Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of 216)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.279962425744585891967345313193.3	x^8 - x^7 + 4711x^6 + 653257x^5 + 31269320x^4 + 1485681448x^3 + 62048882160x^2 + 1357510184208x + 31843864896768	\( 97^{7}\cdot 389^{6} \)	$C_8$ (as 8T1)	$[2, 2, 8, 378161320]$ (GRH)
8.0.81729569074669588344431934238657.1	x^8 - x^7 + 16128x^6 - 1590878x^5 + 108308949x^4 - 12464473129x^3 + 874558747498x^2 - 28290757421944x + 344777897389504	\( 193^{7}\cdot 449^{6} \)	$QD_{16}$ (as 8T8)	$[2, 2, 2, 8, 8, 23228256]$ (GRH)
8.0.464168143996753120817910253432897.1	x^8 - 3x^7 + 19234x^6 + 2260830x^5 + 163692817x^4 + 16594676901x^3 + 1246746053196x^2 + 45581396588928x + 697479143507712	\( 313^{6}\cdot 337^{7} \)	$QD_{16}$ (as 8T8)	$[2, 6, 1120689624]$ (GRH)
8.0.1510269940117393787434340294825833.1	x^8 - x^7 + 3434x^6 + 466106x^5 - 58494895x^4 - 4671184537x^3 + 298254631492x^2 + 83147741664x + 158956300781568	\( 137^{7}\cdot 401^{7} \)	$C_8$ (as 8T1)	$[13544638952]$ (GRH)
8.0.13897275301014211264403977677961177.2	x^8 - x^7 + 4715x^6 + 734293x^5 + 108209412x^4 - 9194607652x^3 + 1474055710240x^2 - 49652339911872x + 2334173324483072	\( 241^{7}\cdot 313^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2, 4, 8, 111018440]$ (GRH)
8.0.20484103524067689958079314502405129.1	x^8 - x^7 + 23601x^6 - 5517263x^5 - 362023474x^4 + 91975332368x^3 - 814150716160x^2 - 397967734046720x + 15240481922613248	\( 421^{6}\cdot 449^{7} \)	$C_8$ (as 8T1)	$[2, 2, 2, 2, 8, 125367496]$ (GRH)
8.0.3192079979985055450294717870083050969.5	x^8 - x^7 + 10251x^6 + 6188777x^5 - 297797660x^4 + 39497233544x^3 + 8368042437008x^2 - 946303903070320x + 49597789483198400	\( 401^{7}\cdot 409^{7} \)	$C_8$ (as 8T1)	$[2, 4, 1612979912]$ (GRH)
8.0.7043484173213574853891721381764967081.2	x^8 - x^7 + 11478x^6 + 6516386x^5 - 588887459x^4 - 13801397365x^3 + 11680953965900x^2 - 914182000547500x + 54366150332000000	\( 409^{7}\cdot 449^{7} \)	$C_8$ (as 8T1)	$[2, 2, 4, 1092083528]$ (GRH)
10.2.3469919342845454006739336964012500000000.1	x^10 - 5x^9 + 5x^8 + 10x^7 - 15x^6 + 172465x^5 - 431175x^4 + 2587150x^3 - 3449525x^2 + 3018325x + 7436044025	\( 2^{8}\cdot 3^{8}\cdot 5^{11}\cdot 1597^{8} \)	$F_5$ (as 10T4)	$[10, 10, 14260, 14260]$ (GRH)
16.0.683567948564897299391469349182811817443328.1	x^16 + 4199x^14 + 5886131x^12 + 3978693634x^10 + 1482245714409x^8 + 318824584999742x^6 + 39051900730883446x^4 + 2486877913489246478x^2 + 61946512496156595137	\( 2^{16}\cdot 17^{15}\cdot 43691^{4} \)	$(C_2\times OD_{16}).D_4$ (as 16T591)	$[2, 2, 2, 2, 2, 1058994498]$ (GRH)
16.0.683567948564897299391469349182811817443328.2	x^16 + 4063x^14 + 6007715x^12 + 4216341258x^10 + 1588534344529x^8 + 337055877573450x^6 + 40036280260158564x^4 + 2475535254818828022x^2 + 61946512496156595137	\( 2^{16}\cdot 17^{15}\cdot 43691^{4} \)	$(C_2\times OD_{16}).D_4$ (as 16T591)	$[2, 2, 2, 2, 2, 1068746342]$ (GRH)
16.0.1861644105089180838863336343231454234279936.1	x^16 + 3192x^14 - 3680x^13 + 3820332x^12 - 8222112x^11 + 2278069768x^10 - 6381521824x^9 + 749980009966x^8 - 2278581253952x^7 + 140107567212424x^6 - 406917584361472x^5 + 14342083431686636x^4 - 34925731551753120x^3 + 706802171767051960x^2 - 1124404063609193536x + 11373046199801545201	\( 2^{62}\cdot 7^{6}\cdot 193^{4}\cdot 223^{4} \)	$(C_2^2\times C_4).C_2^4$ (as 16T471)	$[2, 2, 2, 2, 2, 2, 2, 2, 75774660]$ (GRH)
16.0.8461629347780675963909292061418521600000000.1	x^16 + 3366x^14 + 4288256x^12 + 2643188394x^10 + 843697669633x^8 + 140021879295672x^6 + 11844611939032629x^4 + 481407719903051007x^2 + 7448383238882771641	\( 2^{16}\cdot 5^{8}\cdot 29^{6}\cdot 89^{8}\cdot 109^{4} \)	$C_2^2.C_2^5.C_2$ (as 16T493)	$[2, 2, 2, 2, 2, 2, 2, 252870404]$ (GRH)
16.0.29786305681426893421813381491703267748478976.1	x^16 + 3464x^14 - 3216x^13 + 4898708x^12 - 7958096x^11 + 3643957168x^10 - 7631842416x^9 + 1528170097824x^8 - 3619337419376x^7 + 358605823359368x^6 - 892387439161696x^5 + 43925474650991112x^4 - 109475242669266480x^3 + 2467664760780016224x^2 - 5494406389961891840x + 55151228745540959074	\( 2^{66}\cdot 7^{6}\cdot 193^{4}\cdot 223^{4} \)	$(C_2^2\times C_4).C_2^4$ (as 16T471)	$[2, 2, 2, 2, 2, 2, 2, 6, 106594380]$ (GRH)
16.0.46871787785697452696878168826792882590449664.1	x^16 + 1712x^14 + 1233350x^12 + 488006872x^10 + 115758148212x^8 + 16792514721616x^6 + 1446242915789840x^4 + 67056318133293792x^2 + 1270028532190841476	\( 2^{48}\cdot 23^{6}\cdot 37^{4}\cdot 24499031^{2} \)	16T1765	$[2, 2, 2, 2723433000]$ (GRH)
16.0.96468058006688010602395260507818496203564253184.1	x^16 + 1028x^14 + 255458x^12 + 23931840x^10 + 862829184x^8 + 12850493440x^6 + 71556958208x^4 + 147171966976x^2 + 69257396224	\( 2^{44}\cdot 257^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 4, 4, 40, 687480]$ (GRH)
16.0.288604193782091750893321301214124833643876581376.2	x^16 + 3092x^14 + 3763147x^12 + 2296419422x^10 + 744702238048x^8 + 127016546026864x^6 + 10768253589679158x^4 + 388439643284578428x^2 + 3207580110181323556	\( 2^{46}\cdot 239^{4}\cdot 257^{10} \)	16T875	$[2, 2, 2, 2, 2, 2, 6, 149148972]$ (GRH)
16.0.1543488928107008169638324168125095939257028050944.1	x^16 + 98688x^12 + 30716640x^10 + 2073969697x^8 + 2840635392x^6 + 164025558208x^4 - 2243290349568x^2 + 5648874013696	\( 2^{48}\cdot 257^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 8, 24, 24, 32352]$ (GRH)
16.0.1543488928107008169638324168125095939257028050944.3	x^16 + 123360x^12 + 3810894945x^8 - 521459496960x^4 + 17868678762496	\( 2^{48}\cdot 257^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 2, 2, 2, 2, 4, 4, 8, 16, 80880]$ (GRH)
16.0.9051792270538665113859285354790637594769776181248.1	x^16 + 3264x^14 + 3316496x^12 + 1304953472x^10 + 221639065992x^8 + 16702070265472x^6 + 490448945740944x^4 + 3874220981492640x^2 + 5934553794724178	\( 2^{79}\cdot 23^{4}\cdot 31^{8}\cdot 89^{4} \)	$C_4.C_2^2\wr C_2$ (as 16T385)	$[2, 2, 2, 4, 4, 20, 34192480]$ (GRH)
16.0.9051792270538665113859285354790637594769776181248.2	x^16 + 3264x^14 + 4140208x^12 + 2581228928x^10 + 836309669640x^8 + 142366611859328x^6 + 12437574187407824x^4 + 512785191909377632x^2 + 7658348535725451218	\( 2^{79}\cdot 23^{4}\cdot 31^{8}\cdot 89^{4} \)	$C_4.C_2^2\wr C_2$ (as 16T385)	$[2, 2, 2, 2, 2, 4, 20, 34192480]$ (GRH)
16.0.49504953235652560005667952183459368974585759268864.1	x^16 + 1928x^14 + 1288880x^12 + 405962108x^10 + 65834061236x^8 + 5383868719400x^6 + 189111188166776x^4 + 1503056414236448x^2 + 15977927617600	\( 2^{36}\cdot 7687^{10} \)	16T1543	$[2, 2, 2, 2, 2, 4, 104987608]$ (GRH)
16.0.49504953235652560005667952183459368974585759268864.2	x^16 + 1500x^14 + 889640x^12 + 264096308x^10 + 40486683676x^8 + 2897987746232x^6 + 67780112968120x^4 + 460191898925712x^2 + 781198698804624	\( 2^{36}\cdot 7687^{10} \)	16T1543	$[2, 2, 2, 2, 2, 4, 161966728]$ (GRH)
16.0.247615754888863175950064888078950980890077741301809.2	x^16 - x^15 + 369x^14 - 7127x^13 - 24628x^12 - 3860358x^11 + 3847802x^10 - 31586510x^9 + 11790894313x^8 + 150438196003x^7 + 3045583313341x^6 + 28963391474261x^5 + 215319701431098x^4 + 1030855819624916x^3 + 5228711472095080x^2 + 2899855979953376x + 99902637257197312	\( 41^{14}\cdot 97^{14} \)	$C_8\times C_2$ (as 16T5)	$[21, 4338913908]$ (GRH)
16.0.649575421749918056203935283031437604425079449452544.1	x^16 + 1501x^14 + 911285x^12 + 286021943x^10 + 49105808800x^8 + 4480851471638x^6 + 197363433219140x^4 + 3937312460664784x^2 + 28613530403758336	\( 2^{28}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 2, 2, 4, 24, 8126040]$ (GRH)
16.0.791005910030165719912925444172568170567213001250881.3	x^16 - 5x^15 + 536x^14 - 14970x^13 + 504403x^12 - 11045491x^11 + 220735521x^10 - 3445251317x^9 + 47662575288x^8 - 533426130836x^7 + 5232393557019x^6 - 40295189035117x^5 + 281733439507432x^4 - 1457129277599064x^3 + 7383199674276536x^2 - 21116314559719616x + 31975694368889344	\( 29^{14}\cdot 149^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 24222, 242220]$ (GRH)
16.0.791005910030165719912925444172568170567213001250881.4	x^16 - 3x^15 + 573x^14 + 9272x^13 + 337161x^12 + 6299195x^11 + 87537415x^10 + 1429221904x^9 + 16277482567x^8 + 215209853765x^7 + 2402287099291x^6 + 20641758474146x^5 + 168575519317340x^4 + 882336067964976x^3 + 4598319446544384x^2 + 12600832442989824x + 49455952218418176	\( 29^{14}\cdot 149^{14} \)	$C_2^3.C_4$ (as 16T41)	$[2, 24222, 242220]$ (GRH)
16.0.791005910030165719912925444172568170567213001250881.5	x^16 - 5x^15 + 404x^14 - 7911x^13 + 85309x^12 - 1712558x^11 + 42103059x^10 - 763954787x^9 + 20065856528x^8 - 378903900861x^7 + 3069805875379x^6 - 16152690635942x^5 + 158678336760608x^4 - 1395404638505784x^3 + 4213301148768960x^2 + 9966977583135840x + 414401005855515456	\( 29^{14}\cdot 149^{14} \)	$C_2^3.C_4$ (as 16T36)	$[2, 24222, 242220]$ (GRH)
16.0.2598301686999672224815741132125750417700317797810176.1	x^16 + 1413x^14 + 640747x^12 + 122467295x^10 + 9850573750x^8 + 279518044450x^6 + 1590760453744x^4 + 708784500408x^2 + 1082146816	\( 2^{30}\cdot 193^{8}\cdot 257^{10} \)	16T813	$[2, 2, 2, 2, 2, 4, 12, 32390040]$ (GRH)
16.0.24018728224219728067156294143658245146337540906275473.2	x^16 - x^15 + 246x^14 - 5528x^13 - 102364x^12 + 2534658x^11 + 43785164x^10 - 994326206x^9 + 13045857327x^8 - 278639592799x^7 + 5130957769597x^6 - 53334252425244x^5 + 347355235431558x^4 - 1527640572701475x^3 + 4651932548849904x^2 - 9598577056412940x + 13133394052911819	\( 41^{14}\cdot 97^{15} \)	$C_{16}$ (as 16T1)	$[13002309512]$ (GRH)
16.0.193851685179255766530952003996759265201819225743449601.5	x^16 - x^15 + 594x^14 + 2531x^13 + 47690x^12 - 5352141x^11 + 51739983x^10 + 192556636x^9 + 5083665532x^8 + 450226956190x^7 + 941787543275x^6 - 77428720044109x^5 - 764954674399913x^4 - 18683145716368537x^3 - 73879184588145834x^2 + 2427071999215910603x + 33380320760954558557	\( 37^{14}\cdot 173^{14} \)	$C_8.C_4$ (as 16T49)	$[6, 6, 1682050764]$ (GRH)
16.0.3668342962637889127310596327197122046055622675946369169.4	x^16 - 7x^15 + 757x^14 + 17359x^13 + 505614x^12 + 12895156x^11 + 211899620x^10 + 7541456698x^9 - 1389972933x^8 + 1240781089975x^7 + 4371887866584x^6 - 55659562317467x^5 + 4297633387795179x^4 - 111896064809531971x^3 + 2220052595158974387x^2 - 20096776454760585706x + 78442230270956678147	\( 53^{14}\cdot 149^{14} \)	$C_8.C_4$ (as 16T49)	$[3, 6, 630, 1533420]$ (GRH)
16.0.54602537259435919051622734069846680881723505970000234609.1	x^16 - 6x^15 + 3581x^14 + 35728x^13 + 3184374x^12 - 7157146x^11 + 1115337704x^10 - 3559324740x^9 - 413101870103x^8 - 19670422590640x^7 + 1180694075592x^6 + 4494586179489760x^5 + 79009337564951184x^4 - 636825223635723648x^3 - 12244752595015384320x^2 - 2796479624717236224x + 944525217449845297152	\( 61^{14}\cdot 157^{14} \)	$C_8: C_2$ (as 16T6)	$[168545, 337090]$ (GRH)
18.0.382767468601979969221900924428079566404384980992.2	x^18 - 3x^17 - 42x^16 + 12x^15 + 1512x^14 + 1572x^13 - 5418x^12 - 3414x^11 + 258483x^10 + 481455x^9 + 4287204x^8 + 13613802x^7 + 73994292x^6 + 146257296x^5 + 667973280x^4 + 855399936x^3 + 3840924672x^2 + 1876512768x + 11595603968	\( -\,2^{18}\cdot 3^{30}\cdot 13^{14}\cdot 23^{9} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 3, 6, 236316906]$ (GRH)
18.0.1348608123969580736044287667264238937751275533631.6	x^18 - 666x^15 + 10989x^14 - 132534x^13 + 504828x^12 + 267732x^11 - 2869461x^10 - 2521772x^9 + 77298624x^8 + 21004974x^7 - 459144729x^6 + 1801890306x^5 + 9112996548x^4 - 24669932040x^3 + 41395363200x^2 + 65283984000x + 33270400000	\( -\,3^{45}\cdot 37^{17} \)	$C_{18}$ (as 18T1)	$[14802753096]$ (GRH)
18.0.1968100446373322200925262150357418865721092079616.1	x^18 - 7x^17 + 4x^16 + 184x^15 + 128x^14 - 8092x^13 + 51598x^12 - 134342x^11 + 478943x^10 - 3007341x^9 + 21773822x^8 - 92692658x^7 + 352111696x^6 - 1127712400x^5 + 4235753024x^4 - 12494373536x^3 + 32946159232x^2 - 50298266368x + 59975185408	\( -\,2^{18}\cdot 31^{9}\cdot 127^{14} \)	$S_3 \times C_6$ (as 18T6)	$[9, 9, 244021806]$ (GRH)
18.0.15537225845019417529672325781592151434950300401664.2	x^18 - 7x^17 + 22x^16 + 72x^15 + 648x^14 - 9060x^13 + 72318x^12 - 272982x^11 + 1442715x^10 - 7028429x^9 + 45186124x^8 - 191602578x^7 + 838542252x^6 - 2810738664x^5 + 10903299792x^4 - 31071279168x^3 + 87450314880x^2 - 137349245952x + 194888648704	\( -\,2^{18}\cdot 3^{9}\cdot 13^{9}\cdot 127^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 84, 357158172]$ (GRH)
18.0.17215978016843899580835684099700667905564175265792.1	x^18 - 9x^17 - 420x^16 + 1984x^15 + 73770x^14 - 37218x^13 - 6149376x^12 - 16784976x^11 + 237244221x^10 + 1419179555x^9 - 2094160692x^8 - 40253540568x^7 - 102727801808x^6 + 224932172208x^5 + 2034413940288x^4 + 5797665555712x^3 + 9183109401600x^2 + 8595850543104x + 4021085863936	\( -\,2^{12}\cdot 3^{24}\cdot 7^{9}\cdot 79^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 4, 12, 84, 1009932]$ (GRH)
18.0.22497960113751479934820492718164014658776000000000.1	x^18 - 9x^17 - 402x^16 + 1840x^15 + 69018x^14 - 10914x^13 - 5537100x^12 - 17815248x^11 + 205547661x^10 + 1433969187x^9 - 1050471018x^8 - 39884181384x^7 - 128655698368x^6 + 185836782000x^5 + 2638164247776x^4 + 9516122868224x^3 + 19470659444736x^2 + 24153643711488x + 15157286557696	\( -\,2^{12}\cdot 3^{27}\cdot 5^{9}\cdot 79^{14} \)	$S_3 \times C_6$ (as 18T6)	$[6, 84, 45051972]$ (GRH)
18.0.147244256784536162442327315331004890491666009075712.1	x^18 - 2x^17 - 127x^16 - 1370x^15 + 1071x^14 + 162946x^13 + 2249906x^12 + 19230652x^11 + 121957908x^10 + 608611962x^9 + 2449633407x^8 + 8020398008x^7 + 21278039105x^6 + 45104419528x^5 + 74302857419x^4 + 90626337302x^3 + 75780975570x^2 + 38197162944x + 8660565481	\( -\,2^{12}\cdot 7^{15}\cdot 19^{9}\cdot 31^{15} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 4, 4, 4, 4, 12, 156, 9516]$ (GRH)
18.0.1235093905746889405718571099119702734980596317089792.1	x^18 - 9x^17 + 384x^16 - 2272x^15 + 88605x^14 - 658197x^13 + 12846028x^12 - 64843719x^11 + 865327146x^10 - 5579169113x^9 + 77246982246x^8 - 512686378569x^7 + 3789040141804x^6 - 15288000079185x^5 + 92885783574705x^4 - 423518882731740x^3 + 2727446539429518x^2 - 8733433478069253x + 23845975839012979	\( -\,2^{12}\cdot 3^{27}\cdot 17^{9}\cdot 37^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 78, 70196490]$ (GRH)
18.0.2173089240515381294985625698929389621300732316614656.6	x^18 + 684x^16 + 145692x^14 + 10824528x^12 + 377384688x^10 + 6981100992x^8 + 70338466944x^6 + 363270583296x^4 + 755493868800x^2 + 40292160000	\( -\,2^{27}\cdot 3^{45}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[2, 14851834524]$ (GRH)
18.0.2718642342706308433638679144477426237858460895019008.1	x^18 + 75x^16 - 518x^15 + 14895x^14 + 38628x^13 + 1453312x^12 + 695970x^11 + 97733346x^10 + 422945816x^9 + 8555002947x^8 + 33622267188x^7 + 365903950891x^6 + 1580920554276x^5 + 17528600923959x^4 + 88916584556742x^3 + 542518369755228x^2 + 1475998825390308x + 4052214442111177	\( -\,2^{24}\cdot 3^{27}\cdot 11^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 210, 4951590]$ (GRH)
18.0.3266961213891533812087277880596312351679162976508187.2	x^18 + 109359x^12 + 354417390x^6 + 291038813883	\( -\,3^{27}\cdot 1657^{12} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 1050, 2470650]$ (GRH)
18.0.4083569424758367433043797712456360033585527698911232.1	x^18 - 9x^17 + 12x^16 - 410x^15 + 10995x^14 - 9861x^13 + 162726x^12 - 3204009x^11 + 24015348x^10 + 104943021x^9 + 1568694924x^8 - 152631309x^7 + 19476958064x^6 + 109343418069x^5 + 2476828380501x^4 + 13611173843684x^3 + 68512294190292x^2 + 162135328484937x + 329489799094441	\( -\,2^{12}\cdot 3^{27}\cdot 29^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 378, 4455864]$ (GRH)
18.0.8880520706942285236653498213029984177183105373284187.2	x^18 + 118863x^12 + 418673070x^6 + 373714754427	\( -\,3^{27}\cdot 1801^{12} \)	$S_3 \times C_3$ (as 18T3)	$[26, 26, 312, 67704]$ (GRH)
18.0.21156460455554157443184358692743823704081665160523776.1	x^18 - 388x^16 - 1770x^15 + 79167x^14 + 461226x^13 - 7119103x^12 - 69040572x^11 + 412426863x^10 + 4399169196x^9 - 18676098374x^8 - 265581279066x^7 + 550446017812x^6 + 17062555046622x^5 + 128931293649937x^4 + 697432636061526x^3 + 2270159537466107x^2 + 2634341655131550x + 6328125825565187	\( -\,2^{12}\cdot 7^{12}\cdot 37^{15}\cdot 47^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 3, 3, 3, 3, 777, 46620]$ (GRH)
18.0.76610513899544453304430517636008399400337408000000000.1	x^18 - 4x^17 - 161x^16 + 122x^15 + 12163x^14 + 26048x^13 - 396092x^12 - 1847422x^11 + 4445026x^10 + 49750964x^9 + 101924407x^8 - 223146292x^7 - 1210841585x^6 + 1527209132x^5 + 28187586667x^4 + 108856477778x^3 + 256578470140x^2 + 342514005968x + 299674652229	\( -\,2^{30}\cdot 3^{6}\cdot 5^{9}\cdot 7^{14}\cdot 43^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 6, 12, 252, 212688]$ (GRH)
18.0.125658219152626752999993187563351622531489799076360192.1	x^18 + 242604x^12 + 14701076640x^6 + 1728	\( -\,2^{12}\cdot 3^{27}\cdot 1123^{12} \)	$S_3 \times C_3$ (as 18T3)	$[301, 4515, 58695]$ (GRH)
18.0.844516909583529949970724206594089321365947904000000000.1	x^18 - 3x^17 - 552x^16 + 6240x^15 + 53364x^14 - 1530168x^13 + 13275402x^12 - 60135330x^11 + 149804439x^10 - 232194769x^9 + 966780294x^8 - 7176130086x^7 + 33707047332x^6 - 107168086212x^5 + 257696335560x^4 - 491003942664x^3 + 736717649280x^2 - 788668438368x + 499240711936	\( -\,2^{18}\cdot 3^{31}\cdot 5^{9}\cdot 7^{14}\cdot 13^{14} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 2, 2, 30, 154037940]$ (GRH)