Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 6204 matches)

 

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
12.6.3495224609375.1	$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} - 5 x^{8} + 14 x^{7} - 19 x^{6} + 14 x^{5} - 5 x^{4} + 5 x^{3} - 4 x^{2} - x + 1$	$12$	[6,3]	$-\,5^{10}\cdot 71^{3}$	$2$	$11.0991466793$	$32.21841549588632$			?	$\SOPlus(4,2)$ (as 12T35)	trivial	$2$	$8$	$36.6945439221$
12.6.3647529984375.1	$x^{12} - x^{11} - 5 x^{10} + 3 x^{9} + 10 x^{8} - 4 x^{7} - 7 x^{6} + 6 x^{5} - 9 x^{3} - x^{2} + 5 x + 1$	$12$	[6,3]	$-\,3^{4}\cdot 5^{6}\cdot 79\cdot 191^{2}$	$4$	$11.1386674793$	$475.74678138690547$			✓	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$37.5915890729$
12.6.3722179279923.1	$x^{12} - 3 x^{11} - x^{10} + 11 x^{9} - 10 x^{8} - 14 x^{7} + 24 x^{6} + 10 x^{5} - 12 x^{4} - 2 x^{3} - 3 x^{2} - x + 1$	$12$	[6,3]	$-\,3^{3}\cdot 13^{10}$	$2$	$11.1574883129$	$14.684080418380853$			?	$D_4 \times C_3$ (as 12T14)	trivial	$2$	$8$	$38.0840901912$
12.6.3924967206547.1	$x^{12} - 2 x^{11} - 2 x^{10} + 10 x^{9} - 12 x^{8} + x^{7} + 12 x^{6} - 20 x^{5} + 6 x^{4} + 12 x^{3} - 6 x^{2} - 2 x + 1$	$12$	[6,3]	$-\,43\cdot 302123^{2}$	$2$	$11.2069216589$	$3604.343074680877$			?	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$8$	$39.3020113964$
12.6.3959860197871.1	$x^{12} - x^{11} - 5 x^{10} + 7 x^{9} + 7 x^{8} - 20 x^{7} + 3 x^{6} + 25 x^{5} - 15 x^{4} - 10 x^{3} + 11 x^{2} - x - 1$	$12$	[6,3]	$-\,67^{2}\cdot 151\cdot 2417^{2}$	$3$	$11.2151904896$	$4944.9761374550635$			✓	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$8$	$39.4198384491$
12.6.4008072671875.1	$x^{12} - 4 x^{10} - 4 x^{9} + x^{8} + 8 x^{7} + 8 x^{6} + x^{5} - 5 x^{4} - 6 x^{3} - 2 x^{2} + 1$	$12$	[6,3]	$-\,5^{6}\cdot 61\cdot 4205191$	$3$	$11.2265065033$	$35813.171529480605$			✓	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$8$	$39.6887581471$
12.6.4008854234375.1	$x^{12} - x^{11} - 3 x^{10} + 2 x^{9} + 2 x^{8} - 5 x^{7} + 8 x^{6} + 8 x^{5} - 9 x^{4} - 8 x^{3} + 3 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 19^{2}\cdot 61^{2}\cdot 191$	$4$	$11.226688915$	$1052.0670130747376$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$39.6657239253$
12.6.4457810171875.1	$x^{12} - 3 x^{11} + 2 x^{10} + 3 x^{9} - 8 x^{8} + 3 x^{7} + 7 x^{6} + x^{5} - 4 x^{4} - 5 x^{3} + x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 31\cdot 101\cdot 91121$	$4$	$11.3264409262$	$37769.02507346463$			✓	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$8$	$42.3975316008$
12.6.4466170043531.1	$x^{12} - 2 x^{11} - 4 x^{10} + 10 x^{9} + 3 x^{8} - 22 x^{7} + 7 x^{6} + 22 x^{5} - 17 x^{4} - 8 x^{3} + 11 x^{2} - x - 1$	$12$	[6,3]	$-\,7^{8}\cdot 43^{2}\cdot 419$	$3$	$11.3282094759$	$491.1791606329313$			✓	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$8$	$42.3028923905$
12.6.4471579046875.1	$x^{12} - x^{11} - 3 x^{10} - 3 x^{9} + x^{8} + 9 x^{7} + 11 x^{6} + 9 x^{5} + x^{4} - 3 x^{3} - 3 x^{2} - x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 19\cdot 3881^{2}$	$3$	$11.3293521465$	$607.2026021024614$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$42.5473962095$
12.6.4608482796875.1	$x^{12} - 4 x^{10} - 3 x^{9} + 3 x^{8} + 13 x^{7} + 4 x^{6} - 15 x^{5} - 11 x^{4} + 5 x^{3} + 8 x^{2} + x - 1$	$12$	[6,3]	$-\,5^{6}\cdot 419\cdot 839^{2}$	$3$	$11.3578596444$	$1325.784673316146$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$43.200654948$
12.6.4617771109375.1	$x^{12} - 3 x^{11} + x^{10} + 5 x^{9} - 3 x^{8} - 10 x^{7} + 11 x^{6} + 3 x^{5} - 9 x^{4} + 8 x^{3} - x^{2} - 3 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 151\cdot 1399^{2}$	$3$	$11.3597655143$	$1027.7378070305674$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$43.1943606275$
12.6.4770738948267.1	$x^{12} - 3 x^{10} - 4 x^{9} + 12 x^{7} + x^{6} - 3 x^{5} + 3 x^{4} - 7 x^{3} - 3 x^{2} + 3 x + 1$	$12$	[6,3]	$-\,3^{16}\cdot 19^{2}\cdot 307$	$3$	$11.3906577868$	$330.45144947292306$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$8$	$43.9848803763$
12.6.5029275805211.1	$x^{12} - x^{11} - 4 x^{10} + 7 x^{9} + 2 x^{8} - 14 x^{7} + 7 x^{6} + 8 x^{5} - 10 x^{4} - x^{3} + 5 x^{2} - 1$	$12$	[6,3]	$-\,7^{8}\cdot 872411$	$2$	$11.4408630692$	$3417.899273333768$			✓	$S_4\wr C_3$ (as 12T292)	trivial	$2$	$8$	$45.5165696715$
12.6.5099237430147.1	$x^{12} - x^{11} - 7 x^{10} + 8 x^{9} + 16 x^{8} - 16 x^{7} - 18 x^{6} + 13 x^{5} + 10 x^{4} - 8 x^{3} - 3 x^{2} + 3 x + 1$	$12$	[6,3]	$-\,3^{3}\cdot 7^{8}\cdot 181^{2}$	$3$	$11.4540419535$	$85.27046045212757$			?	$C_2\wr C_6$ (as 12T142)	trivial	$2$	$8$	$45.8680277949$
12.6.5124671732159.1	$x^{12} - x^{11} - x^{10} - x^{9} - 6 x^{8} + 11 x^{7} + 10 x^{6} - 10 x^{5} - 5 x^{4} - x^{3} + 3 x^{2} + 2 x - 1$	$12$	[6,3]	$-\,7^{8}\cdot 888959$	$2$	$11.4587920376$	$3450.1625670601557$			?	$S_4\wr C_3$ (as 12T292)	trivial	$2$	$8$	$45.9665196579$
12.6.5134519671875.1	$x^{12} - 3 x^{11} + 8 x^{9} - 4 x^{8} - 8 x^{7} - 3 x^{6} + 14 x^{5} + 5 x^{4} - 14 x^{3} + 3 x^{2} + 3 x - 1$	$12$	[6,3]	$-\,5^{6}\cdot 11^{3}\cdot 246889$	$3$	$11.4606254269$	$3684.9552236085583$			?	$S_3\wr D_4$ (as 12T274)	trivial	$2$	$8$	$46.0186796017$
12.6.5192327768191.1	$x^{12} - 5 x^{10} + 9 x^{8} - 2 x^{7} - 9 x^{6} + 6 x^{5} + 8 x^{4} - 4 x^{3} - 5 x^{2} + x + 1$	$12$	[6,3]	$-\,5192327768191$	$1$	$11.4713229966$	$2278667.9811220854$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$8$	$46.2686748261$
12.6.5528913603539.1	$x^{12} - 3 x^{11} + 2 x^{10} + 7 x^{9} - 13 x^{8} + 3 x^{7} + 13 x^{6} - 14 x^{5} + 7 x^{3} - 4 x^{2} - x + 1$	$12$	[6,3]	$-\,197\cdot 2251\cdot 12468037$	$3$	$11.5315224888$	$2351364.200531045$			✓	$S_{12}$ (as 12T301)	trivial	$2$	$8$	$48.299736144$
12.6.5559960326067.1	$x^{12} - 5 x^{11} + 6 x^{10} + 9 x^{9} - 26 x^{8} + 15 x^{7} - x^{6} + 12 x^{5} - 6 x^{4} - 16 x^{3} + 5 x^{2} + 6 x + 1$	$12$	[6,3]	$-\,3^{9}\cdot 7^{10}$	$2$	$11.5369047675$	$11.53690476748077$			?	$D_4 \times C_3$ (as 12T14)	trivial	$2$	$8$	$48.1439095362$
12.6.6337710296875.1	$x^{12} - x^{11} - 4 x^{10} + 5 x^{9} + 5 x^{8} - 9 x^{7} - 5 x^{6} + 6 x^{5} + 6 x^{4} - 3 x^{3} - 4 x^{2} + x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 29^{3}\cdot 16631$	$3$	$11.6634679044$	$1552.898902053833$			✓	$S_3\wr D_4$ (as 12T274)	trivial	$2$	$8$	$53.3055263997$
12.6.6395326109375.1	$x^{12} - 4 x^{11} + 17 x^{9} - 14 x^{8} - 23 x^{7} + 32 x^{6} + 4 x^{5} - 21 x^{4} + 11 x^{3} - 5 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 7^{8}\cdot 71$	$3$	$11.672267301$	$68.94660244848463$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$8$	$52.4475924124$
12.6.6574568745051.1	$x^{12} - 3 x^{11} + 3 x^{10} - 3 x^{9} + 3 x^{8} + 3 x^{7} - 8 x^{6} + 6 x^{5} - 3 x^{4} - 3 x^{3} + 6 x^{2} - 1$	$12$	[6,3]	$-\,3^{16}\cdot 163\cdot 937$	$3$	$11.699184928480138$	$1690.928603284853$			?	$S_4\wr C_3$ (as 12T292)	trivial	$2$	$8$	$53.959540130132055$
12.6.6815156734375.1	$x^{12} - 2 x^{11} - 2 x^{10} + 11 x^{9} - 6 x^{8} - 21 x^{7} + 19 x^{6} + 12 x^{5} - 19 x^{4} + 2 x^{3} + 8 x^{2} - x - 1$	$12$	[6,3]	$-\,5^{6}\cdot 11^{4}\cdot 31^{3}$	$3$	$11.7342765866$	$61.57829207131912$			?	$\SOPlus(4,2)$ (as 12T35)	trivial	$2$	$8$	$54.8065567524$
12.6.6889511421875.1	$x^{12} - x^{11} - 5 x^{10} + 5 x^{9} + 6 x^{8} - 6 x^{7} + 2 x^{6} - 3 x^{5} - 3 x^{4} + 7 x^{3} - 3 x^{2} - 2 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 29^{3}\cdot 101\cdot 179$	$4$	$11.7448922107$	$1619.09079424225$			?	$S_3\wr D_4$ (as 12T274)	trivial	$2$	$8$	$55.3025292271$
12.6.7295734234375.1	$x^{12} - 4 x^{11} + 5 x^{10} - 2 x^{9} - 5 x^{8} + 14 x^{7} - 17 x^{6} + 14 x^{5} - 5 x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 31\cdot 3881^{2}$	$3$	$11.8010980058$	$775.5997679215743$			?	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$56.9271303227$
12.6.7811642290603.1	$x^{12} - 3 x^{11} - x^{10} + 7 x^{9} + 4 x^{8} - 11 x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 8 x^{3} + 3 x^{2} - 3 x - 1$	$12$	[6,3]	$-\,491^{3}\cdot 65993$	$2$	$11.8684825518$	$5692.3249204521$			?	$S_3\wr S_4$ (as 12T289)	trivial	$2$	$8$	$58.9525792483$
12.6.8099130339328.1	$x^{12} - 2 x^{11} - 4 x^{10} - 4 x^{9} - 2 x^{8} + 8 x^{7} + 7 x^{6} + 8 x^{5} - 2 x^{4} - 4 x^{3} - 4 x^{2} - 2 x + 1$	$12$	[6,3]	$-\,2^{12}\cdot 7^{11}$	$2$	$11.9042818$	$11.90428180002048$			?	$D_4 \times C_3$ (as 12T14)	trivial	$2$	$8$	$63.8207000652$
12.6.8121007759123.1	$x^{12} - 2 x^{11} - 2 x^{10} + 4 x^{9} - 2 x^{8} + 7 x^{7} - 14 x^{5} + 6 x^{4} + 3 x^{3} - 4 x^{2} + x + 1$	$12$	[6,3]	$-\,7^{8}\cdot 43\cdot 181^{2}$	$3$	$11.906958148$	$322.8287530078796$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$8$	$60.0607066436$
12.6.8192886833152.1	$x^{12} - 2 x^{10} - 2 x^{9} - 2 x^{8} + 4 x^{7} + 3 x^{6} + 4 x^{5} - 2 x^{4} - 2 x^{3} - 2 x^{2} + 1$	$12$	[6,3]	$-\,2^{18}\cdot 7\cdot 2113^{2}$	$3$	$11.915705098690154$	$343.98837189649305$			✓	$S_4^2:D_4$ (as 12T260)	trivial	$2$	$8$	$64.12166932416741$
12.6.9120427796875.1	$x^{12} - x^{11} - x^{10} - x^{9} + 2 x^{8} - 2 x^{7} - 3 x^{6} + 19 x^{5} - 21 x^{4} + 6 x^{3} + 6 x^{2} - 5 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 19\cdot 79\cdot 388879$	$4$	$12.0226794336$	$54023.48466176539$			?	$S_6\wr C_2$ (as 12T299)	trivial	$2$	$8$	$66.162967534$
12.6.9842374000287.1	$x^{12} - 4 x^{11} + 3 x^{10} + 15 x^{9} - 40 x^{8} + 30 x^{7} + 18 x^{6} - 39 x^{5} + 12 x^{4} + 9 x^{3} - 7 x^{2} + 1$	$12$	[6,3]	$-\,3^{6}\cdot 103\cdot 107^{4}$	$3$	$12.0992464222$	$239.30481785925204$			?	$C_2\wr (C_2\times S_4)$ (as 12T250)	trivial	$2$	$8$	$70.0148733812$
12.6.9904396000000.1	$x^{12} - 3 x^{11} - x^{10} + 7 x^{9} - x^{8} - 2 x^{7} + 7 x^{6} - 16 x^{5} - 9 x^{4} + 19 x^{3} + 4 x^{2} - 4 x - 1$	$12$	[6,3]	$-\,2^{8}\cdot 5^{6}\cdot 19^{5}$	$3$	$12.1055817906$	$41.28570135662403$			?	$C_6\wr C_2$ (as 12T42)	trivial	$2$	$8$	$67.9024659123$
12.6.10218945315584.1	$x^{12} - 3 x^{11} - x^{10} + 9 x^{9} - x^{8} - 16 x^{7} + 3 x^{6} + 24 x^{5} - 9 x^{4} - 19 x^{3} + 8 x^{2} + 6 x - 1$	$12$	[6,3]	$-\,2^{8}\cdot 19^{2}\cdot 37^{4}\cdot 59$	$4$	$12.1371626771$	$323.28855651411374$			?	$C_2\wr (C_2\times S_4)$ (as 12T250)	trivial	$2$	$8$	$70.3410949906$
12.6.10513415548928.1	$x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 11 x^{8} + 20 x^{7} - 12 x^{6} + 8 x^{4} - 4 x^{3} - x^{2} - 2 x + 1$	$12$	[6,3]	$-\,2^{12}\cdot 67^{2}\cdot 83^{3}$	$3$	$12.1659301654$	$300.5745763472249$			?	$C_3\wr S_4$ (as 12T231)	trivial	$2$	$8$	$69.1711510134$
12.6.10578455953408.1	$x^{12} - 2 x^{11} - x^{10} - 2 x^{9} + 3 x^{8} + 14 x^{7} - 20 x^{6} + 34 x^{4} + 12 x^{3} - x^{2} + 2 x + 1$	$12$	[6,3]	$-\,2^{18}\cdot 7^{9}$	$2$	$12.1721844145$	$14.315066180821045$			?	$D_4 \times C_3$ (as 12T14)	trivial	$2$	$8$	$74.2304379605$
12.6.10721964631207.1	$x^{12} - 2 x^{11} - x^{10} + 8 x^{9} - 7 x^{8} - 3 x^{7} + 7 x^{6} - 9 x^{5} + 7 x^{4} - 6 x^{2} + 5 x - 1$	$12$	[6,3]	$-\,61^{2}\cdot 1423^{3}$	$2$	$12.1858603703$	$584.5509088050569$			?	$C_3\wr S_4$ (as 12T231)	trivial	$2$	$8$	$73.9804186368$
12.6.10888658888551.1	$x^{12} - 2 x^{11} - 2 x^{10} + 15 x^{9} - 21 x^{8} + x^{7} + 36 x^{6} - 50 x^{5} + 29 x^{4} - 11 x^{2} + 6 x - 1$	$12$	[6,3]	$-\,31\cdot 592661^{2}$	$2$	$12.2015367617$	$4286.3143841766905$			?	$C_2^6.S_6$ (as 12T293)	trivial	$2$	$8$	$70.8841951241$
12.6.10890820856071.1	$x^{12} - 4 x^{11} + 2 x^{10} + 13 x^{9} - 27 x^{8} + 15 x^{7} + 22 x^{6} - 42 x^{5} + 27 x^{4} - 11 x^{2} + 6 x - 1$	$12$	[6,3]	$-\,13^{10}\cdot 79$	$2$	$12.2017386302$	$75.35284821191699$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$8$	$71.0426080758$
12.6.11808520366783.1	$x^{12} - 6 x^{11} + 15 x^{10} - 20 x^{9} + 11 x^{8} + 10 x^{7} - 30 x^{6} + 37 x^{5} - 15 x^{4} - 13 x^{3} + 17 x^{2} - 7 x + 1$	$12$	[6,3]	$-\,7^{8}\cdot 127^{3}$	$2$	$12.2842776429$	$41.23828102000196$			?	$C_2^3.(C_2\times A_4)$ (as 12T104)	trivial	$2$	$8$	$77.2262907733$
12.6.11808520366783.2	$x^{12} - x^{11} - 5 x^{10} + 6 x^{9} + 16 x^{8} - 6 x^{7} - 26 x^{6} - 3 x^{5} + 18 x^{4} + 6 x^{3} - 6 x^{2} - 2 x + 1$	$12$	[6,3]	$-\,7^{8}\cdot 127^{3}$	$2$	$12.2842776429$	$41.23828102000196$			✓	$C_2^3.(C_2\times A_4)$ (as 12T104)	trivial	$2$	$8$	$77.2262907733$
12.6.12110614233088.1	$x^{12} - 4 x^{11} + 4 x^{10} + 4 x^{9} - 15 x^{8} + 14 x^{7} + 12 x^{6} - 22 x^{5} - 7 x^{4} + 10 x^{3} + 5 x^{2} - 2 x - 1$	$12$	[6,3]	$-\,2^{18}\cdot 7^{3}\cdot 367^{2}$	$3$	$12.3101642483$	$143.3596874996594$			?	$D_6\wr C_2$ (as 12T125)	trivial	$2$	$8$	$76.0465779983$
12.6.12520427171875.1	$x^{12} - x^{11} - 3 x^{10} + x^{9} + 2 x^{8} + 10 x^{7} - 7 x^{6} - 12 x^{5} + 11 x^{4} - x^{3} - 5 x^{2} + 2 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 7^{8}\cdot 139$	$3$	$12.3443510061$	$96.46973724535417$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$8$	$76.6620065786$
12.6.12685282671875.1	$x^{12} - 3 x^{11} - x^{10} + 11 x^{9} - 6 x^{8} - 12 x^{7} - x^{6} + x^{5} + 12 x^{4} + 18 x^{3} + 14 x^{2} + 6 x + 1$	$12$	[6,3]	$-\,5^{6}\cdot 11^{5}\cdot 71^{2}$	$3$	$12.3578147066$	$62.489999199871974$			?	$D_6\wr C_2$ (as 12T125)	trivial	$2$	$8$	$79.9911716957$
12.6.12779495296875.1	$x^{12} - 3 x^{11} + 6 x^{10} - 10 x^{9} + 9 x^{8} - 6 x^{7} - 12 x^{6} + 18 x^{5} - 6 x^{4} + 10 x^{3} - 9 x^{2} + 1$	$12$	[6,3]	$-\,3^{16}\cdot 5^{6}\cdot 19$	$3$	$12.365437173107072$	$42.17192986702622$			?	$C_2\wr C_6$ (as 12T134)	trivial	$2$	$8$	$80.39469472298418$
12.6.12782924000000.1	$x^{12} - x^{11} - 2 x^{10} + 14 x^{9} - 15 x^{8} - 16 x^{7} + 37 x^{6} - 16 x^{5} - 15 x^{4} + 14 x^{3} - 2 x^{2} - x + 1$	$12$	[6,3]	$-\,2^{8}\cdot 5^{6}\cdot 7^{4}\cdot 11^{3}$	$4$	$12.3657136068$	$39.242833740697165$			?	$S_3^2:C_2^2$ (as 12T78)	trivial	$2$	$8$	$81.5937102666$
12.6.13409105834831.1	$x^{12} - 4 x^{11} + 5 x^{10} - 10 x^{8} + 18 x^{7} - 11 x^{6} - 16 x^{5} + 22 x^{4} - 8 x^{2} + x + 1$	$12$	[6,3]	$-\,7^{8}\cdot 71\cdot 181^{2}$	$3$	$12.415093221$	$414.8271331635092$			?	$D_4\wr C_3$ (as 12T222)	trivial	$2$	$8$	$82.8552918261$
12.6.13907109998592.1	$x^{12} - 3 x^{10} - 4 x^{9} + 14 x^{7} + 2 x^{6} - 18 x^{5} + 5 x^{4} + 10 x^{3} - 5 x^{2} - 2 x + 1$	$12$	[6,3]	$-\,2^{12}\cdot 3^{6}\cdot 167^{3}$	$3$	$12.4528782135$	$160.92665210764017$			?	$S_4^2:C_2^2$ (as 12T235)	trivial	$2$	$8$	$86.4729185957$
12.6.14501103264256.1	$x^{12} - x^{11} - 7 x^{10} + 6 x^{9} + 13 x^{8} - 16 x^{7} - x^{6} + 19 x^{5} - 17 x^{4} - 5 x^{3} + 13 x^{2} - 3 x - 1$	$12$	[6,3]	$-\,2^{9}\cdot 7^{8}\cdot 17^{3}$	$3$	$12.4963569039$	$42.67447112735335$			?	$C_3\times S_4$ (as 12T45)	trivial	$2$	$8$	$93.643207835$
12.6.14941367239327.1	$x^{12} - x^{11} - 6 x^{10} + 4 x^{9} + 16 x^{8} - 6 x^{7} - 25 x^{6} + x^{5} + 26 x^{4} + 9 x^{3} - 14 x^{2} - 7 x + 1$	$12$	[6,3]	$-\,283^{3}\cdot 659221$	$2$	$12.5275418342$	$13658.68013389288$			?	$S_3\wr S_4$ (as 12T289)	trivial	$2$	$8$	$86.8510076113$