Group GAP4(128,1402)

Name: (C2 x ((C4 x C4) : C2)) : C2
Maximal quotients:GAP4(64,216) GAP4(64,219) GAP4(64,226) GAP4(64,227) GAP4(64,242)
Real polynomial:
x^128-864*x^126+349840*x^124-88560352*x^122+15777577224*x^120-2111462400256*\
x^118+221250145440192*x^116-18683299779107424*x^114+1298697834022825716*x^11\
2-75530162841936532704*x^110+3722955147186815969808*x^108-157160044715964209\
531520*x^106+5730826342427299662421216*x^104-181815440050207399997457888*x^1\
02+5049082246069775889252912112*x^100-123366541806783883414644873568*x^98+26\
63762200233543793182448669338*x^96-51020423386554512872430688105088*x^94+869\
659202714072802223144566847040*x^92-13228695254598448045151824613435616*x^90\
+180003230947608882539660707950563624*x^88-219542166798254069915282077605946\
7936*x^86+24042071729111011243963530198203128656*x^84-2367338387741953796695\
47749886996321920*x^82+2098401324223691498422771814471139727792*x^80-1675936\
1386894925358738424789968056852256*x^78+120689813008664839511268101380305105\
198448*x^76-784042316937628363152174735819201164370912*x^74+4596081211285132\
968669719473438377864114552*x^72-2431384955779899113489039176839613182453945\
6*x^70+116062786437566903918853721926367151118724960*x^68-499779760839800553\
633989819963016153194537376*x^66+1940446560434213272893913648465821687746036\
899*x^64-6788438816897121779156526404109354824498031488*x^62+213799325815218\
17803990205346194161217816423616*x^60-60554505852625315034800968103327598925\
721480544*x^58+154040430303863653533171673825075422124082090600*x^56-3514145\
96965931338491163944391131745305088711200*x^54+71770975127251665286066191331\
6079307465023029904*x^52-1309665349448215302281603847229214008373525342080*x\
^50+2130469080856143245620381754672395456518910552368*x^48-30816704242129793\
80530976373458977548063387453344*x^46+39522476975835150219958375891316581307\
58999087280*x^44-4479625650914407582516375951096449695716526800224*x^42+4470\
871041943890760828709865025964028835349407672*x^40-3912934903360719188243711\
019395469930852991513920*x^38+2989096785013443961680835517517281145748427030\
880*x^36-1982375849056666816909529696106970102092670433568*x^34+113443318439\
0396107665492869860716974882358409050*x^32-556206488083064882815784210348327\
436222351937440*x^30+231713151506594659557495582960901001465516988144*x^28-8\
1218296829085887938612120950142455944794724224*x^26+236716080062082214955553\
57901415476285023697632*x^24-5655251186757391222796193719408904056997242272*\
x^22+1088071046218210681495327613623090952625830800*x^20-1649126222991919484\
80869808808252174118607776*x^18+19146517036559626841423231449746109101726964\
*x^16-1642790449060571769136976477002647425571264*x^14+994193446260743020534\
91075505365375512608*x^12-3985075350069523121648004715798940223072*x^10+9615\
0995988017422129364616764374679832*x^8-1166594923316686037387658782679205344\
*x^6+4418639514711454313242098630449712*x^4-3203303284234028666203844071104*\
x^2+544512140854393476767508801
Common denominator of the automorphisms:
2047240925902230212559731326945387423336880666520189696720208315822148952523\
6033096082649849780914177000235021821791786580325238933306384063316959183137\
0729785908543051410837142398445452707850631691341557009789386042391873370336\
5797612892364561104930463549150128710722692217319103923160040560831682922254\
0774922197326930278783415406172385628133906394322961095761034638799314768484\
6788479654008129602142127216512323092761785587140760780857919222961460031613\
4518499115330747451801118654191346731406933873328674197892280914420456540621\
821337918747168324666924768021275380321924888061283980888558483347865600
Complex polynomial:
x^128-1184*x^124+419248*x^120+56810272*x^116+50007524824*x^112-1428145055043\
2*x^108+4490127088342224*x^104-366191303555485920*x^100+32370403691861123964\
*x^96-673188090993235076896*x^92+138202118817654922026800*x^88-2609442160423\
117686059104*x^84+271247444711676290423296040*x^80+2186979856219843545952996\
064*x^76+208381015156371965820604471760*x^72-5230174811487765790506357880416\
*x^68+71077234753375321779760287041574*x^64-15213476744778529659810253059537\
60*x^60+1139869814689959877458972543201680*x^56+7328781352936305114544537194\
2779232*x^52+2116836413133313574890869663655889768*x^48+62297024841329459433\
82393024268865056*x^44+39290154253117676439965257293333739760*x^40-125501400\
232437014197425334134527590048*x^36+91675298867686272593775861954574777404*x\
^32+1295279727769509922067684166006192302496*x^28+15893765974355867716076578\
42364336402832*x^24+701809937092112487052842561473207141344*x^20+38307364797\
0798986012431348996064851480*x^16+63506853265194432365716946839650460576*x^1\
2+27601429825518641594561583067299999856*x^8+8800472635212172607139350352475\
6960*x^4+330320367097891646718468005888161
Common denominator of the automorphisms:
3901056135047822787051575867390259513531754581994798975438874892272209875436\
3299228553268986375184180037704459071029385728411582610113789807845898512662\
3221924247669145095136106253148410015166190455775998018504764663098782586542\
6084275020904333922197440663332216222072959553919943980285006435286704870559\
6140016009501766843154400357868517548637048947214676579863754818264508661760\
0

Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
Copyleft © 2002-2008 the PARI group.