Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 83 matches)

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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
11.3.95234227200000000.1	$x^{11} - 3 x^{10} + 18 x^{9} - 44 x^{8} + 117 x^{7} - 147 x^{6} + 201 x^{5} + 3 x^{4} - 234 x^{3} + 182 x^{2} - 63 x + 9$	$11$	[3,4]	$2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 7$	$4$	$34.9563953104$	$684.0534527050523$			?	$S_{11}$ (as 11T8)	trivial	trivial	$2$	$6$	$233589.451167$
12.0.98954899456.1	$x^{12} - 4 x^{11} + 10 x^{10} - 18 x^{9} + 24 x^{8} - 24 x^{7} + 18 x^{6} - 8 x^{5} + 2 x^{4} + x^{2} - 2 x + 1$	$12$	[0,6]	$2^{12}\cdot 7^{2}\cdot 79^{3}$	$3$	$8.246818600994315$	$91.99351907925389$			✓	$C_3\wr S_4$ (as 12T231)	trivial	trivial	$2$	$5$	$2.081020151070334$
12.2.16971038906567067.1	$x^{12} - 2 x^{9} + 15 x^{6} + 94 x^{3} + 49$	$12$	[2,5]	$-\,3^{15}\cdot 7^{2}\cdot 17^{6}$	$3$	$22.5151944693$	$112.40462290649258$			?	$C_3^4:S_4$ (as 12T233)	trivial	$[2]$	$2$	$6$	$3122.86046491$
12.12.444...841.1	$x^{12} - x^{11} - 26 x^{10} + 54 x^{9} + 164 x^{8} - 571 x^{7} + 267 x^{6} + 651 x^{5} - 593 x^{4} - 165 x^{3} + 243 x^{2} - 18 x - 13$	$12$	[12,0]	$3^{4}\cdot 7^{2}\cdot 11^{6}\cdot 43^{6}$	$4$	$43.38310799533608$	$644.5189327298262$			?	$C_3\wr A_4$ (as 12T194)	trivial	$[2]$	$2$	$11$	$1244053.7823708528$
12.8.381...809.1	$x^{12} - 2 x^{11} - 38 x^{10} + 134 x^{9} + 320 x^{8} - 1663 x^{7} + 1918 x^{6} + 1507 x^{5} - 10436 x^{4} + 10597 x^{3} + 7939 x^{2} - 14459 x + 4731$	$12$	[8,2]	$3^{12}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$	$4$	$51.9000611973$	$8932.890427024455$			?	$C_3^4:Q_8:S_4$ (as 12T282)	trivial	trivial	$2$	$9$	$1682314.75773$
12.0.599...888.1	$x^{12} + 12 x^{10} - 42 x^{9} + 378 x^{8} - 120 x^{7} + 2960 x^{6} - 6138 x^{5} + 25944 x^{4} - 14318 x^{3} + 5040 x^{2} - 5502 x + 38353$	$12$	[0,6]	$2^{12}\cdot 3^{16}\cdot 7^{2}\cdot 37^{5}$	$4$	$53.8838634613$				?	$C_3^4:S_4$ (as 12T233)	$[3, 3]$	$[3, 3]$	$2$	$5$	$76363.0731406$
12.0.239...552.1	$x^{12} - 24 x^{10} - 46 x^{9} + 216 x^{8} + 816 x^{7} - 164 x^{6} - 4464 x^{5} - 7512 x^{4} + 1256 x^{3} + 26712 x^{2} + 39648 x + 18284$	$12$	[0,6]	$2^{14}\cdot 3^{16}\cdot 7^{2}\cdot 37^{5}$	$4$	$60.4825917516$				?	$C_3^4:S_4$ (as 12T233)	$[3, 3]$	$[3, 3]$	$2$	$5$	$154973.758428$
12.12.274...089.1	$x^{12} - 54 x^{10} - 74 x^{9} + 747 x^{8} + 1773 x^{7} - 2190 x^{6} - 9225 x^{5} - 3573 x^{4} + 11101 x^{3} + 10521 x^{2} + 189 x - 1652$	$12$	[12,0]	$3^{18}\cdot 7^{2}\cdot 53^{2}\cdot 61^{6}$	$4$	$108.786695419$	$3093.7044247668878$			?	$C_3:S_3^3:A_4$ (as 12T271)	trivial	$[2]$	$2$	$11$	$722899713.199$
12.12.785...896.1	$x^{12} - 102 x^{10} + 2691 x^{8} - 1992 x^{7} - 25754 x^{6} + 36360 x^{5} + 77037 x^{4} - 170536 x^{3} + 45990 x^{2} + 60816 x - 22876$	$12$	[12,0]	$2^{22}\cdot 3^{16}\cdot 7^{2}\cdot 31^{6}$	$4$	$118.73548173132174$					$C_3^3:(S_3\times A_4)$ (as 12T234)	trivial	$[2, 2]$	$2$	$11$	$1042522584.0811368$
12.12.660...401.1	$x^{12} - 627 x^{10} - 744 x^{9} + 123147 x^{8} + 383985 x^{7} - 8204224 x^{6} - 39695400 x^{5} + 64333290 x^{4} + 350683050 x^{3} - 54055575 x^{2} - 707046921 x - 390401375$	$12$	[12,0]	$3^{18}\cdot 7^{2}\cdot 53^{2}\cdot 61^{6}\cdot 4903^{2}$	$5$	$448.38674606$	$995198.7782465564$			?	$C_3:S_3^3:A_4$ (as 12T271)	trivial	$[2, 2]$	$2$	$11$	$1561438314170$
13.1.1414971204906609.1	$x^{13} - x^{12} + x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + 4 x^{5} - 5 x^{4} + 4 x^{3} - 2 x + 1$	$13$	[1,6]	$3^{6}\cdot 7^{2}\cdot 29^{2}\cdot 6863^{2}$	$4$	$14.6366646729$	$5305.167415671284$			?	$A_{13}$ (as 13T8)	trivial	trivial	$2$	$6$	$307.196082794$
15.15.416...952.1	$x^{15} - 96 x^{13} - 46 x^{12} + 3483 x^{11} + 2268 x^{10} - 63251 x^{9} - 42696 x^{8} + 626151 x^{7} + 391884 x^{6} - 3388707 x^{5} - 1845144 x^{4} + 9263884 x^{3} + 4127760 x^{2} - 9751392 x - 3146976$	$15$	[15,0]	$2^{10}\cdot 3^{20}\cdot 7^{4}\cdot 36497^{3}$	$4$	$94.332044584$				?	$C_3:S_3^4:S_5$ (as 15T91)	trivial	$[2]$	$2$	$14$	$11897255378.0$
16.8.293...312.1	$x^{16} - 8 x^{15} + 36 x^{14} - 112 x^{13} + 266 x^{12} - 504 x^{11} + 760 x^{10} - 896 x^{9} + 765 x^{8} - 360 x^{7} - 144 x^{6} + 486 x^{5} - 425 x^{4} + 148 x^{3} - 3 x^{2} - 8 x + 1$	$16$	[8,4]	$2^{8}\cdot 3^{13}\cdot 7^{2}\cdot 19^{4}\cdot 103^{4}$	$5$	$29.2894339605$	$3174.004872852932$			?	$C_2^8.S_3\wr S_4$ (as 16T1947)	trivial	$[2]$	$2$	$11$	$1558123.40037$
16.4.222...016.1	$x^{16} - 8 x^{15} + 24 x^{14} - 28 x^{13} - 10 x^{12} + 60 x^{11} + 232 x^{10} - 1424 x^{9} + 2376 x^{8} - 800 x^{7} - 1952 x^{6} + 2400 x^{5} - 784 x^{4} - 352 x^{3} + 384 x^{2} - 128 x + 16$	$16$	[4,6]	$2^{24}\cdot 3^{18}\cdot 7^{2}\cdot 17^{8}$	$4$	$51.1879952229$				?	$A_4\wr A_4.C_2$ (as 16T1920)	trivial	$[2]$	$2$	$9$	$82517016.8954$
16.0.506...984.1	$x^{16} - 4 x^{15} + 4 x^{14} + 36 x^{13} + 196 x^{12} - 356 x^{11} + 648 x^{10} + 3628 x^{9} + 8230 x^{8} - 22644 x^{7} + 21124 x^{6} + 46564 x^{5} + 17920 x^{4} - 350148 x^{3} + 423728 x^{2} + 29308 x + 1022377$	$16$	[0,8]	$2^{32}\cdot 3^{16}\cdot 7^{2}\cdot 37^{6}\cdot 467^{2}$	$5$	$127.808211532$				?	$A_4\wr A_4.C_2$ (as 16T1920)	trivial	trivial	$2$	$7$	$92967806936.2$
16.0.991...904.1	$x^{16} - 4 x^{15} + 28 x^{14} - 52 x^{13} - 64 x^{12} + 1788 x^{11} - 456 x^{10} - 12108 x^{9} + 38154 x^{8} + 101356 x^{7} - 121012 x^{6} - 132308 x^{5} + 1200788 x^{4} + 1727804 x^{3} - 679920 x^{2} - 1085244 x + 831477$	$16$	[0,8]	$2^{32}\cdot 3^{16}\cdot 7^{2}\cdot 37^{6}\cdot 653^{2}$	$5$	$133.277947291$				?	$A_4\wr A_4.C_2$ (as 16T1920)	trivial	trivial	$2$	$7$	$100929536259$
16.0.617...144.1	$x^{16} + 84 x^{14} - 192 x^{13} + 2106 x^{12} - 3600 x^{11} + 21690 x^{10} + 4752 x^{9} + 9081 x^{8} + 323712 x^{7} + 88938 x^{6} + 420984 x^{5} + 1637937 x^{4} + 1058400 x^{3} + 1853604 x^{2} + 1990656 x + 3852036$	$16$	[0,8]	$2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}$	$5$	$199.256256845$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2]$	$[2, 2]$	$2$	$7$	$516916616531$
16.8.280...824.1	$x^{16} - 8 x^{15} - 132 x^{14} + 632 x^{13} + 8770 x^{12} - 6032 x^{11} - 284670 x^{10} - 772754 x^{9} + 2172183 x^{8} + 18297324 x^{7} + 52187014 x^{6} + 84291570 x^{5} + 83346511 x^{4} + 48883050 x^{3} + 14313367 x^{2} + 662458 x - 366343$	$16$	[8,4]	$2^{16}\cdot 7^{2}\cdot 37^{2}\cdot 283^{4}\cdot 13693^{2}\cdot 72871^{2}$	$6$	$219.038644013$	$257127023.53414327$			?	$A_4\wr A_4.C_2$ (as 16T1918)	$[2]$	$[2, 2, 2, 2]$	$2$	$11$	$4428215669470$
16.8.525...672.1	$x^{16} - 28 x^{14} - 264 x^{13} - 1324 x^{12} + 1856 x^{11} + 44960 x^{10} + 214496 x^{9} + 532608 x^{8} + 687488 x^{7} - 859008 x^{6} - 5340800 x^{5} - 13755008 x^{4} - 50221568 x^{3} - 42180864 x^{2} - 5584896 x + 2398464$	$16$	[8,4]	$2^{24}\cdot 3^{12}\cdot 7^{2}\cdot 19^{5}\cdot 23^{2}\cdot 89^{2}\cdot 103^{5}$	$7$	$227.790208906$				?	$C_2^8.C_3^4:Q_8:S_4$ (as 16T1943)	trivial	$[2, 2, 2]$	$2$	$11$	$26209984131700$
16.4.421...176.1	$x^{16} + 60 x^{14} - 88 x^{13} + 1284 x^{12} - 7344 x^{11} + 7136 x^{10} - 62376 x^{9} + 259446 x^{8} - 80320 x^{7} + 215892 x^{6} - 2404296 x^{5} - 1487168 x^{4} + 16403376 x^{3} - 13098456 x^{2} - 13603032 x + 15032061$	$16$	[4,6]	$2^{34}\cdot 3^{16}\cdot 7^{2}\cdot 47^{12}$	$4$	$299.585399538$				?	$C_2^8:(C_3^3:S_4)$ (as 16T1900)	$[2]$	$[2, 4]$	$2$	$9$	$237071551218000$
16.8.436...552.1	$x^{16} - 140 x^{14} - 584 x^{13} + 4768 x^{12} + 41296 x^{11} + 65060 x^{10} - 208952 x^{9} + 181610 x^{8} + 6128608 x^{7} + 4775516 x^{6} - 116939960 x^{5} - 604113720 x^{4} - 1536811568 x^{3} - 2323846644 x^{2} - 1981798344 x - 719543763$	$16$	[8,4]	$2^{24}\cdot 3^{14}\cdot 7^{2}\cdot 19^{5}\cdot 103^{5}\cdot 6221^{2}$	$6$	$300.274190307$				?	$C_2^8.C_3^4:Q_8:S_4$ (as 16T1943)	$[2]$	$[2, 2, 4]$	$2$	$11$	$115132972698000$
16.0.537...816.1	$x^{16} + 108 x^{14} - 592 x^{13} + 4410 x^{12} - 28368 x^{11} + 149010 x^{10} - 545112 x^{9} + 1872495 x^{8} - 5332288 x^{7} + 11900646 x^{6} - 19632240 x^{5} + 21117415 x^{4} - 10401552 x^{3} + 10052910 x^{2} - 22330728 x + 15752961$	$16$	[0,8]	$2^{24}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 59^{2}\cdot 61^{8}$	$6$	$304.186348495$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2, 2]$	$[2, 2, 2]$	$2$	$7$	$8237494058810$
16.12.111...008.1	$x^{16} - 300 x^{14} - 1448 x^{13} + 28908 x^{12} + 282240 x^{11} - 317696 x^{10} - 15140640 x^{9} - 66068064 x^{8} + 88930688 x^{7} + 1810624128 x^{6} + 7150439808 x^{5} + 12640953600 x^{4} + 4105059840 x^{3} - 23962224384 x^{2} - 41990731776 x - 23352198912$	$16$	[12,2]	$2^{24}\cdot 3^{14}\cdot 7^{2}\cdot 19^{5}\cdot 47^{2}\cdot 103^{5}\cdot 211^{2}$	$7$	$318.297346814$				?	$C_2^8.C_3^4:Q_8:S_4$ (as 16T1943)	$[2]$	$[2, 2, 2, 2]$	$2$	$13$	$396395562485000$
16.8.136...096.1	$x^{16} + 12 x^{14} - 16 x^{13} - 582 x^{12} + 2448 x^{11} - 9390 x^{10} - 3960 x^{9} + 154431 x^{8} - 160960 x^{7} + 132246 x^{6} - 6654144 x^{5} + 25793455 x^{4} - 29106480 x^{3} - 10596042 x^{2} + 29779704 x - 4871583$	$16$	[8,4]	$2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 47^{2}\cdot 53^{2}\cdot 61^{8}$	$6$	$322.421652705$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2]$	$[2, 2, 2, 2]$	$2$	$11$	$97260072254000$
16.4.217...304.1	$x^{16} + 12 x^{14} - 1200 x^{13} + 2970 x^{12} + 30960 x^{11} + 131634 x^{10} - 1606824 x^{9} - 5766705 x^{8} + 58631616 x^{7} - 9202410 x^{6} - 653563296 x^{5} + 591965775 x^{4} + 5106890160 x^{3} - 13809580650 x^{2} + 11189335464 x - 1380416175$	$16$	[4,6]	$2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 1879^{2}$	$6$	$511.272948854$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2]$	$[2, 2, 2, 2]$	$2$	$9$	$1751908349350000$
16.12.316...936.1	$x^{16} - 108 x^{14} - 160 x^{13} + 3690 x^{12} - 720 x^{11} - 103926 x^{10} + 520416 x^{9} + 6844545 x^{8} + 8548736 x^{7} - 119716470 x^{6} - 606523896 x^{5} - 1136097455 x^{4} - 528772320 x^{3} + 1117814580 x^{2} + 1556164224 x + 544431780$	$16$	[12,2]	$2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 13^{2}\cdot 19^{2}\cdot 29^{2}\cdot 53^{2}\cdot 61^{8}$	$8$	$604.364347245$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2]$	$[2, 2, 2, 2, 2]$	$2$	$13$	$42251798410900000$
16.8.565...216.1	$x^{16} - 276 x^{14} - 272 x^{13} + 34266 x^{12} + 120240 x^{11} - 3582030 x^{10} - 8441208 x^{9} + 286272351 x^{8} - 525213248 x^{7} - 9212660442 x^{6} + 47497545264 x^{5} + 25755139687 x^{4} - 797099191440 x^{3} + 2452368114414 x^{2} - 3050955724104 x + 1305847085841$	$16$	[8,4]	$2^{24}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 19141^{2}$	$6$	$626.655413848$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2, 2]$	$[2, 2, 2, 2]$	$2$	$11$	$25575062955900000$
16.12.276...936.1	$x^{16} - 276 x^{14} - 912 x^{13} + 27162 x^{12} + 164016 x^{11} - 965646 x^{10} - 9021240 x^{9} + 13029183 x^{8} + 254642112 x^{7} - 240200154 x^{6} - 10351177488 x^{5} - 51875104473 x^{4} - 127752129936 x^{3} - 171268664274 x^{2} - 116057008008 x - 29088131535$	$16$	[12,2]	$2^{26}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 21163^{2}$	$6$	$692.004823359$				?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	trivial	$[2, 2, 2]$	$2$	$13$	$608304983708000000$
16.16.331...664.1	$x^{16} - 492 x^{14} - 2432 x^{13} + 86970 x^{12} + 861552 x^{11} - 4317510 x^{10} - 96130512 x^{9} - 306725895 x^{8} + 2618027392 x^{7} + 24716171466 x^{6} + 64378219800 x^{5} - 106137928895 x^{4} - 1106964640032 x^{3} - 2967469981740 x^{2} - 3684697743168 x - 1806225982524$	$16$	[16,0]	$2^{24}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 787^{2}\cdot 1861^{2}$	$7$	$1077.70117482$	$20951289.925365385$			?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2]$	$[2, 2, 2, 2]$	$2$	$15$	$60173618740500000000$
16.16.450...704.1	$x^{16} - 1068 x^{14} - 8544 x^{13} + 408618 x^{12} + 6785712 x^{11} - 34661430 x^{10} - 1680773760 x^{9} - 12571991199 x^{8} + 64344850560 x^{7} + 1873971439146 x^{6} + 16124526506664 x^{5} + 77834921444865 x^{4} + 227707885994400 x^{3} + 388566640586628 x^{2} + 329477240990016 x + 79336139962212$	$16$	[16,0]	$2^{24}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 17085217^{2}$	$6$	$1465.07811327$	$70787548.11771724$			?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2]$	$[2, 2, 2, 4]$	$2$	$15$	$201262189526000000000$
16.4.105...336.1	$x^{16} + 678 x^{14} - 20664 x^{13} + 335763 x^{12} - 3177936 x^{11} + 95906970 x^{10} - 1479831192 x^{9} + 3077567019 x^{8} + 19177642224 x^{7} + 511118476974 x^{6} + 10024606000224 x^{5} - 313909370993538 x^{4} + 2365075541034576 x^{3} - 4438162825157520 x^{2} - 20179229164826472 x + 74400643256338557$	$16$	[4,6]	$2^{18}\cdot 3^{20}\cdot 7^{2}\cdot 53^{2}\cdot 61^{8}\cdot 73^{2}\cdot 4903^{2}\cdot 5835857^{2}$	$8$	$4885.20895011$	$80403765631.0703$			?	$A_4^2\wr C_2.C_2^2.A_4$ (as 16T1937)	$[2]$	$[2, 2]$	$2$	$9$	$313690967446000000000000$
17.5.878...000.1	$x^{17} - 8 x^{16} - 17 x^{15} + 376 x^{14} - 1517 x^{13} + 2374 x^{12} - 258 x^{11} - 2424 x^{10} - 507 x^{9} - 2266 x^{8} + 26723 x^{7} - 46312 x^{6} + 33731 x^{5} - 13660 x^{4} + 980 x^{3} + 10560 x^{2} - 10440 x + 2880$	$17$	[5,6]	$2^{18}\cdot 3^{28}\cdot 5^{14}\cdot 7^{4}$	$4$	$75.6925905596$	$1452.1836922844575$				$A_{17}$ (as 17T9)	trivial	trivial	$2$	$10$	$270930416645$
18.6.749...576.1	$x^{18} - 4 x^{17} + x^{16} + 10 x^{15} + 6 x^{14} - 25 x^{13} - 60 x^{12} + 108 x^{11} + 63 x^{10} - 61 x^{9} - 205 x^{8} + 98 x^{7} + 189 x^{6} - 80 x^{5} - 73 x^{4} + 20 x^{3} + 17 x^{2} - 3 x - 1$	$18$	[6,6]	$2^{18}\cdot 7^{6}\cdot 79^{6}$	$3$	$16.4161649063$	$91.99351907925389$			?	$C_3\wr S_4$ (as 18T349)	trivial	trivial	$2$	$11$	$9127.05849966$
18.0.254...363.1	$x^{18} - 3 x^{17} + 3 x^{16} + 6 x^{15} - 18 x^{14} + 18 x^{13} + 9 x^{12} - 60 x^{11} + 15 x^{10} - 114 x^{9} - 6 x^{8} + 345 x^{7} + 126 x^{6} + 27 x^{5} + 414 x^{4} + 663 x^{3} + 531 x^{2} + 225 x + 39$	$18$	[0,9]	$-\,3^{24}\cdot 7^{2}\cdot 13^{2}\cdot 37^{2}\cdot 43^{3}$	$5$	$19.9674367485$				?	$C_3\wr \SOPlus(4,2)$ (as 18T724)	trivial	trivial	$6$	$8$	$84250.4131558$
18.0.109...691.1	$x^{18} - 12 x^{15} + 61 x^{12} - 172 x^{9} + 292 x^{6} - 290 x^{3} + 133$	$18$	[0,9]	$-\,3^{27}\cdot 7^{2}\cdot 19^{2}\cdot 433^{3}$	$4$	$24.6082112943$				?	$C_3\wr \SOPlus(4,2)$ (as 18T724)	trivial	trivial	$6$	$8$	$401085.116763$
18.0.170...043.1	$x^{18} - 4 x^{9} + 7$	$18$	[0,9]	$-\,3^{45}\cdot 7^{8}$	$2$	$37.0170892193$	$115.29463846308026$				$C_9^2:C_6$ (as 18T158)	trivial	trivial	$6$	$8$	$34267449.4062$
18.14.771...704.1	$x^{18} - 12 x^{16} - 6 x^{15} + 51 x^{14} + 60 x^{13} - 71 x^{12} - 204 x^{11} - 88 x^{10} + 238 x^{9} + 338 x^{8} + 56 x^{7} - 244 x^{6} - 236 x^{5} - 28 x^{4} + 80 x^{3} + 51 x^{2} + 12 x + 1$	$18$	[14,2]	$2^{18}\cdot 7^{3}\cdot 11\cdot 131\cdot 887^{6}\cdot 1223$	$6$	$59.0916204878$	$295870.0753641706$			✓	$C_3^6.C_2\wr A_5$ (as 18T948)	trivial	$[2, 2, 2]$	$2$	$15$	$7858717893.11$
18.6.305...456.1	$x^{18} - 12 x^{16} - 122 x^{15} - 468 x^{14} + 1560 x^{13} + 10011 x^{12} + 15084 x^{11} - 147948 x^{10} - 387936 x^{9} + 1815912 x^{8} + 2469180 x^{7} - 11166365 x^{6} + 1358280 x^{5} + 55523076 x^{4} + 51513798 x^{3} + 153522684 x^{2} + 329210028 x + 136213189$	$18$	[6,6]	$2^{18}\cdot 3^{24}\cdot 7^{6}\cdot 37^{8}$	$4$	$82.3890621678$				?	$C_3^4:S_4$ (as 18T359)	$[3]$	$[3]$	$2$	$11$	$16987371929.3$
18.12.445...968.1	$x^{18} - 42 x^{16} - 28 x^{15} + 711 x^{14} + 948 x^{13} - 5948 x^{12} - 12528 x^{11} + 22347 x^{10} + 80008 x^{9} + 1674 x^{8} - 230916 x^{7} - 263585 x^{6} + 109404 x^{5} + 499140 x^{4} + 503520 x^{3} + 257040 x^{2} + 68544 x + 7616$	$18$	[12,3]	$-\,2^{46}\cdot 3^{18}\cdot 7^{2}\cdot 17^{2}\cdot 487^{3}$	$5$	$84.1313688489$				?	$C_3^6.S_3^2:C_4$ (as 18T794)	trivial	$[2]$	$2$	$14$	$370442126441$
18.0.886...963.1	$x^{18} - 234 x^{15} + 16551 x^{12} - 350298 x^{9} + 4274559 x^{6} - 46772397 x^{3} + 275894451$	$18$	[0,9]	$-\,3^{37}\cdot 7^{4}\cdot 31^{10}$	$3$	$99.3306059022$				?	$C_3^5:S_3^2$ (as 18T531)	$[3]$	$[3]$	$6$	$8$	$57317288877.9$
18.18.442...849.1	$x^{18} - 3 x^{17} - 103 x^{16} + 216 x^{15} + 3824 x^{14} - 7039 x^{13} - 66104 x^{12} + 132989 x^{11} + 557576 x^{10} - 1402052 x^{9} - 1905544 x^{8} + 7379003 x^{7} - 842713 x^{6} - 15264046 x^{5} + 14866651 x^{4} + 2454212 x^{3} - 10399124 x^{2} + 5354400 x - 858688$	$18$	[18,0]	$3^{12}\cdot 7^{6}\cdot 11^{6}\cdot 43^{12}$	$4$	$108.615060537$	$644.5189327298262$				$C_3\wr A_4$ (as 18T242)	trivial	$[2]$	$2$	$17$	$21558313000000$
18.18.113...329.1	$x^{18} - 6 x^{17} - 96 x^{16} + 318 x^{15} + 3270 x^{14} - 5370 x^{13} - 50151 x^{12} + 39603 x^{11} + 378048 x^{10} - 174053 x^{9} - 1452684 x^{8} + 651354 x^{7} + 2801832 x^{6} - 1564176 x^{5} - 2295849 x^{4} + 1423866 x^{3} + 674187 x^{2} - 390774 x - 39743$	$18$	[18,0]	$3^{32}\cdot 7^{6}\cdot 23^{6}\cdot 61^{2}\cdot 307^{2}$	$5$	$114.430785557$				?	$C_3\wr A_6$ (as 18T856)	$[3]$	$[2, 2, 6]$	$2$	$17$	$2092363401060$
18.12.643...416.1	$x^{18} - 42 x^{16} - 28 x^{15} + 711 x^{14} + 948 x^{13} - 6191 x^{12} - 13014 x^{11} + 27126 x^{10} + 93544 x^{9} - 17523 x^{8} - 334218 x^{7} - 340580 x^{6} + 283392 x^{5} + 918720 x^{4} + 900960 x^{3} + 457920 x^{2} + 122112 x + 13568$	$18$	[12,3]	$-\,2^{13}\cdot 3^{18}\cdot 7^{4}\cdot 53^{2}\cdot 113^{9}$	$5$	$126.025027555$					$C_3^4.S_3^2\wr C_2$ (as 18T852)	trivial	$[2]$	$2$	$14$	$47584951256000$
18.12.631...848.1	$x^{18} - 90 x^{16} - 108 x^{15} + 3411 x^{14} + 8292 x^{13} - 63920 x^{12} - 252936 x^{11} + 460305 x^{10} + 3580064 x^{9} + 2115126 x^{8} - 20941188 x^{7} - 45997591 x^{6} + 10388700 x^{5} + 154753788 x^{4} + 218061312 x^{3} + 120311856 x^{2} + 19032384 x - 906304$	$18$	[12,3]	$-\,2^{46}\cdot 3^{18}\cdot 7^{4}\cdot 17^{4}\cdot 487^{3}$	$5$	$143.078468929$				?	$C_3^6.S_3^2:C_4$ (as 18T794)	trivial	trivial	$2$	$14$	$33611417484400$
18.0.851...443.1	$x^{18} - 36 x^{15} - 513 x^{12} + 252774 x^{9} + 22388076 x^{6} + 392318640 x^{3} + 7449150177$	$18$	[0,9]	$-\,3^{37}\cdot 7^{4}\cdot 31^{12}$	$3$	$145.475527113$				?	$C_3^5:S_3^2$ (as 18T531)	$[3, 3]$	$[3, 3]$	$6$	$8$	$883358781930$
18.12.180...544.1	$x^{18} - 90 x^{16} - 54 x^{15} + 3978 x^{14} + 7266 x^{13} - 97220 x^{12} - 340038 x^{11} + 1019979 x^{10} + 6783722 x^{9} + 2374488 x^{8} - 53964816 x^{7} - 115372576 x^{6} + 71786592 x^{5} + 538625856 x^{4} + 632845440 x^{3} + 90607104 x^{2} - 211416576 x - 46022656$	$18$	[12,3]	$-\,2^{13}\cdot 3^{18}\cdot 7^{4}\cdot 53^{4}\cdot 113^{9}$	$5$	$195.903867028$					$C_3^4.S_3^2\wr C_2$ (as 18T852)	trivial	$[2]$	$2$	$14$	$9034997967190000$
18.18.702...704.1	$x^{18} - 261 x^{16} - 556 x^{15} + 25263 x^{14} + 101466 x^{13} - 1031704 x^{12} - 6292872 x^{11} + 13342305 x^{10} + 159863828 x^{9} + 148816899 x^{8} - 1526334264 x^{7} - 4402449765 x^{6} + 918053514 x^{5} + 21638662542 x^{4} + 37604417508 x^{3} + 26082902664 x^{2} + 5985124992 x - 128024064$	$18$	[18,0]	$2^{28}\cdot 3^{24}\cdot 7^{6}\cdot 31^{12}$	$4$	$240.088319069$	$1018.3929351373382$				$C_3^3:(S_3\times A_4)$ (as 18T348)	trivial	$[2, 2]$	$2$	$17$	$91814301407800000$
18.18.253...413.1	$x^{18} - 252 x^{16} - 72 x^{15} + 26460 x^{14} + 15120 x^{13} - 1493643 x^{12} - 1270080 x^{11} + 48671784 x^{10} + 54170600 x^{9} - 909917064 x^{8} - 1224442800 x^{7} + 9033279723 x^{6} + 13787522784 x^{5} - 38882845260 x^{4} - 63120546048 x^{3} + 40037795532 x^{2} + 76943534976 x + 11763367231$	$18$	[18,0]	$3^{37}\cdot 7^{4}\cdot 31^{15}$	$3$	$257.839958016$					$C_3^4.(C_3\times S_3)$ (as 18T331)	$[3]$	$[6]$	$2$	$17$	$86517352526000000$
18.18.253...413.2	$x^{18} - 252 x^{16} - 18 x^{15} + 26460 x^{14} + 3780 x^{13} - 1503201 x^{12} - 317520 x^{11} + 50277528 x^{10} + 13592228 x^{9} - 1011078936 x^{8} - 312357528 x^{7} + 11975478255 x^{6} + 3709247472 x^{5} - 77836389372 x^{4} - 19645748850 x^{3} + 233488824156 x^{2} + 27319937652 x - 191560930799$	$18$	[18,0]	$3^{37}\cdot 7^{4}\cdot 31^{15}$	$3$	$257.839958016$					$C_3^4.(C_3\times S_3)$ (as 18T331)	$[3]$	$[2, 2, 6]$	$2$	$17$	$116638180189000000$
18.6.653...256.1	$x^{18} - 54 x^{10} - 48 x^{9} + 567 x^{2} + 1008 x + 448$	$18$	[6,6]	$2^{76}\cdot 3^{36}\cdot 7^{8}$	$3$	$398.893698463$				?	$A_9^2.C_4$ (as 18T979)	trivial	trivial	$2$	$11$	$164021949951000000$

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