| 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 |
| 16.0.10749542400000000.1 |
$x^{16} - 2 x^{15} + x^{14} + 6 x^{13} - 15 x^{12} + 13 x^{11} + 15 x^{10} - 45 x^{9} + 42 x^{8} + 14 x^{7} - 65 x^{6} + 50 x^{5} + 3 x^{4} - 29 x^{3} + 21 x^{2} - 7 x + 1$ |
$16$ |
[0,8] |
$2^{22}\cdot 3^{8}\cdot 5^{8}$ |
$3$ |
$10.0452759957$ |
$26.054222497305222$ |
|
|
? |
$D_8:C_4$ (as 16T114) |
trivial |
$6$ |
$7$ |
$52.8621079118$ |
| 16.0.12370583534765625.1 |
$x^{16} - 7 x^{15} + 24 x^{14} - 50 x^{13} + 65 x^{12} - 40 x^{11} - 28 x^{10} + 94 x^{9} - 94 x^{8} + 16 x^{7} + 82 x^{6} - 128 x^{5} + 108 x^{4} - 59 x^{3} + 22 x^{2} - 6 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{8}\cdot 13^{6}$ |
$3$ |
$10.1338480169$ |
$13.96424004376894$ |
|
|
? |
$D_8:C_2$ (as 16T44) |
trivial |
$6$ |
$7$ |
$50.440336623$ |
| 16.2.19666546293359375.1 |
$x^{16} - 3 x^{15} + 5 x^{14} - 4 x^{13} - x^{12} + 6 x^{11} - 6 x^{10} - 8 x^{9} + 20 x^{8} - 19 x^{7} + 11 x^{6} + 4 x^{5} - 14 x^{4} + 4 x^{3} + 5 x^{2} - x - 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 31^{2}\cdot 71\cdot 859^{2}$ |
$4$ |
$10.4317700725$ |
$3074.621114869278$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$8$ |
$28.6747805181$ |
| 16.0.22028181368750000.1 |
$x^{16} - 3 x^{15} + 3 x^{14} - 2 x^{13} + 2 x^{12} + 5 x^{11} - 19 x^{10} + 28 x^{9} - 27 x^{8} + 12 x^{7} + 19 x^{6} - 58 x^{5} + 78 x^{4} - 62 x^{3} + 32 x^{2} - 9 x + 1$ |
$16$ |
[0,8] |
$2^{4}\cdot 5^{8}\cdot 59^{3}\cdot 131^{2}$ |
$4$ |
$10.5059702151$ |
$1541.007144503574$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$7$ |
$26.6804881826$ |
| 16.0.26987918400000000.1 |
$x^{16} - x^{15} + x^{14} - 5 x^{13} + 4 x^{12} + 5 x^{11} - 4 x^{10} - 9 x^{8} + 12 x^{7} + 2 x^{6} - 9 x^{5} + 8 x^{4} - 7 x^{3} + x^{2} + x + 1$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{2}\cdot 5^{8}\cdot 37^{4}$ |
$4$ |
$10.6401582389$ |
$59.363543824214226$ |
|
|
? |
$(C_2^3\times C_4):S_4$ (as 16T1046) |
trivial |
$2$ |
$7$ |
$31.5416353238$ |
| 16.0.29862086714453125.1 |
$x^{16} - 3 x^{15} + 3 x^{14} + x^{13} - 4 x^{12} + 2 x^{11} + 5 x^{10} - 9 x^{9} + 3 x^{8} + 9 x^{7} - 9 x^{6} - 4 x^{5} + 9 x^{4} - x^{3} - 4 x^{2} + x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 11^{4}\cdot 151^{2}\cdot 229$ |
$4$ |
$10.7076707724$ |
$1379.0739646588938$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$7$ |
$29.6941711926$ |
| 16.0.31269954097265625.1 |
$x^{16} - 4 x^{15} + 5 x^{14} + 5 x^{13} - 24 x^{12} + 31 x^{11} - 4 x^{10} - 44 x^{9} + 69 x^{8} - 44 x^{7} - 4 x^{6} + 31 x^{5} - 24 x^{4} + 5 x^{3} + 5 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$3^{8}\cdot 5^{8}\cdot 7^{2}\cdot 499^{2}$ |
$4$ |
$10.7385452804$ |
$228.89954128394405$ |
|
|
? |
$S_4^2:C_2^2$ (as 16T1494) |
trivial |
$6$ |
$7$ |
$88.6200748108$ |
| 16.0.31673320900000000.1 |
$x^{16} - 2 x^{15} + 2 x^{14} - 8 x^{13} + 14 x^{12} - 10 x^{11} + 20 x^{10} - 34 x^{9} + 20 x^{8} - 12 x^{7} + 20 x^{6} - 10 x^{5} - x^{4} - 4 x^{3} + 8 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{8}\cdot 13^{2}\cdot 37^{4}$ |
$4$ |
$10.7471509801$ |
$77.84741646319638$ |
|
|
? |
$(C_2^3\times C_4):S_4$ (as 16T1046) |
trivial |
$2$ |
$7$ |
$27.3219740008$ |
| 16.2.36286162879296875.1 |
$x^{16} - 2 x^{15} + x^{14} + 3 x^{13} - 11 x^{12} + 16 x^{11} - 17 x^{10} + 16 x^{9} - 13 x^{8} + 16 x^{7} - 17 x^{6} + 16 x^{5} - 11 x^{4} + 3 x^{3} + x^{2} - 2 x + 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 31^{2}\cdot 131\cdot 859^{2}$ |
$4$ |
$10.8388652059$ |
$4176.361454663616$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$8$ |
$40.8815236048$ |
| 16.2.45287535480859375.1 |
$x^{16} - 3 x^{15} + 6 x^{14} - 11 x^{13} + 14 x^{12} - 16 x^{11} + 13 x^{10} - 8 x^{9} + 7 x^{8} - 8 x^{7} + 13 x^{6} - 16 x^{5} + 14 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 11^{4}\cdot 151\cdot 229^{2}$ |
$4$ |
$10.9900246863$ |
$1379.0739646588938$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$8$ |
$46.4808624$ |
| 16.2.67969704100000000.1 |
$x^{16} - 3 x^{14} + x^{12} + 3 x^{10} + 2 x^{8} - x^{6} - 9 x^{4} - 4 x^{2} - 1$ |
$16$ |
[2,7] |
$-\,2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 31^{2}$ |
$4$ |
$11.2724861714$ |
$245.92126826496147$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$8$ |
$62.5995169928$ |
| 16.2.80157081600000000.1 |
$x^{16} - 2 x^{15} + x^{14} - 3 x^{12} - 2 x^{11} + 19 x^{10} - 4 x^{9} - 37 x^{8} + 28 x^{7} + 19 x^{6} - 30 x^{5} + 6 x^{4} + 10 x^{3} - 6 x^{2} + 1$ |
$16$ |
[2,7] |
$-\,2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151$ |
$4$ |
$11.3892825843$ |
|
|
|
? |
$C_2\wr D_4.C_2$ (as 16T1577) |
trivial |
$2$ |
$8$ |
$69.1847935897$ |
| 16.2.86899140707421875.1 |
$x^{16} - 5 x^{15} + 10 x^{14} - 9 x^{13} - 2 x^{12} + 17 x^{11} - 21 x^{10} + 11 x^{9} + x^{8} - 7 x^{7} + 2 x^{6} + 5 x^{5} - 12 x^{4} + 14 x^{3} - 9 x^{2} + 4 x - 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 7^{4}\cdot 29^{4}\cdot 131$ |
$4$ |
$11.4469152552$ |
$364.64366167534024$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1778) |
trivial |
$2$ |
$8$ |
$67.4836755215$ |
| 16.2.115558273191796875.1 |
$x^{16} + 2 x^{14} - 5 x^{13} - x^{12} - 10 x^{11} + 3 x^{10} - 4 x^{9} + 9 x^{8} - 4 x^{7} + 8 x^{6} - x^{5} + 7 x^{4} + 4 x^{2} - x + 1$ |
$16$ |
[2,7] |
$-\,3^{4}\cdot 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 691$ |
$5$ |
$11.6526597417$ |
$1471.8304929576639$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$8$ |
$84.8251848921$ |
| 16.0.122444006400000000.1 |
$x^{16} - 2 x^{15} + 9 x^{14} - 10 x^{13} + 32 x^{12} - 21 x^{11} + 64 x^{10} - 17 x^{9} + 81 x^{8} + x^{7} + 52 x^{6} + 9 x^{5} + 8 x^{4} + 5 x^{3} - 3 x^{2} + x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 3^{14}\cdot 5^{8}$ |
$3$ |
$11.6948887732$ |
$33.07814062698043$ |
|
|
? |
$(C_4\times C_8):D_4$ (as 16T513) |
trivial |
$6$ |
$7$ |
$230.49973438$ |
| 16.0.152812774400000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} + 6 x^{11} - 4 x^{10} - 4 x^{9} + 15 x^{8} - 4 x^{7} - 4 x^{6} + 6 x^{5} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 11\cdot 13^{4}\cdot 19$ |
$5$ |
$11.8579599391$ |
$329.66649814623264$ |
|
|
|
$C_2^7.C_2\wr D_4$ (as 16T1778) |
trivial |
$2$ |
$7$ |
$101.255505806$ |
| 16.0.156383420761328125.1 |
$x^{16} - 3 x^{15} + 4 x^{14} + x^{13} - 5 x^{12} + 12 x^{10} - 5 x^{9} - 8 x^{8} + 10 x^{7} + 11 x^{6} - 8 x^{5} - x^{4} + 7 x^{3} + x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 19\cdot 29^{4}\cdot 31^{3}$ |
$4$ |
$11.8750902602$ |
$689.5758953208109$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$7$ |
$72.7900412777$ |
| 16.2.173942237590234375.1 |
$x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 3 x^{11} + 2 x^{10} + x^{8} + 2 x^{6} - 3 x^{5} + 2 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 31\cdot 119851^{2}$ |
$3$ |
$11.9543320753$ |
$4310.093386459277$ |
|
|
✓ |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$8$ |
$97.0131796811$ |
| 16.0.178853944618750000.1 |
$x^{16} - 4 x^{15} + 11 x^{14} - 19 x^{13} + 24 x^{12} - 21 x^{11} + 11 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{6} - 9 x^{5} + 9 x^{4} - 4 x^{3} + 2 x^{2} - x + 1$ |
$16$ |
[0,8] |
$2^{4}\cdot 5^{8}\cdot 19\cdot 197^{4}$ |
$4$ |
$11.9751553939$ |
$386.9366873275265$ |
|
|
? |
$C_2\wr C_2^3.S_4$ (as 16T1846) |
trivial |
$2$ |
$7$ |
$95.7565158318$ |
| 16.0.180355734956640625.1 |
$x^{16} - 5 x^{15} + 14 x^{14} - 28 x^{13} + 46 x^{12} - 63 x^{11} + 73 x^{10} - 72 x^{9} + 57 x^{8} - 34 x^{7} + 23 x^{6} - 21 x^{5} + 8 x^{4} + 8 x^{3} - 7 x^{2} + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 59^{3}\cdot 131^{3}$ |
$3$ |
$11.9814153093$ |
$665.0655921280412$ |
|
|
? |
$Q_8^2.A_4^2.D_4$ (as 16T1871) |
trivial |
$2$ |
$7$ |
$69.5094645498$ |
| 16.0.180355734956640625.2 |
$x^{16} - 5 x^{15} + 7 x^{14} + 2 x^{13} - 10 x^{12} + 2 x^{11} + 7 x^{10} - 8 x^{9} + 3 x^{8} + 10 x^{7} - 16 x^{6} + 8 x^{5} + 5 x^{4} - 7 x^{3} + 3 x^{2} - 2 x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 59^{3}\cdot 131^{3}$ |
$3$ |
$11.9814153093$ |
$665.0655921280412$ |
|
|
|
$Q_8^2.A_4^2.D_4$ (as 16T1871) |
trivial |
$2$ |
$7$ |
$103.70582268$ |
| 16.4.188981478400000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 7 x^{12} + 10 x^{11} + 4 x^{10} - 22 x^{9} + 17 x^{8} + 20 x^{7} - 36 x^{6} + 28 x^{4} - 8 x^{3} - 10 x^{2} + 2 x + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2}$ |
$5$ |
$12.0164505235$ |
$329.66649814623264$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
$2$ |
$9$ |
$145.296666367$ |
| 16.0.189837888276953125.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 8 x^{13} + 9 x^{12} - 5 x^{11} + 12 x^{10} - 7 x^{9} - 2 x^{8} - 11 x^{7} + 7 x^{6} + 5 x^{5} + 6 x^{4} - 7 x^{3} - x^{2} + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 11^{4}\cdot 29^{3}\cdot 1361$ |
$4$ |
$12.0198467592$ |
$3419.077190924994$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$7$ |
$77.7064932253$ |
| 16.2.195238297600000000.1 |
$x^{16} - 4 x^{15} + 6 x^{14} - 6 x^{13} + 10 x^{12} - 26 x^{11} + 52 x^{10} - 54 x^{9} - 12 x^{8} + 82 x^{7} - 54 x^{6} - 24 x^{5} + 49 x^{4} - 32 x^{3} + 16 x^{2} - 6 x + 1$ |
$16$ |
[2,7] |
$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ |
$3$ |
$12.0409378082$ |
|
|
|
? |
$C_4^4:D_4$ (as 16T1477) |
trivial |
$2$ |
$8$ |
$106.032960978$ |
| 16.2.195238297600000000.2 |
$x^{16} - 6 x^{15} + 14 x^{14} - 14 x^{13} + 2 x^{12} - 4 x^{11} + 40 x^{10} - 78 x^{9} + 79 x^{8} - 52 x^{7} + 36 x^{6} - 34 x^{5} + 26 x^{4} - 18 x^{3} + 10 x^{2} - 4 x + 1$ |
$16$ |
[2,7] |
$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ |
$3$ |
$12.0409378082$ |
$45.66643307539152$ |
|
|
? |
$D_8\wr C_2$ (as 16T972) |
trivial |
$2$ |
$8$ |
$107.164441498$ |
| 16.2.195238297600000000.3 |
$x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 51 x^{12} - 46 x^{11} + 18 x^{10} - 4 x^{9} + 44 x^{8} - 118 x^{7} + 160 x^{6} - 138 x^{5} + 72 x^{4} - 16 x^{3} - 4 x^{2} + 4 x - 1$ |
$16$ |
[2,7] |
$-\,2^{24}\cdot 5^{8}\cdot 31^{3}$ |
$3$ |
$12.0409378082$ |
$45.66643307539152$ |
|
|
? |
$D_8\wr C_2$ (as 16T972) |
trivial |
$2$ |
$8$ |
$109.456398528$ |
| 16.4.232292068597265625.1 |
$x^{16} - x^{15} + 5 x^{14} - x^{13} + x^{11} - 19 x^{10} - 13 x^{9} - 20 x^{8} - 11 x^{7} + 17 x^{6} + 35 x^{5} + 46 x^{4} + 36 x^{3} + 22 x^{2} + 4 x - 1$ |
$16$ |
[4,6] |
$3^{6}\cdot 5^{8}\cdot 13^{8}$ |
$3$ |
$12.1724261633$ |
$13.96424004376894$ |
|
|
? |
$D_8:C_2$ (as 16T44) |
trivial |
$2$ |
$9$ |
$167.322044256$ |
| 16.4.232322192503515625.1 |
$x^{16} - 3 x^{15} + 2 x^{14} + 7 x^{13} - 15 x^{12} + 12 x^{11} - 6 x^{10} + 16 x^{9} - 24 x^{8} - 5 x^{7} + 67 x^{6} - 114 x^{5} + 110 x^{4} - 70 x^{3} + 30 x^{2} - 8 x + 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 131^{2}$ |
$4$ |
$12.1725248157$ |
$364.64366167534024$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
$2$ |
$9$ |
$155.818339721$ |
| 16.0.243112369495703125.1 |
$x^{16} - 2 x^{15} + 5 x^{14} - x^{13} + 11 x^{11} + x^{10} - x^{9} + 23 x^{8} - 8 x^{7} + 14 x^{6} + 2 x^{5} + 10 x^{4} - 3 x^{3} + 5 x^{2} + x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 11^{4}\cdot 349^{3}$ |
$3$ |
$12.2071123311$ |
$138.54602123482292$ |
|
|
? |
$D_8\wr C_2$ (as 16T972) |
trivial |
$2$ |
$7$ |
$96.4469143559$ |
| 16.4.243112369495703125.1 |
$x^{16} - x^{15} - 3 x^{14} + x^{13} + x^{12} - 3 x^{10} + 2 x^{9} - 4 x^{8} + 11 x^{7} + 13 x^{6} - 25 x^{5} - 4 x^{4} + 13 x^{3} - 2 x^{2} - 2 x + 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 11^{4}\cdot 349^{3}$ |
$3$ |
$12.2071123311$ |
$598.8256781260396$ |
|
|
? |
$C_4\wr D_4$ (as 16T1432) |
trivial |
$2$ |
$9$ |
$160.28330134$ |
| 16.0.256572640900000000.1 |
$x^{16} - 3 x^{15} + 14 x^{14} - 27 x^{13} + 67 x^{12} - 89 x^{11} + 151 x^{10} - 144 x^{9} + 188 x^{8} - 132 x^{7} + 139 x^{6} - 68 x^{5} + 57 x^{4} - 16 x^{3} + 11 x^{2} - x + 1$ |
$16$ |
[0,8] |
$2^{8}\cdot 5^{8}\cdot 37^{6}$ |
$3$ |
$12.2482952463$ |
$53.25041037185324$ |
|
|
? |
$Q_8.(C_2\times S_4)$ (as 16T739) |
trivial |
$2$ |
$7$ |
$99.8521394856$ |
| 16.0.311829406284765625.1 |
$x^{16} + 2 x^{14} - 3 x^{13} + 3 x^{12} - x^{11} + 6 x^{10} + 13 x^{9} + 8 x^{8} + 19 x^{7} + 4 x^{5} + 12 x^{4} - 17 x^{3} + 12 x^{2} - x + 1$ |
$16$ |
[0,8] |
$5^{8}\cdot 61^{2}\cdot 97^{2}\cdot 151^{2}$ |
$4$ |
$12.3985191384$ |
$2113.6071063468726$ |
|
|
? |
$C_2^6.S_4^2:C_2^2$ (as 16T1884) |
trivial |
$2$ |
$7$ |
$90.9680140734$ |
| 16.2.398383834480859375.1 |
$x^{16} - 3 x^{15} + 6 x^{14} - 4 x^{13} - x^{12} + 9 x^{11} - 15 x^{10} + 16 x^{9} - 17 x^{8} + 16 x^{7} - 15 x^{6} + 9 x^{5} - x^{4} - 4 x^{3} + 6 x^{2} - 3 x + 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 71\cdot 119851^{2}$ |
$3$ |
$12.589800745$ |
$6522.814193275783$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$8$ |
$157.185388951$ |
| 16.2.472848769600000000.1 |
$x^{16} - 4 x^{14} + 9 x^{12} - 14 x^{10} + 17 x^{8} - 13 x^{6} + 4 x^{4} + 2 x^{2} - 1$ |
$16$ |
[2,7] |
$-\,2^{12}\cdot 5^{8}\cdot 17191^{2}$ |
$3$ |
$12.7253618781$ |
$1147.5942836556544$ |
|
|
|
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$8$ |
$253.004443883$ |
| 16.4.499382553081640625.1 |
$x^{16} - 3 x^{15} + x^{14} + 9 x^{13} - 21 x^{12} + 24 x^{11} - 12 x^{10} - 8 x^{9} + 17 x^{8} - 8 x^{7} - 12 x^{6} + 24 x^{5} - 21 x^{4} + 9 x^{3} + x^{2} - 3 x + 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 89\cdot 119851^{2}$ |
$3$ |
$12.7688588246$ |
$7302.99219498419$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$9$ |
$251.294326231$ |
| 16.4.499382553081640625.2 |
$x^{16} - 2 x^{15} + 4 x^{14} - 5 x^{13} - 2 x^{12} - x^{11} - 8 x^{10} + 3 x^{9} + 6 x^{8} + 10 x^{7} + 4 x^{6} - x^{5} - 16 x^{4} - 24 x^{3} - 18 x^{2} - 9 x - 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 89\cdot 119851^{2}$ |
$3$ |
$12.7688588246$ |
$7302.99219498419$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$9$ |
$239.201457412$ |
| 16.6.505241847543359375.1 |
$x^{16} - x^{15} - 3 x^{14} + 10 x^{13} - 13 x^{12} + 6 x^{11} + 12 x^{10} - 33 x^{9} + 41 x^{8} - 33 x^{7} + 12 x^{6} + 6 x^{5} - 13 x^{4} + 10 x^{3} - 3 x^{2} - x + 1$ |
$16$ |
[6,5] |
$-\,5^{8}\cdot 71^{3}\cdot 1901^{2}$ |
$3$ |
$12.7781713387$ |
$2384.6235143470617$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$10$ |
$335.766972694$ |
| 16.0.513114342400000000.1 |
$x^{16} - 4 x^{13} + 7 x^{12} - 8 x^{11} + 8 x^{10} - 20 x^{9} + 49 x^{8} - 36 x^{7} - 28 x^{6} + 44 x^{5} + 5 x^{4} - 20 x^{3} - 2 x^{2} + 4 x + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2}$ |
$4$ |
$12.7905254044$ |
$165.46778321069314$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
$2$ |
$7$ |
$136.008808013$ |
| 16.4.513114342400000000.2 |
$x^{16} - 4 x^{15} + 6 x^{14} - 12 x^{13} + 25 x^{12} - 10 x^{11} - 15 x^{10} - 36 x^{9} + 83 x^{8} + 2 x^{7} - 81 x^{6} + 32 x^{5} + 20 x^{4} - 12 x^{3} + 3 x^{2} - 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2}$ |
$4$ |
$12.7905254044$ |
|
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
$2$ |
$9$ |
$278.178633436$ |
| 16.6.561298201600000000.1 |
$x^{16} - 8 x^{15} + 28 x^{14} - 56 x^{13} + 61 x^{12} - 2 x^{11} - 107 x^{10} + 172 x^{9} - 129 x^{8} + 34 x^{7} + 21 x^{6} - 20 x^{5} + 8 x^{4} - 6 x^{3} + 3 x^{2} - 1$ |
$16$ |
[6,5] |
$-\,2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 31$ |
$4$ |
$12.8624767625$ |
|
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$10$ |
$359.922310966$ |
| 16.0.590315622400000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 7 x^{13} + 12 x^{12} - 11 x^{11} + 14 x^{10} - 9 x^{9} + 5 x^{8} - 3 x^{7} + x^{6} - 8 x^{5} + 27 x^{4} - 14 x^{3} + 2 x^{2} - x + 1$ |
$16$ |
[0,8] |
$2^{18}\cdot 5^{8}\cdot 7^{8}$ |
$3$ |
$12.9030615011$ |
$16.73320053068151$ |
|
|
? |
$D_8:C_2$ (as 16T44) |
trivial |
$2$ |
$7$ |
$200.438586587$ |
| 16.4.611603351526953125.1 |
$x^{16} - x^{15} + x^{13} - 12 x^{12} - 2 x^{11} - 14 x^{10} - 25 x^{9} - 5 x^{8} - 25 x^{7} - 14 x^{6} - 2 x^{5} - 12 x^{4} + x^{3} - x + 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 109\cdot 119851^{2}$ |
$3$ |
$12.9316626336$ |
$8082.004392475916$ |
|
|
✓ |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$9$ |
$276.170960833$ |
| 16.2.638966001996484375.1 |
$x^{16} - x^{13} + 2 x^{12} - 6 x^{11} + 4 x^{10} - x^{9} + x^{8} - x^{7} + 4 x^{6} - 6 x^{5} + 2 x^{4} - x^{3} + 1$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 29^{2}\cdot 31\cdot 89^{4}$ |
$4$ |
$12.9670850523$ |
$632.4990118569357$ |
|
|
|
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$8$ |
$298.472419612$ |
| 16.2.641424792100000000.1 |
$x^{16} - 2 x^{14} - 8 x^{12} + 16 x^{10} + 11 x^{8} - 18 x^{6} + 3 x^{4} - x^{2} - 1$ |
$16$ |
[2,7] |
$-\,2^{8}\cdot 5^{8}\cdot 283^{4}$ |
$3$ |
$12.9701980869$ |
$137.97787808682992$ |
|
|
? |
$C_{2440}.D_6$ (as 16T1759) |
trivial |
$2$ |
$8$ |
$222.353266912$ |
| 16.4.683032622823828125.1 |
$x^{16} - x^{15} - 2 x^{14} - 4 x^{13} - 5 x^{12} - x^{11} + 6 x^{10} + 13 x^{9} + 15 x^{8} + 13 x^{7} + 6 x^{6} - x^{5} - 5 x^{4} - 4 x^{3} - 2 x^{2} - x + 1$ |
$16$ |
[4,6] |
$5^{8}\cdot 29\cdot 31^{2}\cdot 89^{4}$ |
$4$ |
$13.0212473992$ |
$632.4990118569357$ |
|
|
? |
$C_4^4.C_2\wr D_4$ (as 16T1823) |
trivial |
$2$ |
$9$ |
$306.896910129$ |
| 16.0.748709478400000000.1 |
$x^{16} - 2 x^{15} + 3 x^{14} - 2 x^{13} - 3 x^{12} + 6 x^{11} - 8 x^{10} - 10 x^{9} + 48 x^{8} - 90 x^{7} + 122 x^{6} - 114 x^{5} + 83 x^{4} - 44 x^{3} + 17 x^{2} - 4 x + 1$ |
$16$ |
[0,8] |
$2^{26}\cdot 5^{8}\cdot 13^{4}$ |
$3$ |
$13.0961784201$ |
$73.44965995393171$ |
|
|
|
$C_2^2.C_2\wr C_2^3$ (as 16T1701) |
trivial |
$2$ |
$7$ |
$301.521901775$ |
| 16.4.771024486400000000.1 |
$x^{16} - 2 x^{15} - x^{14} - 6 x^{11} + 24 x^{10} + 20 x^{9} - 24 x^{8} - 38 x^{7} + 5 x^{6} + 20 x^{5} - 18 x^{4} + 6 x^{3} - 4 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{24}\cdot 5^{8}\cdot 7^{6}$ |
$3$ |
$13.1202394348$ |
$16.73320053068151$ |
|
|
? |
$D_8:C_2$ (as 16T44) |
trivial |
$2$ |
$9$ |
$321.249071894$ |
| 16.6.847267028262109375.1 |
$x^{16} - 7 x^{15} + 19 x^{14} - 27 x^{13} + 19 x^{12} + 6 x^{11} - 38 x^{10} + 66 x^{9} - 77 x^{8} + 66 x^{7} - 38 x^{6} + 6 x^{5} + 19 x^{4} - 27 x^{3} + 19 x^{2} - 7 x + 1$ |
$16$ |
[6,5] |
$-\,5^{8}\cdot 151\cdot 119851^{2}$ |
$3$ |
$13.1977916845$ |
$9512.492049930976$ |
|
|
? |
$C_2^6.S_4^2:D_4$ (as 16T1905) |
trivial |
$2$ |
$10$ |
$448.860326258$ |
| 16.4.882697830400000000.1 |
$x^{16} - 2 x^{15} + x^{14} + 4 x^{13} - 5 x^{12} + 2 x^{11} + 3 x^{10} + x^{8} + 3 x^{6} - 2 x^{5} - 5 x^{4} - 4 x^{3} + x^{2} + 2 x + 1$ |
$16$ |
[4,6] |
$2^{24}\cdot 5^{8}\cdot 367^{2}$ |
$3$ |
$13.2316271246$ |
$121.16104984688768$ |
|
|
? |
$S_4^2:C_2^2$ (as 16T1494) |
trivial |
$2$ |
$9$ |
$407.518266474$ |
| 16.4.887213286400000000.2 |
$x^{16} - 2 x^{15} - 3 x^{14} + 8 x^{12} + 4 x^{11} - x^{10} + 10 x^{9} + 15 x^{8} + 10 x^{7} - x^{6} + 4 x^{5} + 8 x^{4} - 3 x^{2} - 2 x + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4}$ |
$4$ |
$13.235847427471171$ |
$116.85956436561077$ |
|
|
? |
$C_2^7.C_2\wr D_4$ (as 16T1772) |
trivial |
$2$ |
$9$ |
$355.4268966475079$ |
