| 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 |
| 18.4.343...543.1 |
$x^{18} - 2 x^{17} - 3 x^{15} + 6 x^{14} + 11 x^{13} - 22 x^{12} + 12 x^{11} - 27 x^{10} + 47 x^{9} - 27 x^{8} + 12 x^{7} - 22 x^{6} + 11 x^{5} + 6 x^{4} - 3 x^{3} - 2 x + 1$ |
$18$ |
[4,7] |
$-\,167\cdot 453771377^{2}$ |
$2$ |
$12.1718064291$ |
$275281.34691438865$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$279.477800199$ |
| 18.4.428...056.1 |
$x^{18} - x^{17} - 5 x^{16} + 9 x^{15} + 3 x^{14} - 13 x^{13} + 2 x^{12} - 3 x^{11} + 10 x^{10} + 13 x^{9} - 23 x^{8} - 5 x^{7} + 8 x^{6} - 4 x^{5} + 8 x^{4} + 9 x^{3} - 6 x^{2} - 5 x + 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 37^{6}\cdot 151^{2}\cdot 179$ |
$4$ |
$12.3221821174$ |
$1587.4589910492273$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$10$ |
$322.345419595$ |
| 18.4.602...171.1 |
$x^{18} - 5 x^{17} + 8 x^{16} - 2 x^{15} - 2 x^{14} - 10 x^{13} + 12 x^{12} + 16 x^{11} - 39 x^{10} + 26 x^{9} + 6 x^{8} - 28 x^{7} + 27 x^{6} - 6 x^{5} - 12 x^{4} + 11 x^{3} - x^{2} - 2 x + 1$ |
$18$ |
[4,7] |
$-\,3331\cdot 134479871^{2}$ |
$2$ |
$12.5569086075$ |
$669292.4998093136$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$383.239217214$ |
| 18.4.603...771.1 |
$x^{18} - 3 x^{17} + 2 x^{16} + 7 x^{15} - 16 x^{14} + 13 x^{13} + 8 x^{12} - 38 x^{11} + 62 x^{10} - 47 x^{9} - 28 x^{8} + 114 x^{7} - 123 x^{6} + 42 x^{5} + 42 x^{4} - 60 x^{3} + 33 x^{2} - 9 x + 1$ |
$18$ |
[4,7] |
$-\,131\cdot 678717521^{2}$ |
$2$ |
$12.5581298005$ |
$298181.1450293261$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$393.57161577$ |
| 18.4.997...107.1 |
$x^{18} - x^{17} - 3 x^{16} + 8 x^{15} + 5 x^{14} - 19 x^{13} + 8 x^{12} + 32 x^{11} - 16 x^{10} - 13 x^{9} + 26 x^{8} + 7 x^{7} - 8 x^{6} + 7 x^{5} + 10 x^{4} + 3 x^{3} - 2 x^{2} - 3 x - 1$ |
$18$ |
[4,7] |
$-\,7^{14}\cdot 43^{5}$ |
$2$ |
$12.9133735209$ |
$116.27117990738293$ |
|
|
? |
$C_6^3:C_6$ (as 18T282) |
trivial |
$2$ |
$10$ |
$536.666144093$ |
| 18.4.122...543.1 |
$x^{18} - 5 x^{17} + 11 x^{16} - 13 x^{15} + x^{14} + 20 x^{13} - 28 x^{12} + 10 x^{11} + 21 x^{10} - 35 x^{9} + 21 x^{8} + 10 x^{7} - 28 x^{6} + 20 x^{5} + x^{4} - 13 x^{3} + 11 x^{2} - 5 x + 1$ |
$18$ |
[4,7] |
$-\,23\cdot 2307632671^{2}$ |
$2$ |
$13.061811129$ |
$230381.317456516$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$583.930631067$ |
| 18.4.153...736.1 |
$x^{18} - 6 x^{17} + 17 x^{16} - 34 x^{15} + 57 x^{14} - 86 x^{13} + 121 x^{12} - 148 x^{11} + 136 x^{10} - 72 x^{9} - 7 x^{8} + 34 x^{7} + 13 x^{6} - 76 x^{5} + 94 x^{4} - 64 x^{3} + 24 x^{2} - 4 x - 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 353\cdot 587^{3}\cdot 8191$ |
$4$ |
$13.2257504935$ |
|
|
|
? |
$C_3^6.(C_2^6.S_6)$ (as 18T962) |
trivial |
$2$ |
$10$ |
$654.309173347$ |
| 18.4.169...264.1 |
$x^{18} - x^{14} + 3 x^{12} - 9 x^{10} - 2 x^{8} - 24 x^{6} - 9 x^{4} - x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{24}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$13.2987995223$ |
$22.58643281430495$ |
|
|
? |
$A_4\times D_6$ (as 18T60) |
trivial |
$2$ |
$10$ |
$727.594007806$ |
| 18.4.214...875.1 |
$x^{18} - 4 x^{16} - 6 x^{15} + 7 x^{14} + 20 x^{13} + 7 x^{12} - 28 x^{11} - 35 x^{10} + 4 x^{9} + 39 x^{8} + 30 x^{7} - 8 x^{6} - 25 x^{5} - 15 x^{4} + 2 x^{3} + 7 x^{2} + 4 x + 1$ |
$18$ |
[4,7] |
$-\,5^{9}\cdot 109\cdot 409^{3}\cdot 14699$ |
$4$ |
$13.4734423824$ |
$57240.550268144696$ |
|
|
? |
$C_3^6.S_4^2:D_4$ (as 18T951) |
trivial |
$2$ |
$10$ |
$810.772032377$ |
| 18.4.225...784.1 |
$x^{18} - x^{16} - 2 x^{15} + x^{14} - 3 x^{13} - x^{12} + 8 x^{11} + x^{10} - 4 x^{9} - x^{8} + 10 x^{7} + 8 x^{6} - 17 x^{5} - 14 x^{4} + 8 x^{3} + 7 x^{2} - x - 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 7^{12}\cdot 13^{4}\cdot 139$ |
$4$ |
$13.5109131439$ |
$477.0511978447962$ |
|
|
? |
$A_4^3.(C_2^2\times A_4)$ (as 18T766) |
trivial |
$2$ |
$10$ |
$914.746353585$ |
| 18.4.303...344.1 |
$x^{18} - 3 x^{16} + 6 x^{14} - 4 x^{12} - 3 x^{10} + 9 x^{8} - 15 x^{6} - 3 x^{4} + 3 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{30}\cdot 3^{24}$ |
$2$ |
$13.7365709106$ |
$22.444395485436836$ |
|
|
? |
$A_4\times D_6$ (as 18T60) |
trivial |
$2$ |
$10$ |
$1060.79230558$ |
| 18.4.303...344.2 |
$x^{18} - 6 x^{16} + 15 x^{14} - 23 x^{12} + 33 x^{10} - 48 x^{8} + 44 x^{6} - 15 x^{4} - 3 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{30}\cdot 3^{24}$ |
$2$ |
$13.7365709106$ |
|
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$10$ |
$995.284407545$ |
| 18.4.338...283.1 |
$x^{18} - x^{17} + 2 x^{16} - 3 x^{15} + 5 x^{14} - 13 x^{13} + 14 x^{12} - 2 x^{11} + 20 x^{10} - 16 x^{9} - 10 x^{8} + 6 x^{7} - 3 x^{6} - 6 x^{5} - x^{4} + 8 x^{3} + 3 x^{2} - 2 x - 1$ |
$18$ |
[4,7] |
$-\,3^{9}\cdot 107^{8}$ |
$2$ |
$13.8200295929$ |
$23.579404344249447$ |
|
|
? |
$S_3\times S_4$ (as 18T69) |
trivial |
$2$ |
$10$ |
$998.242216235$ |
| 18.4.378...111.1 |
$x^{18} + 2 x^{16} - 2 x^{15} - 5 x^{13} - 7 x^{12} - 7 x^{11} - 14 x^{10} - 7 x^{9} - 14 x^{8} - 7 x^{7} - 7 x^{6} - 5 x^{5} - 2 x^{3} + 2 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,71\cdot 2307632671^{2}$ |
$2$ |
$13.905914002$ |
$404773.91175939195$ |
|
|
✓ |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$1047.72676322$ |
| 18.4.390...896.1 |
$x^{18} - 3 x^{16} - 2 x^{14} + 12 x^{12} - 7 x^{10} - 11 x^{8} + 5 x^{6} + x^{4} - 5 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{24}\cdot 13^{12}$ |
$2$ |
$13.9316395358$ |
$18.59650768627035$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
$2$ |
$10$ |
$1241.30215537$ |
| 18.4.496...736.1 |
$x^{18} + x^{16} - x^{15} - x^{14} - 7 x^{13} - 11 x^{12} - 12 x^{11} - 49 x^{10} - 52 x^{9} - 87 x^{8} - 127 x^{7} - 112 x^{6} - 125 x^{5} - 99 x^{4} - 62 x^{3} - 37 x^{2} - 14 x - 2$ |
$18$ |
[4,7] |
$-\,2^{6}\cdot 3^{6}\cdot 7^{6}\cdot 67^{6}$ |
$4$ |
$14.1180494166$ |
$75.0199973340442$ |
|
|
? |
$C_2\times C_6^2:D_6$ (as 18T228) |
trivial |
$2$ |
$10$ |
$2626.15382099$ |
| 18.4.550...543.1 |
$x^{18} - 3 x^{17} + 3 x^{16} + 4 x^{15} - 15 x^{14} + 13 x^{13} + 17 x^{12} - 44 x^{11} + 7 x^{10} + 53 x^{9} - 30 x^{8} - 39 x^{7} + 25 x^{6} + 22 x^{5} - 8 x^{4} - 9 x^{3} + 3 x + 1$ |
$18$ |
[4,7] |
$-\,7^{15}\cdot 41^{5}$ |
$2$ |
$14.198546315$ |
$111.74675329686076$ |
|
|
? |
$C_6^3:C_6$ (as 18T282) |
trivial |
$2$ |
$10$ |
$1517.59667152$ |
| 18.4.734...375.1 |
$x^{18} + 3 x^{16} - 3 x^{14} - 3 x^{13} + 6 x^{12} - 21 x^{11} + 21 x^{10} + 2 x^{9} - 27 x^{8} + 48 x^{7} - 36 x^{6} + 6 x^{5} + 15 x^{4} - 21 x^{3} + 15 x^{2} - 6 x + 1$ |
$18$ |
[4,7] |
$-\,3^{24}\cdot 5^{9}\cdot 11^{3}$ |
$3$ |
$14.4281989664$ |
$34.10748949793651$ |
|
|
? |
$S_3^3:C_2$ (as 18T150) |
trivial |
$2$ |
$10$ |
$1741.77203769$ |
| 18.4.745...171.1 |
$x^{18} - 9 x^{16} - 3 x^{15} + 36 x^{14} + 24 x^{13} - 79 x^{12} - 81 x^{11} + 93 x^{10} + 145 x^{9} - 39 x^{8} - 132 x^{7} - 23 x^{6} + 60 x^{5} + 9 x^{4} - 16 x^{3} - 3 x^{2} + 3 x + 1$ |
$18$ |
[4,7] |
$-\,3^{18}\cdot 7^{12}\cdot 139$ |
$3$ |
$14.4403036567$ |
|
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T657) |
trivial |
$2$ |
$10$ |
$1855.03913853$ |
| 18.4.877...424.1 |
$x^{18} - 3 x^{16} - x^{14} + 2 x^{12} + 31 x^{10} - 52 x^{8} + 35 x^{6} - 12 x^{4} - 6 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{20}\cdot 307^{6}$ |
$2$ |
$14.572158894$ |
$106.53724651066035$ |
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T662) |
trivial |
$2$ |
$10$ |
$1983.80084473$ |
| 18.4.981...544.1 |
$x^{18} - 5 x^{16} + 5 x^{14} + 8 x^{12} - 8 x^{10} - 17 x^{8} + 19 x^{6} - x^{4} - 2 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{24}\cdot 37^{6}\cdot 151^{2}$ |
$3$ |
$14.6627619978$ |
|
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$10$ |
$1986.19687482$ |
| 18.4.981...544.2 |
$x^{18} + 2 x^{16} - 3 x^{14} - 9 x^{12} - x^{10} + 4 x^{8} - 10 x^{6} - 11 x^{4} + x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{24}\cdot 37^{6}\cdot 151^{2}$ |
$3$ |
$14.6627619978$ |
|
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$10$ |
$2067.74392254$ |
| 18.4.100...011.1 |
$x^{18} - 3 x^{17} + x^{16} + 8 x^{15} - 10 x^{14} - 3 x^{13} + 15 x^{12} - 8 x^{11} + 5 x^{10} - 14 x^{9} - 6 x^{8} + 62 x^{7} - 84 x^{6} + 28 x^{5} + 44 x^{4} - 60 x^{3} + 33 x^{2} - 9 x + 1$ |
$18$ |
[4,7] |
$-\,7^{12}\cdot 1091\cdot 8161^{2}$ |
$3$ |
$14.682664936$ |
$10918.99727396971$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$10$ |
$2171.02250653$ |
| 18.4.108...088.1 |
$x^{18} - 2 x^{17} + x^{16} - 4 x^{15} + 18 x^{14} - 15 x^{13} - 10 x^{12} + 22 x^{11} - 6 x^{10} - 15 x^{9} + 49 x^{8} - 64 x^{7} + 35 x^{6} - 13 x^{5} - 15 x^{4} + 23 x^{3} - 12 x^{2} + 7 x - 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 3^{11}\cdot 107^{6}$ |
$3$ |
$14.7476228674$ |
$37.4299712608451$ |
|
|
? |
$C_6^2:D_6$ (as 18T153) |
trivial |
$2$ |
$10$ |
$2175.25856413$ |
| 18.4.110...363.1 |
$x^{18} - 9 x^{17} + 41 x^{16} - 124 x^{15} + 274 x^{14} - 462 x^{13} + 605 x^{12} - 614 x^{11} + 473 x^{10} - 264 x^{9} + 102 x^{8} - 40 x^{7} + 43 x^{6} - 50 x^{5} + 32 x^{4} - 7 x^{3} - 7 x^{2} + 6 x - 1$ |
$18$ |
[4,7] |
$-\,23^{6}\cdot 97^{4}\cdot 84307$ |
$3$ |
$14.7595528131$ |
$29397.488238864145$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$10$ |
$1851.9190837$ |
| 18.4.113...751.1 |
$x^{18} - 5 x^{17} + 10 x^{16} - 12 x^{15} + 41 x^{13} - 90 x^{12} + 125 x^{11} - 171 x^{10} + 201 x^{9} - 171 x^{8} + 125 x^{7} - 90 x^{6} + 41 x^{5} - 12 x^{3} + 10 x^{2} - 5 x + 1$ |
$18$ |
[4,7] |
$-\,3\cdot 11^{4}\cdot 37^{5}\cdot 139^{4}$ |
$4$ |
$14.783063223$ |
$1515.2388979303266$ |
|
|
? |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$10$ |
$2637.81846478$ |
| 18.4.115...187.1 |
$x^{18} - 2 x^{17} - x^{16} + 3 x^{15} + 13 x^{14} - 22 x^{13} - 28 x^{12} + 63 x^{11} + 27 x^{10} - 98 x^{9} - 22 x^{8} + 99 x^{7} + 28 x^{6} - 60 x^{5} - 26 x^{4} + 17 x^{3} + 9 x^{2} - x - 1$ |
$18$ |
[4,7] |
$-\,31^{8}\cdot 67^{5}$ |
$2$ |
$14.7934824293$ |
$436.76745746862207$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$2$ |
$10$ |
$1878.68485993$ |
| 18.4.131...064.1 |
$x^{18} - 2 x^{17} - 2 x^{16} + 13 x^{15} - 16 x^{14} - 17 x^{13} + 62 x^{12} - 44 x^{11} - 62 x^{10} + 115 x^{9} - 51 x^{8} - 77 x^{7} + 114 x^{6} + 7 x^{5} - 62 x^{4} + 8 x^{3} + 7 x^{2} - 3 x + 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 13^{2}\cdot 37^{6}\cdot 61^{2}\cdot 199$ |
$5$ |
$14.9030821995$ |
$3835.75321455073$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$10$ |
$2598.22327083$ |
| 18.4.141...536.1 |
$x^{18} - 3 x^{16} + 6 x^{14} + 3 x^{12} + 30 x^{10} + 39 x^{8} - 6 x^{6} - 21 x^{4} - 3 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{6}\cdot 3^{20}\cdot 43^{6}$ |
$3$ |
$14.9612384443$ |
|
|
|
? |
$S_4^2:C_2^2$ (as 18T370) |
trivial |
$2$ |
$10$ |
$2708.15340583$ |
| 18.4.154...391.1 |
$x^{18} - 8 x^{16} - 5 x^{15} + 27 x^{14} + 36 x^{13} - 49 x^{12} - 95 x^{11} + 31 x^{10} + 147 x^{9} + 7 x^{8} - 126 x^{7} - 35 x^{6} + 76 x^{5} + 17 x^{4} - 24 x^{3} - 3 x^{2} + 5 x - 1$ |
$18$ |
[4,7] |
$-\,11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 151$ |
$4$ |
$15.0379852577$ |
$4358.715530432155$ |
|
|
? |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$10$ |
$4246.06379679$ |
| 18.4.159...536.1 |
$x^{18} - 6 x^{16} + 13 x^{14} - 13 x^{12} + 4 x^{10} + 12 x^{8} - 36 x^{6} + 56 x^{4} - 48 x^{2} + 16$ |
$18$ |
[4,7] |
$-\,2^{20}\cdot 3^{6}\cdot 113^{6}$ |
$3$ |
$15.0618276024$ |
$111.95207035008517$ |
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T662) |
trivial |
$2$ |
$10$ |
$2810.65653223$ |
| 18.4.178...443.1 |
$x^{18} + 2 x^{16} - 7 x^{15} + 3 x^{14} - 12 x^{13} + 24 x^{12} - 16 x^{11} + 28 x^{10} - 44 x^{9} + 27 x^{8} - 28 x^{7} + 39 x^{6} - 19 x^{5} + 8 x^{4} - 12 x^{3} + 5 x^{2} + 3 x - 1$ |
$18$ |
[4,7] |
$-\,11\cdot 23^{6}\cdot 43^{2}\cdot 347^{2}\cdot 4937$ |
$5$ |
$15.1604519887$ |
$136518.27416503624$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$10$ |
$2695.97159414$ |
| 18.4.183...224.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 47 x^{15} + 75 x^{14} - 81 x^{13} + 36 x^{12} + 45 x^{11} - 138 x^{10} + 169 x^{9} - 138 x^{8} + 45 x^{7} + 36 x^{6} - 81 x^{5} + 75 x^{4} - 47 x^{3} + 21 x^{2} - 6 x + 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 19$ |
$4$ |
$15.1818010913$ |
|
|
|
? |
$A_4^3.C_2^3:A_4$ (as 18T839) |
trivial |
$2$ |
$10$ |
$3117.95057969$ |
| 18.4.197...824.1 |
$x^{18} - 3 x^{16} + 4 x^{14} - 16 x^{12} + 14 x^{10} + 26 x^{8} - 12 x^{6} - 8 x^{4} + 9 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{26}\cdot 37^{6}\cdot 107^{2}$ |
$3$ |
$15.2420049833$ |
|
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$10$ |
$4535.3857477$ |
| 18.4.221...000.1 |
$x^{18} - 3 x^{17} + 3 x^{16} - 2 x^{15} - x^{14} + 9 x^{13} - 14 x^{12} + 18 x^{11} - 23 x^{10} + 26 x^{9} - 30 x^{8} + 24 x^{7} - 21 x^{6} + 19 x^{5} - 8 x^{4} + 5 x^{3} - 5 x^{2} + 4 x - 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 5^{9}\cdot 6521^{3}$ |
$3$ |
$15.3423080799$ |
$510.7249749131131$ |
|
|
? |
$S_3\wr D_4$ (as 18T555) |
trivial |
$2$ |
$10$ |
$3192.51916324$ |
| 18.4.231...096.1 |
$x^{18} + 2 x^{16} - 2 x^{15} - 3 x^{14} + 6 x^{13} - 11 x^{12} + 24 x^{11} - 39 x^{10} + 68 x^{9} - 102 x^{8} + 120 x^{7} - 134 x^{6} + 114 x^{5} - 45 x^{4} - 8 x^{3} + 15 x^{2} - 6 x + 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 37^{6}\cdot 151^{3}$ |
$3$ |
$15.3789515324$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T486) |
trivial |
$2$ |
$10$ |
$3147.19977452$ |
| 18.4.231...096.2 |
$x^{18} - 2 x^{17} - 2 x^{16} - 4 x^{15} + 25 x^{14} - 2 x^{13} - 27 x^{12} - 42 x^{11} + 65 x^{10} + 42 x^{9} - 82 x^{8} + 20 x^{7} + 34 x^{6} - 38 x^{5} + 3 x^{4} + 16 x^{3} - 5 x^{2} - 2 x + 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 37^{6}\cdot 151^{3}$ |
$3$ |
$15.3789515324$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T885) |
trivial |
$2$ |
$10$ |
$3229.31541588$ |
| 18.4.231...096.3 |
$x^{18} - 2 x^{17} - 2 x^{16} + 8 x^{15} - 19 x^{14} + 18 x^{13} - 3 x^{12} - 26 x^{11} + 49 x^{10} - 40 x^{9} - 2 x^{8} + 72 x^{7} - 126 x^{6} + 142 x^{5} - 121 x^{4} + 74 x^{3} - 33 x^{2} + 10 x - 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 37^{6}\cdot 151^{3}$ |
$3$ |
$15.3789515324$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T885) |
trivial |
$2$ |
$10$ |
$3273.91491754$ |
| 18.4.242...752.1 |
$x^{18} - 6 x^{16} + 18 x^{14} - 38 x^{12} + 57 x^{10} - 60 x^{8} + 37 x^{6} + 6 x^{4} - 24 x^{2} + 8$ |
$18$ |
[4,7] |
$-\,2^{33}\cdot 3^{24}$ |
$2$ |
$15.4187795211$ |
$20.58160140743025$ |
|
|
? |
$S_3\times A_4$ (as 18T32) |
trivial |
$2$ |
$10$ |
$3365.40255182$ |
| 18.4.259...367.1 |
$x^{18} - 8 x^{17} + 23 x^{16} - 23 x^{15} - 21 x^{14} + 81 x^{13} - 69 x^{12} - 90 x^{11} + 270 x^{10} - 157 x^{9} - 204 x^{8} + 298 x^{7} - 22 x^{6} - 170 x^{5} + 102 x^{4} + 5 x^{3} - 25 x^{2} + 9 x - 1$ |
$18$ |
[4,7] |
$-\,23^{7}\cdot 59^{4}\cdot 251^{2}$ |
$3$ |
$15.4779666966$ |
$583.6154555869815$ |
|
|
? |
$S_4^3.S_4$ (as 18T884) |
trivial |
$2$ |
$10$ |
$2767.55771655$ |
| 18.4.259...367.2 |
$x^{18} - 3 x^{17} - 3 x^{16} + 20 x^{15} - 11 x^{14} - 39 x^{13} + 43 x^{12} + 20 x^{11} - 20 x^{10} - 33 x^{9} - 15 x^{8} + 94 x^{7} - 43 x^{6} - 39 x^{5} + 25 x^{4} + 11 x^{3} - 7 x^{2} - x + 1$ |
$18$ |
[4,7] |
$-\,23^{7}\cdot 59^{4}\cdot 251^{2}$ |
$3$ |
$15.4779666966$ |
$583.6154555869815$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T773) |
trivial |
$2$ |
$10$ |
$3371.21728578$ |
| 18.4.266...007.1 |
$x^{18} - 5 x^{15} + 3 x^{12} + 7 x^{9} - 13 x^{6} - 8 x^{3} - 1$ |
$18$ |
[4,7] |
$-\,3^{6}\cdot 7^{9}\cdot 67^{6}$ |
$3$ |
$15.4981920814$ |
$61.01288466109334$ |
|
|
|
$C_2\times C_6^2:D_6$ (as 18T228) |
trivial |
$2$ |
$10$ |
$5730.4211423$ |
| 18.4.280...912.1 |
$x^{18} - 2 x^{17} + 5 x^{16} - 8 x^{15} + 14 x^{14} - 24 x^{13} + 18 x^{12} - 10 x^{11} + 3 x^{10} - 6 x^{9} + 21 x^{8} - 14 x^{7} + 10 x^{6} - 8 x^{5} + x^{4} - 6 x^{3} + 11 x^{2} - 6 x + 1$ |
$18$ |
[4,7] |
$-\,2^{27}\cdot 7^{3}\cdot 31^{3}\cdot 127^{3}$ |
$4$ |
$15.5449347214$ |
$469.54446008871196$ |
|
|
? |
$S_3\wr D_4$ (as 18T555) |
trivial |
$2$ |
$10$ |
$3637.80520981$ |
| 18.4.310...176.1 |
$x^{18} - 9 x^{17} + 42 x^{16} - 132 x^{15} + 309 x^{14} - 567 x^{13} + 842 x^{12} - 1035 x^{11} + 1080 x^{10} - 989 x^{9} + 834 x^{8} - 675 x^{7} + 520 x^{6} - 357 x^{5} + 195 x^{4} - 74 x^{3} + 12 x^{2} + 3 x - 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 3^{24}\cdot 41959$ |
$3$ |
$15.6320266549$ |
|
|
|
|
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$2$ |
$10$ |
$4354.75390036$ |
| 18.4.316...016.1 |
$x^{18} + 2 x^{12} - 6 x^{10} + 9 x^{8} - 16 x^{6} + 11 x^{4} - 3 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 367^{2}\cdot 299401^{2}$ |
$3$ |
$15.6482391458$ |
|
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$10$ |
$3152.93462735$ |
| 18.4.322...824.1 |
$x^{18} - 4 x^{16} + 10 x^{14} - 16 x^{12} + 4 x^{10} + 20 x^{8} - 26 x^{6} + 14 x^{4} - 5 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 31^{6}\cdot 61^{4}$ |
$3$ |
$15.6635617531$ |
|
|
|
? |
$A_4^3:D_6$ (as 18T632) |
trivial |
$2$ |
$10$ |
$3213.27559105$ |
| 18.4.322...824.2 |
$x^{18} + x^{16} - 3 x^{14} - 12 x^{12} - 17 x^{10} - 4 x^{8} + 14 x^{6} + 14 x^{4} + 6 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{18}\cdot 31^{6}\cdot 61^{4}$ |
$3$ |
$15.6635617531$ |
|
|
|
? |
$A_4^3:D_6$ (as 18T632) |
trivial |
$2$ |
$10$ |
$3429.63729039$ |
| 18.4.329...112.1 |
$x^{18} - 2 x^{17} - x^{16} + 12 x^{14} - 12 x^{13} - 10 x^{12} + 4 x^{11} + 42 x^{10} - 34 x^{9} - 20 x^{8} + 16 x^{7} + 18 x^{6} - 24 x^{5} + 8 x^{4} + 6 x^{3} - 9 x^{2} + 2 x + 1$ |
$18$ |
[4,7] |
$-\,2^{20}\cdot 37^{6}\cdot 107^{3}$ |
$3$ |
$15.6834755277$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T486) |
trivial |
$2$ |
$10$ |
$6053.9754173$ |
| 18.4.338...944.1 |
$x^{18} - x^{16} - 7 x^{14} + 19 x^{12} + 5 x^{10} - 42 x^{8} - 11 x^{6} + 19 x^{4} + 9 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{6}\cdot 7^{12}\cdot 113^{2}\cdot 547^{2}$ |
$4$ |
$15.7066174544$ |
$1819.539859819959$ |
|
|
? |
$S_4^3.C_6$ (as 18T768) |
trivial |
$2$ |
$10$ |
$4448.86682201$ |
| 18.4.351...696.1 |
$x^{18} - x^{16} - 5 x^{14} + 5 x^{12} + 7 x^{10} + 2 x^{8} - 26 x^{6} + 23 x^{4} - 8 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{22}\cdot 307^{6}$ |
$2$ |
$15.7388021302$ |
|
|
|
? |
$C_2^2:A_4^2:D_6$ (as 18T521) |
trivial |
$2$ |
$10$ |
$4629.22495617$ |
