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 |
18.2.483...741.1 |
$x^{18} - 3 x^{17} + 2 x^{16} - 5 x^{15} + 15 x^{14} - 6 x^{13} + 2 x^{12} - 29 x^{11} + 17 x^{10} + 11 x^{9} + 17 x^{8} - 29 x^{7} + 2 x^{6} - 6 x^{5} + 15 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$23^{6}\cdot 59^{2}\cdot 149\cdot 251^{2}$ |
$4$ |
$10.9152477415$ |
$7123.934516824253$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$9$ |
$67.155663406$ |
18.2.642...321.1 |
$x^{18} - 2 x^{17} - x^{16} + 6 x^{15} - 4 x^{14} - 10 x^{13} + 11 x^{12} + 9 x^{11} - 16 x^{10} - 5 x^{9} + 16 x^{8} + 5 x^{7} - 15 x^{6} - 5 x^{5} + 12 x^{4} + x^{3} - 5 x^{2} + 1$ |
$18$ |
[2,8] |
$23^{6}\cdot 208333^{2}$ |
$2$ |
$11.0887450226$ |
$2188.985838236511$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$9$ |
$79.1741198129$ |
18.2.718...137.1 |
$x^{18} - 5 x^{17} + 12 x^{16} - 22 x^{15} + 39 x^{14} - 63 x^{13} + 85 x^{12} - 97 x^{11} + 99 x^{10} - 98 x^{9} + 91 x^{8} - 71 x^{7} + 53 x^{6} - 44 x^{5} + 29 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$ |
$18$ |
[2,8] |
$7^{12}\cdot 113\cdot 2143^{2}$ |
$3$ |
$11.1576358018$ |
$1800.7316613040525$ |
|
|
? |
$C_2\times S_4^3.A_4$ (as 18T879) |
trivial |
$2$ |
$9$ |
$84.7255286435$ |
18.2.867...481.1 |
$x^{18} - x^{17} + 2 x^{16} - 5 x^{15} + x^{14} - 6 x^{13} + 2 x^{12} + 4 x^{10} + 3 x^{9} + 4 x^{8} + 2 x^{6} - 6 x^{5} + x^{4} - 5 x^{3} + 2 x^{2} - x + 1$ |
$18$ |
[2,8] |
$41^{3}\cdot 11221481^{2}$ |
$2$ |
$11.2755106154$ |
$21449.492324994546$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$9$ |
$93.6283865561$ |
18.2.897...489.1 |
$x^{18} - x^{17} + 3 x^{15} - x^{14} + x^{13} + 7 x^{12} + 2 x^{11} + 3 x^{10} + 11 x^{9} + 3 x^{8} + 2 x^{7} + 7 x^{6} + x^{5} - x^{4} + 3 x^{3} - x + 1$ |
$18$ |
[2,8] |
$7^{12}\cdot 41^{3}\cdot 97^{2}$ |
$3$ |
$11.2966173384$ |
$230.76847964399414$ |
|
|
✓ |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$9$ |
$95.2465332123$ |
18.2.109...009.1 |
$x^{18} - 2 x^{17} + 4 x^{15} - 7 x^{14} + x^{13} + 7 x^{12} + 2 x^{11} - 10 x^{10} + x^{9} + 20 x^{8} - 22 x^{7} - 2 x^{6} + 7 x^{5} + 2 x^{4} - 10 x^{3} + 11 x^{2} - 5 x + 1$ |
$18$ |
[2,8] |
$43^{2}\cdot 83\cdot 107\cdot 311^{2}\cdot 2621^{2}$ |
$5$ |
$11.4198009312$ |
$557928.9127415785$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$9$ |
$106.811954559$ |
18.2.109...837.1 |
$x^{18} - x^{17} + 3 x^{16} - 5 x^{15} + 4 x^{14} - 6 x^{13} - 5 x^{12} - 2 x^{11} - 16 x^{10} + x^{9} - 16 x^{8} - 2 x^{7} - 5 x^{6} - 6 x^{5} + 4 x^{4} - 5 x^{3} + 3 x^{2} - x + 1$ |
$18$ |
[2,8] |
$53\cdot 453771377^{2}$ |
$2$ |
$11.4199418508$ |
$155080.2469078509$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$9$ |
$106.041791279$ |
18.2.109...889.1 |
$x^{18} - x^{16} - 4 x^{15} - x^{14} + 3 x^{13} + 9 x^{12} + x^{11} - 2 x^{10} - 13 x^{9} - 2 x^{8} + x^{7} + 9 x^{6} + 3 x^{5} - x^{4} - 4 x^{3} - x^{2} + 1$ |
$18$ |
[2,8] |
$23^{6}\cdot 379^{2}\cdot 719^{2}$ |
$3$ |
$11.4245490763$ |
$2503.5021469932876$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$9$ |
$107.172918917$ |
18.2.116...689.1 |
$x^{18} - 4 x^{17} + 4 x^{16} + 9 x^{15} - 27 x^{14} + 17 x^{13} + 26 x^{12} - 46 x^{11} + 12 x^{10} + 20 x^{9} - 12 x^{8} + 15 x^{7} - 48 x^{6} + 48 x^{5} - x^{4} - 29 x^{3} + 20 x^{2} - 5 x + 1$ |
$18$ |
[2,8] |
$5881\cdot 44555813^{2}$ |
$2$ |
$11.4628396707$ |
$511891.332465202$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$9$ |
$111.7260845$ |
18.2.153...696.1 |
$x^{18} + 5 x^{16} + 5 x^{14} - 8 x^{12} - 8 x^{10} + 17 x^{8} + 19 x^{6} + x^{4} - 2 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 37^{6}\cdot 151^{2}$ |
$3$ |
$11.6378419101$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T483) |
trivial |
$2$ |
$9$ |
$139.095050977$ |
18.2.184...177.1 |
$x^{18} - 2 x^{17} + 4 x^{15} - 5 x^{14} - 6 x^{13} + 18 x^{12} - x^{11} - 18 x^{10} + 9 x^{9} + 13 x^{8} - 25 x^{7} - 6 x^{6} + 23 x^{5} + 10 x^{4} - 11 x^{3} - 5 x^{2} + x + 1$ |
$18$ |
[2,8] |
$7^{4}\cdot 23^{6}\cdot 83^{2}\cdot 7537$ |
$4$ |
$11.7581679653$ |
$10035.78253052546$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$9$ |
$146.457400567$ |
18.2.210...728.1 |
$x^{18} - 5 x^{17} + 6 x^{16} + 9 x^{15} - 20 x^{14} - 15 x^{13} + 52 x^{12} - 6 x^{11} - 57 x^{10} + 25 x^{9} + 37 x^{8} - 29 x^{7} - 14 x^{6} + 24 x^{5} + x^{4} - 13 x^{3} + 4 x + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 7^{12}\cdot 13^{5}$ |
$3$ |
$11.8444272855$ |
$62.04614678346354$ |
|
|
? |
$C_6^3:C_6$ (as 18T282) |
trivial |
$2$ |
$9$ |
$159.599072679$ |
18.2.212...913.1 |
$x^{18} - 3 x^{17} + 5 x^{16} - 6 x^{15} + 5 x^{14} + x^{13} - 9 x^{12} + 18 x^{11} - 26 x^{10} + 29 x^{9} - 26 x^{8} + 18 x^{7} - 9 x^{6} + x^{5} + 5 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$7^{12}\cdot 41^{2}\cdot 97^{3}$ |
$3$ |
$11.8501956854$ |
$230.76847964399414$ |
|
|
? |
$D_6\wr C_3$ (as 18T472) |
trivial |
$2$ |
$9$ |
$158.336114215$ |
18.2.246...625.1 |
$x^{18} - 2 x^{17} + 4 x^{16} - 7 x^{15} + 7 x^{14} - 10 x^{13} + 15 x^{12} - 23 x^{11} + 21 x^{10} - 13 x^{9} + 21 x^{8} - 23 x^{7} + 15 x^{6} - 10 x^{5} + 7 x^{4} - 7 x^{3} + 4 x^{2} - 2 x + 1$ |
$18$ |
[2,8] |
$5^{8}\cdot 83^{6}\cdot 193$ |
$3$ |
$11.948721501$ |
$370.0817794070252$ |
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T662) |
trivial |
$2$ |
$9$ |
$174.087268526$ |
18.2.299...000.1 |
$x^{18} - 5 x^{17} + 14 x^{16} - 25 x^{15} + 23 x^{14} + 21 x^{13} - 137 x^{12} + 330 x^{11} - 559 x^{10} + 747 x^{9} - 826 x^{8} + 768 x^{7} - 606 x^{6} + 405 x^{5} - 226 x^{4} + 102 x^{3} - 35 x^{2} + 8 x - 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 5^{3}\cdot 37^{6}\cdot 151^{2}$ |
$4$ |
$12.0788092314$ |
$265.31450970051856$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$9$ |
$193.593644649$ |
18.2.308...216.1 |
$x^{18} - 2 x^{17} + 3 x^{16} - 2 x^{15} + 6 x^{14} - 12 x^{13} + 14 x^{12} + 2 x^{11} - 24 x^{10} + 36 x^{9} - 24 x^{8} + 2 x^{7} + 14 x^{6} - 12 x^{5} + 6 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$18$ |
[2,8] |
$2^{20}\cdot 37^{6}\cdot 107^{2}$ |
$3$ |
$12.0975873723$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T483) |
trivial |
$2$ |
$9$ |
$333.51149291$ |
18.2.350...173.1 |
$x^{18} + x^{16} - 2 x^{15} + 4 x^{13} + 5 x^{12} - 25 x^{11} + x^{10} + 27 x^{9} + 41 x^{8} - 93 x^{7} + 10 x^{6} + 54 x^{5} - 9 x^{4} - 21 x^{3} + 2 x^{2} + 4 x - 1$ |
$18$ |
[2,8] |
$11^{7}\cdot 23^{9}$ |
$2$ |
$12.1856854158$ |
$34.833107461122644$ |
|
|
? |
$C_2\times C_3^3:S_4$ (as 18T301) |
trivial |
$2$ |
$9$ |
$213.366849664$ |
18.2.380...000.1 |
$x^{18} - 2 x^{17} + 2 x^{16} - 3 x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 10 x^{11} + 2 x^{10} - 3 x^{9} - 2 x^{8} - 10 x^{7} - 2 x^{6} - 4 x^{5} - 2 x^{4} - 3 x^{3} - 2 x^{2} - 2 x - 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 5^{9}\cdot 41^{6}$ |
$3$ |
$12.2395735055$ |
$22.728124217737328$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$9$ |
$225.62524734$ |
18.2.433...096.1 |
$x^{18} - x^{15} - 8 x^{12} + 17 x^{9} - 8 x^{6} - x^{3} + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{6}\cdot 29^{9}$ |
$3$ |
$12.3289497064$ |
$18.65475810617763$ |
|
|
? |
$S_3\times D_6$ (as 18T29) |
trivial |
$2$ |
$9$ |
$230.414214587$ |
18.2.440...413.1 |
$x^{18} - 5 x^{17} + 14 x^{16} - 27 x^{15} + 44 x^{14} - 68 x^{13} + 98 x^{12} - 117 x^{11} + 102 x^{10} - 50 x^{9} - 18 x^{8} + 74 x^{7} - 101 x^{6} + 95 x^{5} - 69 x^{4} + 39 x^{3} - 17 x^{2} + 5 x - 1$ |
$18$ |
[2,8] |
$23^{7}\cdot 59^{3}\cdot 251^{2}$ |
$3$ |
$12.3405137584$ |
$1278.0820739142598$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$9$ |
$226.057810023$ |
18.2.625...168.1 |
$x^{18} + 2 x^{16} - x^{15} + 2 x^{14} - 2 x^{13} + 2 x^{12} - 4 x^{11} + 2 x^{10} - 5 x^{9} + 2 x^{8} - 4 x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{4} - x^{3} + 2 x^{2} + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 37^{7}\cdot 401^{2}$ |
$3$ |
$12.582911829$ |
$476.8811357378442$ |
|
|
✓ |
$S_4^3.S_4$ (as 18T884) |
trivial |
$2$ |
$9$ |
$294.2519764$ |
18.2.631...281.1 |
$x^{18} - x^{17} + 2 x^{16} - 4 x^{15} + 6 x^{14} - 20 x^{13} + 22 x^{12} - 27 x^{11} + 19 x^{10} - 11 x^{9} + 16 x^{8} - 5 x^{7} + 2 x^{6} - 5 x^{5} - 9 x^{4} - 7 x^{3} - x^{2} + 2 x + 1$ |
$18$ |
[2,8] |
$23^{7}\cdot 2647^{3}$ |
$2$ |
$12.5898285346$ |
$246.74075463935827$ |
|
|
? |
$S_4^3.S_4$ (as 18T880) |
trivial |
$2$ |
$9$ |
$291.939159084$ |
18.2.645...809.1 |
$x^{18} - x^{17} + x^{16} - x^{15} + 9 x^{13} - 17 x^{12} + 12 x^{11} - x^{10} - 15 x^{9} + 47 x^{8} - 76 x^{7} + 56 x^{6} + 14 x^{5} - 70 x^{4} + 68 x^{3} - 34 x^{2} + 9 x - 1$ |
$18$ |
[2,8] |
$19\cdot 31^{2}\cdot 59\cdot 7742417^{2}$ |
$4$ |
$12.6055011861$ |
$518706.7892046527$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$9$ |
$308.996338318$ |
18.2.733...089.1 |
$x^{18} - 5 x^{16} - 7 x^{15} + 10 x^{14} + 25 x^{13} + x^{12} - 36 x^{11} - 15 x^{10} + 36 x^{9} + 20 x^{8} - 40 x^{7} - 43 x^{6} + 7 x^{5} + 28 x^{4} + 8 x^{3} - 7 x^{2} - 5 x - 1$ |
$18$ |
[2,8] |
$11^{6}\cdot 23^{10}$ |
$2$ |
$12.6953991394$ |
$63.43667197535253$ |
|
|
? |
$A_4^3:S_4$ (as 18T713) |
trivial |
$2$ |
$9$ |
$305.528305053$ |
18.2.785...649.1 |
$x^{18} - 3 x^{17} + 4 x^{16} - 2 x^{15} - 9 x^{14} + 22 x^{13} - 21 x^{12} + 9 x^{11} + 15 x^{10} - 31 x^{9} + 15 x^{8} + 9 x^{7} - 21 x^{6} + 22 x^{5} - 9 x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$7^{14}\cdot 41^{5}$ |
$2$ |
$12.7436545809$ |
$111.74675329686076$ |
|
|
? |
$C_6^3:C_6$ (as 18T282) |
trivial |
$2$ |
$9$ |
$355.232713744$ |
18.2.791...504.1 |
$x^{18} - 3 x^{16} + x^{14} + 8 x^{12} - 20 x^{10} + 25 x^{8} - 17 x^{6} + 5 x^{4} + 2 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 7^{6}\cdot 37^{6}$ |
$3$ |
$12.7486221759$ |
$36.12863417970694$ |
|
|
? |
$C_6^2:D_6$ (as 18T154) |
trivial |
$2$ |
$9$ |
$351.495037427$ |
18.2.802...089.1 |
$x^{18} - x^{17} + 4 x^{16} - x^{15} + 6 x^{14} - 4 x^{13} + 10 x^{12} - 6 x^{11} + x^{10} - 3 x^{9} + 2 x^{8} - 7 x^{7} - 10 x^{6} + x^{5} - 9 x^{4} - 4 x^{2} - 2 x - 1$ |
$18$ |
[2,8] |
$31^{6}\cdot 67^{6}$ |
$2$ |
$12.7588686215$ |
$185.1014620777746$ |
|
|
? |
$A_4^3.S_4$ (as 18T711) |
trivial |
$2$ |
$9$ |
$326.952777148$ |
18.2.844...312.1 |
$x^{18} + 3 x^{16} - 4 x^{15} + 12 x^{14} + 6 x^{13} + 47 x^{12} - 6 x^{11} + 24 x^{10} - 88 x^{9} - 21 x^{8} - 120 x^{7} - 40 x^{6} - 60 x^{5} - 27 x^{4} - 10 x^{3} - 9 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{6}\cdot 3^{18}\cdot 23^{7}$ |
$3$ |
$12.7945616635$ |
|
|
|
? |
$C_2^7.C_6^2:D_6$ (as 18T734) |
trivial |
$2$ |
$9$ |
$385.83435797$ |
18.2.859...768.1 |
$x^{18} - 8 x^{17} + 32 x^{16} - 83 x^{15} + 154 x^{14} - 216 x^{13} + 232 x^{12} - 192 x^{11} + 130 x^{10} - 101 x^{9} + 130 x^{8} - 192 x^{7} + 232 x^{6} - 216 x^{5} + 154 x^{4} - 83 x^{3} + 32 x^{2} - 8 x + 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 13^{3}\cdot 37^{6}\cdot 61^{2}$ |
$4$ |
$12.8070108912$ |
$271.90933608453196$ |
|
|
? |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$9$ |
$365.762580816$ |
18.2.103...441.1 |
$x^{18} - 4 x^{16} - 2 x^{15} + 6 x^{14} + x^{13} - 6 x^{12} - 8 x^{11} - 3 x^{10} - x^{9} - 2 x^{8} - 10 x^{7} - 3 x^{6} - 5 x^{5} - 12 x^{4} - 6 x^{3} - 3 x^{2} - 3 x - 1$ |
$18$ |
[2,8] |
$23^{6}\cdot 101^{2}\cdot 8263^{2}$ |
$3$ |
$12.9374648131$ |
$4381.204058247002$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$9$ |
$432.085458037$ |
18.2.104...408.1 |
$x^{18} + 2 x^{16} - 6 x^{15} + 2 x^{14} - 10 x^{13} + 15 x^{12} - 8 x^{11} + 19 x^{10} - 20 x^{9} + 10 x^{8} - 18 x^{7} + 14 x^{6} - 6 x^{5} + 9 x^{4} - 6 x^{3} + 2 x^{2} - 2 x + 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 11\cdot 43\cdot 587^{3}\cdot 4153$ |
$5$ |
$12.944735568$ |
|
|
|
? |
$C_3^6.(C_2^6.S_6)$ (as 18T962) |
trivial |
$2$ |
$9$ |
$410.045077467$ |
18.2.107...649.1 |
$x^{18} - 2 x^{17} + 4 x^{16} - 9 x^{15} + 15 x^{14} - 22 x^{13} + 35 x^{12} - 47 x^{11} + 53 x^{10} - 67 x^{9} + 66 x^{8} - 59 x^{7} + 56 x^{6} - 39 x^{5} + 26 x^{4} - 17 x^{3} + 7 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$23^{6}\cdot 317^{2}\cdot 2687^{2}$ |
$3$ |
$12.966850179$ |
$4426.162785076934$ |
|
|
? |
$A_4^3.(C_2\times S_4)$ (as 18T776) |
trivial |
$2$ |
$9$ |
$414.56387322$ |
18.2.108...696.1 |
$x^{18} + 5 x^{16} + x^{14} - 36 x^{12} - 88 x^{10} - 99 x^{8} - 69 x^{6} - 35 x^{4} - 10 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 37^{6}\cdot 401^{2}$ |
$3$ |
$12.9718574447$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T483) |
trivial |
$2$ |
$9$ |
$417.015615194$ |
18.2.111...312.1 |
$x^{18} - 4 x^{17} + 8 x^{16} - 8 x^{15} + x^{14} + 8 x^{13} - 10 x^{12} + 2 x^{11} + 6 x^{10} - 4 x^{9} - 4 x^{8} + 10 x^{7} - 6 x^{6} + 4 x^{5} + x^{4} + 2 x^{2} + 1$ |
$18$ |
[2,8] |
$2^{27}\cdot 97^{6}$ |
$2$ |
$12.9957766336$ |
$27.85677655436824$ |
|
|
|
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$9$ |
$473.705580838$ |
18.2.131...961.1 |
$x^{18} - 5 x^{16} - 3 x^{15} + 8 x^{14} + 10 x^{13} + 4 x^{12} - 4 x^{11} - 21 x^{10} - 15 x^{9} + 15 x^{8} + 7 x^{7} - 8 x^{6} + 8 x^{5} + 5 x^{4} - 3 x^{3} + x^{2} + 1$ |
$18$ |
[2,8] |
$3^{12}\cdot 23^{4}\cdot 31^{6}$ |
$3$ |
$13.1161866077$ |
$122.8041869892042$ |
|
|
? |
$A_4^3:S_4$ (as 18T718) |
trivial |
$2$ |
$9$ |
$505.71690915$ |
18.2.139...829.1 |
$x^{18} - 7 x^{17} + 21 x^{16} - 35 x^{15} + 41 x^{14} - 54 x^{13} + 81 x^{12} - 80 x^{11} + 28 x^{10} + 12 x^{9} + 7 x^{8} - 14 x^{7} - 33 x^{6} + 46 x^{5} - 3 x^{4} - 27 x^{3} + 21 x^{2} - 7 x + 1$ |
$18$ |
[2,8] |
$3^{6}\cdot 29\cdot 433^{6}$ |
$3$ |
$13.1557026925$ |
$194.0901852232616$ |
|
|
? |
$C_2^4.S_4^2:C_2^2$ (as 18T691) |
trivial |
$2$ |
$9$ |
$511.222708619$ |
18.2.145...272.1 |
$x^{18} + 4 x^{16} + 3 x^{14} - 12 x^{12} + 7 x^{10} + 6 x^{8} - 11 x^{6} + 4 x^{4} + 4 x^{2} - 2$ |
$18$ |
[2,8] |
$2^{33}\cdot 19^{8}$ |
$2$ |
$13.1893459319$ |
$15.533349925214662$ |
|
|
? |
$S_3^2$ (as 18T9) |
trivial |
$2$ |
$9$ |
$965.073685258$ |
18.2.169...264.1 |
$x^{18} - x^{14} - 3 x^{12} - 9 x^{10} + 2 x^{8} - 24 x^{6} + 9 x^{4} - x^{2} - 1$ |
$18$ |
[2,8] |
$2^{24}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$13.2987995223$ |
$20.122224041627174$ |
|
|
? |
$S_3\times A_4$ (as 18T31) |
trivial |
$2$ |
$9$ |
$522.985932438$ |
18.2.215...493.1 |
$x^{18} + 6 x^{16} - 7 x^{15} + 15 x^{14} - 35 x^{13} + 39 x^{12} - 70 x^{11} + 91 x^{10} - 95 x^{9} + 120 x^{8} - 110 x^{7} + 92 x^{6} - 82 x^{5} + 49 x^{4} - 28 x^{3} + 15 x^{2} - 3 x + 1$ |
$18$ |
[2,8] |
$257^{6}\cdot 749557$ |
$2$ |
$13.4799747288$ |
$13879.342527655985$ |
|
|
? |
$C_3^6.C_2\wr A_4.C_2$ (as 18T930) |
trivial |
$2$ |
$9$ |
$627.643142925$ |
18.2.219...856.1 |
$x^{18} + x^{16} - 5 x^{14} - 5 x^{12} + 7 x^{10} - 2 x^{8} - 26 x^{6} - 23 x^{4} - 8 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 307^{6}$ |
$2$ |
$13.4919934234$ |
$61.99002107508509$ |
|
|
? |
$C_2^2:A_4^2:S_3$ (as 18T437) |
trivial |
$2$ |
$9$ |
$730.001621669$ |
18.2.227...125.1 |
$x^{18} - 2 x^{17} - x^{16} + 6 x^{15} - 9 x^{14} + 6 x^{13} + 13 x^{11} - 52 x^{10} + 77 x^{9} - 52 x^{8} + 13 x^{7} + 6 x^{5} - 9 x^{4} + 6 x^{3} - x^{2} - 2 x + 1$ |
$18$ |
[2,8] |
$5^{9}\cdot 13^{6}\cdot 17^{6}$ |
$3$ |
$13.5191408688$ |
$33.24154027718932$ |
|
|
? |
$S_3^2:C_2^2$ (as 18T63) |
trivial |
$2$ |
$9$ |
$715.911525302$ |
18.2.228...384.1 |
$x^{18} - 3 x^{16} + 6 x^{14} - 8 x^{12} + 8 x^{10} - 5 x^{8} + 3 x^{6} - x^{4} + x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 101^{2}\cdot 292181^{2}$ |
$3$ |
$13.5215672971$ |
|
|
|
✓ |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$9$ |
$571.6445084$ |
18.2.228...384.2 |
$x^{18} + 2 x^{16} + 2 x^{14} - 3 x^{10} - 7 x^{8} - 8 x^{6} - 6 x^{4} - 3 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 101^{2}\cdot 292181^{2}$ |
$3$ |
$13.5215672971$ |
|
|
|
✓ |
$C_2^8.S_9$ (as 18T964) |
trivial |
$2$ |
$9$ |
$585.079655294$ |
18.2.234...216.1 |
$x^{18} + 9 x^{16} + 36 x^{14} + 84 x^{12} + 126 x^{10} + 126 x^{8} + 83 x^{6} + 33 x^{4} + 6 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{18}\cdot 23^{6}$ |
$3$ |
$13.5430723064$ |
$62.3845893751363$ |
|
|
? |
$C_2^2:A_4^2:D_6$ (as 18T520) |
trivial |
$2$ |
$9$ |
$573.045111995$ |
18.2.254...009.1 |
$x^{18} - 5 x^{17} + 16 x^{16} - 35 x^{15} + 59 x^{14} - 73 x^{13} + 59 x^{12} - 5 x^{11} - 79 x^{10} + 163 x^{9} - 224 x^{8} + 229 x^{7} - 192 x^{6} + 127 x^{5} - 59 x^{4} + 24 x^{3} - 4 x - 1$ |
$18$ |
[2,8] |
$7^{12}\cdot 97^{2}\cdot 1399^{2}$ |
$3$ |
$13.6046198172$ |
$1348.010942860009$ |
|
|
? |
$S_4^3.A_4$ (as 18T838) |
trivial |
$2$ |
$9$ |
$661.987726773$ |
18.2.271...744.1 |
$x^{18} + x^{16} - 2 x^{12} + 5 x^{8} + 8 x^{6} + 6 x^{4} + x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 23^{6}\cdot 2647^{2}$ |
$3$ |
$13.6535400259$ |
|
|
|
? |
$S_3^3:S_4$ (as 18T483) |
trivial |
$2$ |
$9$ |
$636.303906811$ |
18.2.271...744.2 |
$x^{18} - 3 x^{16} + 8 x^{14} - 12 x^{12} + 11 x^{10} - 5 x^{8} - 2 x^{6} + 2 x^{4} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 23^{6}\cdot 2647^{2}$ |
$3$ |
$13.6535400259$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$2$ |
$9$ |
$656.67762437$ |
18.2.271...744.3 |
$x^{18} - 5 x^{16} + 11 x^{14} - 15 x^{12} + 19 x^{10} - 20 x^{8} + 14 x^{6} - 10 x^{4} + 5 x^{2} - 1$ |
$18$ |
[2,8] |
$2^{18}\cdot 23^{6}\cdot 2647^{2}$ |
$3$ |
$13.6535400259$ |
|
|
|
? |
$S_4^3.S_4$ (as 18T883) |
trivial |
$2$ |
$9$ |
$608.086604501$ |
18.2.297...352.1 |
$x^{18} - 3 x^{17} + 2 x^{16} + 10 x^{14} - 23 x^{13} + 6 x^{12} + 20 x^{11} - 11 x^{10} + 7 x^{9} - 65 x^{8} + 106 x^{7} - 43 x^{6} - 60 x^{5} + 101 x^{4} - 69 x^{3} + 28 x^{2} - 7 x + 1$ |
$18$ |
[2,8] |
$2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4}$ |
$4$ |
$13.722519205$ |
$310.23790129978926$ |
|
|
? |
$A_4^3.(C_2^2\times S_4)$ (as 18T835) |
trivial |
$2$ |
$9$ |
$695.730594256$ |
18.2.297...352.2 |
$x^{18} - 4 x^{17} + 10 x^{16} - 27 x^{15} + 57 x^{14} - 83 x^{13} + 97 x^{12} - 102 x^{11} + 82 x^{10} - 36 x^{9} + 13 x^{8} - 34 x^{7} + 37 x^{6} - 5 x^{5} - 2 x^{4} - 15 x^{3} + 16 x^{2} - 7 x + 1$ |
$18$ |
[2,8] |
$2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4}$ |
$4$ |
$13.722519205$ |
$679.4019872233262$ |
|
|
? |
$A_4^3.(C_2^2\times S_4)$ (as 18T835) |
trivial |
$2$ |
$9$ |
$940.892214705$ |