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 |
18.0.923324627983045303.1 |
$x^{18} - 4 x^{17} + 10 x^{16} - 17 x^{15} + 24 x^{14} - 28 x^{13} + 28 x^{12} - 22 x^{11} + 14 x^{10} - 8 x^{9} + 5 x^{8} - 3 x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 2 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,31^{6}\cdot 463\cdot 1499^{2}$ |
$3$ |
$9.95577895498$ |
$4638.442303187569$ |
|
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
trivial |
$2$ |
$8$ |
$19.2198611118$ |
18.0.111...168.1 |
$x^{18} - 4 x^{17} + 14 x^{16} - 31 x^{15} + 64 x^{14} - 100 x^{13} + 146 x^{12} - 176 x^{11} + 202 x^{10} - 205 x^{9} + 202 x^{8} - 176 x^{7} + 146 x^{6} - 100 x^{5} + 64 x^{4} - 31 x^{3} + 14 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$10.0611120208$ |
$10.061112020813587$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$6$ |
$8$ |
$64.801283476$ |
18.0.118...699.1 |
$x^{18} - 5 x^{17} + 16 x^{16} - 39 x^{15} + 80 x^{14} - 141 x^{13} + 221 x^{12} - 312 x^{11} + 400 x^{10} - 465 x^{9} + 489 x^{8} - 463 x^{7} + 395 x^{6} - 300 x^{5} + 195 x^{4} - 101 x^{3} + 38 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,7^{4}\cdot 139\cdot 1373^{4}$ |
$3$ |
$10.0952263665$ |
$5329.499816940617$ |
|
|
✓ |
$C_2^9.A_9$ (as 18T966) |
trivial |
$2$ |
$8$ |
$22.1660529321$ |
18.0.119...867.1 |
$x^{18} - 4 x^{17} + 9 x^{16} - 14 x^{15} + 17 x^{14} - 16 x^{13} + 15 x^{12} - 23 x^{11} + 45 x^{10} - 65 x^{9} + 62 x^{8} - 40 x^{7} + 29 x^{6} - 39 x^{5} + 49 x^{4} - 41 x^{3} + 22 x^{2} - 7 x + 1$ |
$18$ |
[0,9] |
$-\,31^{6}\cdot 67^{5}$ |
$2$ |
$10.1009812596$ |
$185.1014620777746$ |
|
|
? |
$C_6\wr S_3$ (as 18T284) |
trivial |
$2$ |
$8$ |
$22.3834819773$ |
18.0.141...707.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 12 x^{14} - 15 x^{13} + 21 x^{12} - 29 x^{11} + 36 x^{10} - 38 x^{9} + 36 x^{8} - 32 x^{7} + 31 x^{6} - 32 x^{5} + 30 x^{4} - 23 x^{3} + 13 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,23^{6}\cdot 43^{3}\cdot 347^{2}$ |
$3$ |
$10.1956014831$ |
$585.8182311946258$ |
|
|
✓ |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$8$ |
$24.7750980478$ |
18.0.154...467.1 |
$x^{18} + 9 x^{16} - 9 x^{15} + 36 x^{14} - 63 x^{13} + 109 x^{12} - 189 x^{11} + 252 x^{10} - 335 x^{9} + 378 x^{8} - 378 x^{7} + 334 x^{6} - 243 x^{5} + 147 x^{4} - 67 x^{3} + 21 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 23^{6}$ |
$2$ |
$10.2459148551$ |
$22.05628309434856$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$78.7017437829$ |
18.0.167...571.1 |
$x^{18} - 2 x^{17} + x^{16} + 5 x^{15} - 10 x^{14} + 5 x^{13} + 13 x^{12} - 29 x^{11} + 24 x^{10} + 9 x^{9} - 48 x^{8} + 56 x^{7} - 16 x^{6} - 44 x^{5} + 74 x^{4} - 60 x^{3} + 29 x^{2} - 8 x + 1$ |
$18$ |
[0,9] |
$-\,139\cdot 367^{2}\cdot 299401^{2}$ |
$3$ |
$10.2918122937$ |
$123585.36811856006$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$8$ |
$27.3003078572$ |
18.0.196...487.1 |
$x^{18} - x^{17} - 7 x^{15} + 5 x^{14} + 6 x^{13} + 21 x^{12} - 29 x^{11} - 13 x^{10} - 11 x^{9} + 49 x^{8} - 8 x^{7} - 3 x^{6} - 24 x^{5} + 14 x^{4} + 3 x^{3} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,31^{6}\cdot 1303^{3}$ |
$2$ |
$10.3819269139$ |
$200.98009851724126$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$8$ |
$29.661621596$ |
18.0.199...128.1 |
$x^{18} - 6 x^{17} + 24 x^{16} - 68 x^{15} + 159 x^{14} - 300 x^{13} + 479 x^{12} - 630 x^{11} + 702 x^{10} - 636 x^{9} + 480 x^{8} - 270 x^{7} + 114 x^{6} - 12 x^{5} - 12 x^{4} + 14 x^{3} - 3 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{27}$ |
$2$ |
$10.3923048454$ |
$14.696938456699069$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$269.804731118$ |
18.0.252...912.1 |
$x^{18} - 9 x^{17} + 36 x^{16} - 81 x^{15} + 105 x^{14} - 63 x^{13} - 21 x^{12} + 72 x^{11} - 63 x^{10} + 27 x^{9} - 6 x^{6} - 9 x^{5} + 18 x^{4} - 9 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{31}$ |
$2$ |
$10.5292028184$ |
$10.529202818387967$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$404.056392969$ |
18.0.274...447.1 |
$x^{18} - 5 x^{17} + 12 x^{16} - 17 x^{15} + 12 x^{14} - 2 x^{13} + 8 x^{12} - 46 x^{11} + 111 x^{10} - 168 x^{9} + 188 x^{8} - 173 x^{7} + 137 x^{6} - 102 x^{5} + 70 x^{4} - 40 x^{3} + 19 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,23^{6}\cdot 2647^{3}$ |
$2$ |
$10.577140393$ |
$246.74075463935827$ |
|
|
? |
$S_3\wr S_3$ (as 18T314) |
trivial |
$2$ |
$8$ |
$35.6314081744$ |
18.0.319...743.1 |
$x^{18} - 5 x^{17} + 15 x^{16} - 36 x^{15} + 75 x^{14} - 137 x^{13} + 221 x^{12} - 312 x^{11} + 384 x^{10} - 411 x^{9} + 384 x^{8} - 312 x^{7} + 221 x^{6} - 137 x^{5} + 75 x^{4} - 36 x^{3} + 15 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,11^{6}\cdot 23^{9}$ |
$2$ |
$10.6658338256$ |
$34.833107461122644$ |
|
|
? |
$C_3^3:S_4$ (as 18T221) |
trivial |
$2$ |
$8$ |
$39.4992656122$ |
18.0.405...267.1 |
$x^{18} - 3 x^{15} + 15 x^{12} + 20 x^{9} + 33 x^{6} + 6 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{39}$ |
$1$ |
$10.8084325966$ |
$10.808432596584025$ |
|
✓ |
? |
$S_3 \times C_3$ (as 18T3) |
trivial |
$18$ |
$8$ |
$529.942929585$ |
18.0.455...263.1 |
$x^{18} + 6 x^{16} - 2 x^{15} + 15 x^{14} - 10 x^{13} + 22 x^{12} - 20 x^{11} + 23 x^{10} - 20 x^{9} + 18 x^{8} - 10 x^{7} + 9 x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 229\cdot 433^{3}\cdot 12457$ |
$4$ |
$10.8792816009$ |
$60873.60878903107$ |
|
|
? |
$C_3^6.S_4^2:D_4$ (as 18T951) |
trivial |
$6$ |
$8$ |
$147.731826961$ |
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 |
$2$ |
$9$ |
$67.155663406$ |
18.0.504...712.1 |
$x^{18} - x^{15} + 2 x^{12} - 9 x^{9} + 12 x^{6} - 5 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{21}\cdot 7^{6}$ |
$3$ |
$10.940255742$ |
$20.927956356407396$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
$6$ |
$8$ |
$153.95173876$ |
18.0.513...176.1 |
$x^{18} - 6 x^{17} + 16 x^{16} - 20 x^{15} - 2 x^{14} + 51 x^{13} - 87 x^{12} + 64 x^{11} + 16 x^{10} - 108 x^{9} + 181 x^{8} - 232 x^{7} + 253 x^{6} - 224 x^{5} + 154 x^{4} - 79 x^{3} + 29 x^{2} - 7 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{12}\cdot 11^{9}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
? |
$C_3^2:C_6$ (as 18T23) |
trivial |
$2$ |
$8$ |
$51.3669704577$ |
18.0.546...107.1 |
$x^{18} - 9 x^{17} + 35 x^{16} - 76 x^{15} + 100 x^{14} - 84 x^{13} + 57 x^{12} - 56 x^{11} + 62 x^{10} - 35 x^{9} + 3 x^{8} - 28 x^{7} + 63 x^{6} - 32 x^{5} - 10 x^{3} + 16 x^{2} - 7 x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 23^{6}\cdot 37^{4}$ |
$3$ |
$10.9890254211$ |
$92.23427989230532$ |
|
|
? |
$C_3^3:D_6$ (as 18T137) |
trivial |
$6$ |
$8$ |
$162.382523466$ |
18.0.558...424.1 |
$x^{18} - 2 x^{17} + 5 x^{16} - 7 x^{15} + 10 x^{14} - 13 x^{13} + 17 x^{12} - 24 x^{11} + 28 x^{10} - 28 x^{9} + 25 x^{8} - 24 x^{7} + 28 x^{6} - 31 x^{5} + 29 x^{4} - 22 x^{3} + 13 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{12}\cdot 37^{6}$ |
$3$ |
$11.0027541313$ |
$71.59022882794918$ |
|
|
? |
$C_3\wr D_4$ (as 18T189) |
trivial |
$6$ |
$8$ |
$172.576549312$ |
18.0.610...264.1 |
$x^{18} + 5 x^{16} + 12 x^{14} + 29 x^{12} + 55 x^{10} + 57 x^{8} + 39 x^{6} + 22 x^{4} + 8 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 13^{12}$ |
$2$ |
$11.0575496274$ |
$11.057549627357744$ |
|
✓ |
|
$S_3 \times C_3$ (as 18T3) |
trivial |
$4$ |
$8$ |
$132.794513852$ |
18.0.622...163.1 |
$x^{18} - 4 x^{15} + 6 x^{12} - 5 x^{9} + 6 x^{6} - 4 x^{3} + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 29^{6}$ |
$2$ |
$11.0689764419$ |
$35.71970195840605$ |
|
|
? |
$C_3^3:D_6$ (as 18T119) |
trivial |
$6$ |
$8$ |
$184.401892895$ |
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 |
$2$ |
$9$ |
$79.1741198129$ |
18.0.664...399.1 |
$x^{18} - 9 x^{17} + 42 x^{16} - 132 x^{15} + 310 x^{14} - 574 x^{13} + 865 x^{12} - 1082 x^{11} + 1139 x^{10} - 1020 x^{9} + 787 x^{8} - 532 x^{7} + 321 x^{6} - 174 x^{5} + 85 x^{4} - 37 x^{3} + 14 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,17^{2}\cdot 43^{2}\cdot 2311\cdot 73363^{2}$ |
$4$ |
$11.1096245283$ |
$352044.20714308025$ |
|
|
? |
$C_2^9.S_9$ (as 18T968) |
trivial |
$2$ |
$8$ |
$61.0464139366$ |
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 |
$2$ |
$9$ |
$84.7255286435$ |
18.0.817...000.1 |
$x^{18} + x^{16} - 6 x^{14} - 5 x^{12} + 2 x^{10} + 7 x^{8} + 18 x^{6} + 7 x^{4} - 3 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{6}\cdot 5^{8}\cdot 83^{6}$ |
$3$ |
$11.2380087164$ |
$53.27813877645612$ |
|
|
? |
$C_6^2:D_6$ (as 18T156) |
trivial |
$2$ |
$8$ |
$72.3431657313$ |
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 |
$2$ |
$9$ |
$95.2465332123$ |
18.0.928...243.1 |
$x^{18} - 9 x^{16} - 11 x^{15} + 21 x^{14} + 69 x^{13} + 54 x^{12} - 75 x^{11} - 219 x^{10} - 205 x^{9} - 6 x^{8} + 231 x^{7} + 342 x^{6} + 303 x^{5} + 201 x^{4} + 103 x^{3} + 39 x^{2} + 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 31^{6}$ |
$2$ |
$11.3178003472$ |
$25.606443093809357$ |
|
|
? |
$C_3^2:D_6$ (as 18T57) |
trivial |
$6$ |
$8$ |
$296.277259881$ |
18.0.929...543.1 |
$x^{18} - 4 x^{17} + 10 x^{16} - 21 x^{15} + 37 x^{14} - 58 x^{13} + 80 x^{12} - 97 x^{11} + 107 x^{10} - 106 x^{9} + 92 x^{8} - 71 x^{7} + 52 x^{6} - 39 x^{5} + 30 x^{4} - 20 x^{3} + 11 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,7^{15}\cdot 1399^{2}$ |
$2$ |
$11.3183642997$ |
$189.30288116733712$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$14$ |
$8$ |
$509.337225135$ |
18.0.965...875.1 |
$x^{18} - 9 x^{17} + 36 x^{16} - 78 x^{15} + 84 x^{14} - 111 x^{12} + 90 x^{11} + 72 x^{10} - 156 x^{9} + 45 x^{8} + 81 x^{7} - 57 x^{6} - 27 x^{5} + 36 x^{4} - 9 x^{2} + 3$ |
$18$ |
[0,9] |
$-\,3^{31}\cdot 5^{6}$ |
$2$ |
$11.3422399052$ |
$14.831798946842026$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$868.676171318$ |
18.0.103...863.1 |
$x^{18} - 4 x^{17} + 11 x^{16} - 22 x^{15} + 36 x^{14} - 53 x^{13} + 80 x^{12} - 116 x^{11} + 154 x^{10} - 173 x^{9} + 154 x^{8} - 116 x^{7} + 80 x^{6} - 53 x^{5} + 36 x^{4} - 22 x^{3} + 11 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,7^{8}\cdot 23^{9}$ |
$2$ |
$11.3884087646$ |
$17.5494136775664$ |
|
|
? |
$C_9:C_6$ (as 18T18) |
trivial |
$2$ |
$8$ |
$77.8161636269$ |
18.0.104...432.1 |
$x^{18} - 4 x^{17} + 11 x^{16} - 20 x^{15} + 31 x^{14} - 41 x^{13} + 56 x^{12} - 69 x^{11} + 64 x^{10} - 59 x^{9} + 49 x^{8} - 48 x^{7} + 28 x^{6} - 5 x^{5} + 17 x^{4} - 5 x^{3} - 2 x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,2^{8}\cdot 3^{9}\cdot 113^{6}$ |
$3$ |
$11.3949183527$ |
$29.22715298876584$ |
|
|
|
$C_3^2:D_6$ (as 18T52) |
trivial |
$6$ |
$8$ |
$327.87771807$ |
18.0.108...103.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 6 x^{15} - 2 x^{14} + 21 x^{13} - 47 x^{12} + 61 x^{11} - 35 x^{10} - 37 x^{9} + 119 x^{8} - 155 x^{7} + 130 x^{6} - 79 x^{5} + 43 x^{4} - 27 x^{3} + 16 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,7^{15}\cdot 1511^{2}$ |
$2$ |
$11.4156323582$ |
$196.7345330512998$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$14$ |
$8$ |
$524.185517787$ |
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 |
$2$ |
$9$ |
$107.172918917$ |
18.0.111...771.1 |
$x^{18} - 8 x^{17} + 28 x^{16} - 54 x^{15} + 55 x^{14} - 8 x^{13} - 55 x^{12} + 69 x^{11} - 19 x^{10} - 37 x^{9} + 44 x^{8} - 16 x^{7} - 6 x^{6} + 15 x^{5} - 14 x^{4} + 3 x^{3} + 7 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,3^{4}\cdot 11^{5}\cdot 31^{8}$ |
$3$ |
$11.432207825$ |
$167.845280953044$ |
|
|
? |
$C_6^3:S_4$ (as 18T485) |
trivial |
$2$ |
$8$ |
$80.526625464$ |
18.0.114...403.1 |
$x^{18} - 4 x^{17} + 7 x^{16} - 9 x^{15} + 15 x^{14} - 24 x^{13} + 28 x^{12} - 30 x^{11} + 36 x^{10} - 39 x^{9} + 36 x^{8} - 30 x^{7} + 28 x^{6} - 24 x^{5} + 15 x^{4} - 9 x^{3} + 7 x^{2} - 4 x + 1$ |
$18$ |
[0,9] |
$-\,23^{6}\cdot 43^{2}\cdot 347^{3}$ |
$3$ |
$11.4496976774$ |
$585.8182311946258$ |
|
|
✓ |
$D_6\wr S_3$ (as 18T556) |
trivial |
$2$ |
$8$ |
$88.267766218$ |
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 |
$2$ |
$9$ |
$111.7260845$ |
18.0.122...031.1 |
$x^{18} - 3 x^{17} - 3 x^{16} + 9 x^{15} + 24 x^{14} - 30 x^{13} - 78 x^{12} + 60 x^{11} + 141 x^{10} - 56 x^{9} - 150 x^{8} + 12 x^{7} + 81 x^{6} + 12 x^{5} - 15 x^{4} - 3 x^{3} + 3 x^{2} + 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{33}\cdot 13^{3}$ |
$2$ |
$11.4915742027$ |
$29.311381743553262$ |
|
|
? |
$S_3^2:C_6$ (as 18T93) |
trivial |
$18$ |
$8$ |
$1025.11738531$ |
18.0.126...967.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 7 x^{15} + 4 x^{14} + 2 x^{13} - 4 x^{12} - 3 x^{11} + 14 x^{10} - 19 x^{9} + 17 x^{8} - 6 x^{7} - 10 x^{6} + 18 x^{5} - 9 x^{4} - 6 x^{3} + 10 x^{2} - 5 x + 1$ |
$18$ |
[0,9] |
$-\,23^{9}\cdot 2647^{2}$ |
$2$ |
$11.5125071118$ |
$246.74075463935827$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$8$ |
$86.4501902329$ |
18.0.128...283.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 3 x^{14} + 18 x^{13} - 47 x^{12} + 90 x^{11} - 87 x^{10} + 43 x^{9} + 63 x^{8} - 186 x^{7} + 274 x^{6} - 270 x^{5} + 198 x^{4} - 106 x^{3} + 39 x^{2} - 9 x + 1$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 1297^{2}$ |
$2$ |
$11.522961256$ |
$187.13364208500832$ |
|
|
? |
$S_3^3:C_6$ (as 18T286) |
trivial |
$18$ |
$8$ |
$784.727413524$ |
18.0.129...896.1 |
$x^{18} - 9 x^{17} + 41 x^{16} - 124 x^{15} + 276 x^{14} - 476 x^{13} + 646 x^{12} - 678 x^{11} + 517 x^{10} - 231 x^{9} - 15 x^{8} + 98 x^{7} - 48 x^{6} - 18 x^{5} + 36 x^{4} - 22 x^{3} + 9 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,2^{16}\cdot 11^{9}\cdot 17^{4}$ |
$3$ |
$11.5268768841$ |
$40.60484358442798$ |
|
|
? |
$C_3^3:S_3$ (as 18T88) |
trivial |
$2$ |
$8$ |
$113.075873428$ |
18.0.134...623.1 |
$x^{18} - 6 x^{17} + 15 x^{16} - 23 x^{15} + 37 x^{14} - 78 x^{13} + 152 x^{12} - 240 x^{11} + 302 x^{10} - 308 x^{9} + 300 x^{8} - 298 x^{7} + 220 x^{6} - 85 x^{5} + 25 x^{4} - 26 x^{3} + 12 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,7^{15}\cdot 41^{4}$ |
$2$ |
$11.5516701463$ |
$60.17797984027825$ |
|
|
? |
$C_3^3:C_6$ (as 18T85) |
trivial |
$14$ |
$8$ |
$765.05787444$ |
18.0.135...707.1 |
$x^{18} - 6 x^{17} + 9 x^{16} + 14 x^{15} - 42 x^{14} - 21 x^{13} + 131 x^{12} - 51 x^{11} - 162 x^{10} + 126 x^{9} + 108 x^{8} - 138 x^{7} - 18 x^{6} + 84 x^{5} - 33 x^{4} - 11 x^{3} + 15 x^{2} - 6 x + 1$ |
$18$ |
[0,9] |
$-\,3^{27}\cdot 11^{6}$ |
$2$ |
$11.5561395357$ |
$17.233687939614086$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$18$ |
$8$ |
$835.1622079049273$ |
18.0.139...207.1 |
$x^{18} - x^{17} + 4 x^{15} - 5 x^{14} + x^{13} + 6 x^{12} - 9 x^{11} + 7 x^{10} + x^{9} - 12 x^{8} + 11 x^{7} - 2 x^{6} - 5 x^{5} + 6 x^{4} - x^{3} - x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,11^{4}\cdot 23^{11}$ |
$2$ |
$11.5767753983$ |
$34.833107461122644$ |
|
|
? |
$C_3^3:S_4$ (as 18T217) |
trivial |
$2$ |
$8$ |
$91.5286994248$ |
18.0.141...912.1 |
$x^{18} - 7 x^{17} + 29 x^{16} - 86 x^{15} + 204 x^{14} - 403 x^{13} + 684 x^{12} - 1007 x^{11} + 1301 x^{10} - 1479 x^{9} + 1488 x^{8} - 1316 x^{7} + 1016 x^{6} - 673 x^{5} + 378 x^{4} - 171 x^{3} + 58 x^{2} - 10 x + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 3^{6}\cdot 7^{15}$ |
$3$ |
$11.5871185062$ |
$13.915398818088354$ |
|
|
? |
$S_3 \times C_6$ (as 18T6) |
trivial |
$14$ |
$8$ |
$720.4866908744744$ |
18.0.149...783.1 |
$x^{18} - x^{17} - x^{16} + x^{15} + 3 x^{14} + 2 x^{13} - 5 x^{12} + 4 x^{11} + 5 x^{10} + 5 x^{9} + 6 x^{8} - 4 x^{7} + 8 x^{6} - 5 x^{5} + 5 x^{4} + x^{3} + 2 x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,23^{9}\cdot 2879^{2}$ |
$2$ |
$11.6204809482$ |
$257.3266406729004$ |
|
|
? |
$S_3\wr S_3$ (as 18T319) |
trivial |
$2$ |
$8$ |
$92.6925275389$ |
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 |
$2$ |
$9$ |
$139.095050977$ |
18.0.162...343.1 |
$x^{18} - x^{17} - 5 x^{16} + 9 x^{15} + 2 x^{14} - 32 x^{13} + 37 x^{12} + 40 x^{11} - 100 x^{10} + 31 x^{9} + 83 x^{8} - 97 x^{7} + 27 x^{6} + 18 x^{5} - 15 x^{4} + 5 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,7^{15}\cdot 43^{4}$ |
$2$ |
$11.6745824541$ |
$62.11941212361736$ |
|
|
? |
$C_3^3:C_6$ (as 18T85) |
trivial |
$14$ |
$8$ |
$847.661854898$ |