Group GAP4(128,329)

Name: ((C2 x Q8) : C4) : C2
Maximal quotients:GAP4(64,130) GAP4(64,135) GAP4(64,138)
Real polynomial:
x^128-704*x^126+239040*x^124-52161792*x^122+8224008336*x^120-998612811072*x^\
118+97211663375808*x^116-7797746757826560*x^114+525753451896715584*x^112-302\
45766158208461312*x^110+1501995100909040697088*x^108-64983666133912741673472\
*x^106+2467794790788173007648480*x^104-82761753297308491698270336*x^102+2463\
484691224527301853762688*x^100-65355565640515213406000785920*x^98+1550736691\
885648301370233458320*x^96-33004643932268207204380292286720*x^94+63159680035\
9348275683336637630720*x^92-10889227128000940007938482910295040*x^90+1694153\
00792838869130844749460487616*x^88-2381624978195549775921638425483417344*x^8\
6+30283178851174646327849702254911479040*x^84-348550975733374587232699359107\
200376832*x^82+3633238437016307605006607099402224709376*x^80-343094801077410\
66761574254516132625377280*x^78+293539381475714279733956669729015286021120*x\
^76-2275116115065083469868801069016310377359360*x^74+15969637916145177499951\
034149046749191155840*x^72-101467802508003066678317138349989067902400000*x^7\
0+583188555900288845788912103280162899299653120*x^68-30294307595888609025599\
55650646572673832704000*x^66+14207715804189828862669180379870608328104518240\
*x^64-60083032698767791203883980294905792783682585600*x^62+22877370995959328\
7243120167461808623921480381440*x^60-782984492321061265002858827956729487715\
845222400*x^58+2404119088773079292637140566288969143396005384960*x^56-660793\
8635256137848311754070233412310774984064000*x^54+162185808431891829974064186\
41290510816457161036800*x^52-35448022169796897406529769242887116758655060049\
920*x^50+68778102536540885816421712360041397057972731657216*x^48-11805054842\
7254749780321503056002028898339689816064*x^46+178541654059058355377366786568\
116835174107378749440*x^44-2368908930498952481871197938825725213783583363153\
92*x^42+274371650446142002387136369818455747335435566496256*x^40-27585774249\
8300981051678849619691417811492678768640*x^38+239248288198803080607697892247\
419244422483340810240*x^36-1777205435062790050163869381258670394339997572710\
40*x^34+112163586936829954549570741781584485600736902600960*x^32-59597139861\
729888194079509799028472771146835374080*x^30+2638504368472847752998956552629\
8565854420186673152*x^28-9619161563364929420003608151878200981405151838208*x\
^26+2849374996537111173539770527383491416533410944000*x^24-67540455429747443\
8768400513864118981008998846464*x^22+125883073946574585858791447024054896643\
824218112*x^20-18075744409991215344110556786343530051845881856*x^18+19515266\
31607821805390026324890096932482207744*x^16-15372092201367082847739642811087\
4579339673600*x^14+8498526558671696672517991246879973309693952*x^12-31307688\
8790664454367156337290402713665536*x^10+715283497619134661165557593929842095\
5136*x^8-91516396463730843764147329460176625664*x^6+555665489217621879807239\
462378741760*x^4-1257359164299053470719215871229952*x^2+57233198414963537102\
4619069696
Common denominator of the automorphisms:
3520190335193950554206100027941727010763854472232776517995326405723143339824\
9036125094689837556804890554705139589906544770414045613836910056617124248260\
6886654660549115513924713034494360479158979626646060529104053219379153559563\
2784745321971272710892071106696035542881288442296174408845986357099230106192\
8962969846425244251576635109424852949162789634500857253021234144125966234393\
0191199170450226634030186921182031974684060889062812112788104750157476598306\
6062864131530799163655580165599573932366277849066652445017081307535107831752\
3648631924358983781672296312138876120989040770601126249763464247435487120075\
0359281664000
Complex polynomial:
x^128+288*x^124+280128*x^120-105442560*x^116+30366230976*x^112-5038618452480\
*x^108+851751469135872*x^104+307495049460332544*x^100+2701955510923627008*x^\
96-3070587117431075143680*x^92+231123609024331468161024*x^88+364332796183163\
97593395200*x^84+3385133438516377971464798208*x^80+2244504818719952517406225\
85856*x^76+10346389968291196458021846515712*x^72+189328591115020513509948071\
608320*x^68+3870005102429055580610409249570816*x^64-678729359082224526380261\
51409745920*x^60+3687258281197106137362626996393213952*x^56-3796535810319061\
5455580857562474479616*x^52+349562862395087155332801304399202746368*x^48-961\
594949272408196945316408086558146560*x^44+4764171675282649137376927815158112\
190464*x^40-57476929575517291814846254609019028111360*x^36+15830134589695951\
9463850878308140227493888*x^32-410528580668289562938667713862133102936064*x^\
28+2265530779510962636939574154974743591124992*x^24-506163352730572464977664\
6119409693229056000*x^20+19435484012676978581600947796929283616669696*x^16+7\
214148028542246072354437469829400352522240*x^12+4479849358885574691134783924\
5625013093531648*x^8-21397836924988933260727428709136865687502848*x^4+140963\
58955362920411171614011103014819987456
Common denominator of the automorphisms:
1822138168122501224284347404474925891923883276374274428829009912445671621221\
5201406277669664162762845264134262916467761984237596166548859154711174268204\
1378306410270481959858879677675649753318197952909321018598002502231863367322\
4331094784815634281192411206390990356207109434431386685263146560485158980165\
815957570553408324706928019011389407975957729990672384000000000

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.