^{16} - 15 x^{14} + 105 x^{12} - 450 x^{10} + 1305 x^{8} - 2700 x^{6} + 4050 x^{4} - 4050 x^{2} + 2025$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{12}\cdot 5^{14}$ |
$3$ |
$18.6410207764$ |
$31.350335095103276$ |
|
|
? |
$\OD_{16}:C_2^2$ (as 16T99) |
$[2]$ |
$[2]$ |
$30$ |
$7$ |
$20903.9321104$ |
$0$ |
$5$ |
| 16.4.212...000.3 |
$x^{16} - 2 x^{14} - 7 x^{12} + 31 x^{10} - 35 x^{8} - 4 x^{6} + 38 x^{4} - 22 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{16}\cdot 3^{12}\cdot 5^{14}$ |
$3$ |
$18.641020776408162$ |
$31.350335095103276$ |
|
|
? |
$C_2^3:\OD_{16}$ (as 16T252) |
trivial |
$[2]$ |
$2$ |
$9$ |
$7303.182009845615$ |
$3$ |
$5$ |
| 16.0.215...664.1 |
$x^{16} - 6 x^{15} + 17 x^{14} - 30 x^{13} + 38 x^{12} - 48 x^{11} + 89 x^{10} - 168 x^{9} + 217 x^{8} - 156 x^{7} + 7 x^{6} + 72 x^{5} - 10 x^{4} - 30 x^{3} + 7 x^{2} + 6 x + 1$ |
$16$ |
(0, 8) |
$2^{24}\cdot 3^{12}\cdot 17^{6}$ |
$3$ |
$18.6553877424$ |
$26.58339198612739$ |
|
|
? |
$D_8:C_2$ (as 16T38) |
trivial |
trivial |
$6$ |
$7$ |
$13426.5980282$ |
$0$ |
$17$ |
| 16.4.242...816.1 |
$x^{16} - 11 x^{14} + 32 x^{12} - 38 x^{10} + 58 x^{8} - 112 x^{6} + 41 x^{4} - 7 x^{2} + 4$ |
$16$ |
(4, 6) |
$2^{16}\cdot 3^{12}\cdot 17^{8}$ |
$3$ |
$18.7972967403$ |
$18.7972967403308$ |
|
|
|
$D_8:C_2$ (as 16T38) |
trivial |
$[2]$ |
$2$ |
$9$ |
$41451.3896818$ |
$3$ |
$17$ |
| 16.6.315...875.1 |
$x^{16} - 2 x^{15} + 2 x^{14} - 6 x^{13} - 9 x^{12} + 23 x^{11} - 35 x^{10} - 23 x^{9} + 4 x^{8} - 9 x^{7} - 15 x^{6} + 61 x^{5} + 36 x^{4} - 18 x^{3} - 17 x^{2} + x + 1$ |
$16$ |
(6, 5) |
$-\,3^{12}\cdot 5^{14}\cdot 97379$ |
$3$ |
$19.1081559342$ |
$2908.521979174126$ |
|
|
? |
$C_2\wr \OD_{16}$ (as 16T1604) |
trivial |
$[2]$ |
$2$ |
$10$ |
$14615.2381034$ |
$5$ |
$97379$ |
| 16.4.363...125.2 |
$x^{16} - 8 x^{15} + 25 x^{14} - 35 x^{13} + 5 x^{12} + 61 x^{11} - 98 x^{10} + 50 x^{9} + 40 x^{8} - 75 x^{7} + 37 x^{6} + 9 x^{5} - 20 x^{4} + 10 x^{3} - 5 x^{2} + 3 x + 1$ |
$16$ |
(4, 6) |
$3^{12}\cdot 5^{15}\cdot 22409$ |
$3$ |
$19.2764352967$ |
$1542.8956635169225$ |
|
|
? |
$C_2\wr \OD_{16}$ (as 16T1604) |
trivial |
$[2]$ |
$2$ |
$9$ |
$7804.59009464$ |
$3$ |
$22409$ |
| 16.4.486...000.1 |
$x^{16} - 4 x^{15} + 2 x^{14} + 3 x^{13} + 6 x^{12} + 4 x^{11} - 38 x^{10} - 16 x^{9} + 7 x^{8} + 120 x^{7} + 288 x^{6} + 152 x^{5} - 3 x^{4} + 39 x^{3} + 79 x^{2} + 20 x + 1$ |
$16$ |
(4, 6) |
$2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4}$ |
$4$ |
$19.6305113881$ |
$71.50061550080385$ |
|
|
? |
$D_4^2:C_4$ (as 16T610) |
trivial |
$[2]$ |
$2$ |
$9$ |
$8719.05707723$ |
$3$ |
$11$ |
| 16.4.486...000.2 |
$x^{16} - 5 x^{15} + 17 x^{14} - 51 x^{13} + 99 x^{12} - 139 x^{11} + 139 x^{10} - 17 x^{9} - 143 x^{8} + 252 x^{7} - 246 x^{6} + 82 x^{5} + 51 x^{4} - 45 x^{3} - 5 x^{2} + 10 x - 5$ |
$16$ |
(4, 6) |
$2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 11^{4}$ |
$4$ |
$19.6305113881$ |
$71.50061550080385$ |
|
|
? |
$D_4^2:C_4$ (as 16T610) |
trivial |
$[2]$ |
$2$ |
$9$ |
$18262.28001$ |
$3$ |
$11$ |
| 16.0.570...000.1 |
$x^{16} - 12 x^{14} - 16 x^{13} + 104 x^{12} + 60 x^{11} - 306 x^{10} - 420 x^{9} + 1023 x^{8} + 344 x^{7} - 102 x^{6} - 4476 x^{5} + 7782 x^{4} - 5876 x^{3} + 2322 x^{2} - 464 x + 37$ |
$16$ |
(0, 8) |
$2^{36}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$19.827692862$ |
$31.44341312700351$ |
|
|
? |
$D_8:C_2^2$ (as 16T80) |
$[2]$ |
$[2]$ |
$12$ |
$7$ |
$17177.70305$ |
$0$ |
$5$ |
| 16.4.598...184.3 |
$x^{16} - 24 x^{12} + 18 x^{8} + 216 x^{4} + 81$ |
$16$ |
(4, 6) |
$2^{50}\cdot 3^{12}$ |
$2$ |
$19.8865605782$ |
$23.64923933252054$ |
|
|
? |
$C_8.D_4$ (as 16T132) |
trivial |
$[2]$ |
$2$ |
$9$ |
$18098.5715144$ |
$3$ |
$3$ |
