Group GAP4(128,2077)

Name: (C2 x (C8 : C4)) : C2
Maximal quotients:GAP4(64,228) GAP4(64,254) GAP4(64,258)
Real polynomial:
x^128-512*x^126+125984*x^124-19858432*x^122+2255111584*x^120-196724067840*x^\
118+13726938648576*x^116-787716987339264*x^114+37932245029490528*x^112-15564\
03497842457600*x^110+55066504000134365568*x^108-1696045745597909386240*x^106\
+45828055045431093539712*x^104-1093293411869450436151296*x^102+2315036529269\
1023842859008*x^100-437047266943462208388923392*x^98+73837959059136939533180\
12096*x^96-111993322465866757703833550848*x^94+15290964638981152027123274449\
92*x^92-18836337688197610692028210257920*x^90+209753345502476092708280782311\
936*x^88-2114787870635241980121999850561536*x^86+193304846823180074785804600\
81823744*x^84-160361223050712059325394175047000064*x^82+12083682080634220774\
26021205337969152*x^80-8275857724976102302431666221038518272*x^78+5153771480\
4457123798606050464440629248*x^76-291903597496658746138882095131359166464*x^\
74+1503774001761105539567082133384507512832*x^72-704542289063111008093521858\
1239550607360*x^70+30011890712254895951818485458247434141696*x^68-1161852662\
64914192799552567053601507180544*x^66+40852587846478222143680663332501172212\
2752*x^64-1303671083355087070116968636038555998224384*x^62+37721989578076556\
26197408678709852020826112*x^60-9886101197691544079637142122457609994764288*\
x^58+23437473775184823401653600150380200511594496*x^56-501910117166995510722\
12077262203328119046144*x^54+96931209861766171346073953508284562258001920*x^\
52-168512161828338501846538469550364227820978176*x^50+2631749331142510841173\
85461826593099421753344*x^48-368400388648397848456364647727080394765631488*x\
^46+461069383041283345273060723032198244042833920*x^44-514483971178319689115\
027140968459505529257984*x^42+510260288915146891438305591172269560699191296*\
x^40-448259904622212385476824483865998835316162560*x^38+34746996284149990310\
4994286117671707857125376*x^36-236638385402645451310328739822824684368429056\
*x^34+140906669106520569900087530394514680193925120*x^32-7295893451432854424\
5252913538508264080146432*x^30+32645170957932176313248065572501086759944192*\
x^28-12532813427269962164602759159826283862425600*x^26+409428475846958792235\
4766694626969197608960*x^24-1127246764603464937770383092789560261738496*x^22\
+258602878754184745994455238277803269947392*x^20-487675386243637007539540290\
51101535272960*x^18+7436884432580744570495927052987720925184*x^16-8988179756\
14350114079743490324598620160*x^14+83953367091293970516090119670100131840*x^\
12-5868037834038215104302565878703063040*x^10+294153359405180385214742624398\
213120*x^8-9975259413412440674178391911432192*x^6+21020603976662585063429465\
3878272*x^4-2398174599979946460870151766016*x^2+1082047200550075221202704793\
6
Common denominator of the automorphisms:
3883576064256081644797176352976890137737860034079616500572800777885873476684\
1851729911288584067631366144104785972396433576367301577966672062414958887288\
8356629872682156988273964520474912271800896306506154167655622676720271792613\
9611409828446397583137910499240183920040046828492475101115423581340782797886\
8170213420064059795138408001263431860252879541180548129455179627206990567471\
9233666618112422016093130265874576536157301750786814832175532472080126169488\
8041430005271807871007860204424716853151392887424480706560
Complex polynomial:
x^128+5480*x^120+28740100*x^112+7079038000*x^104+1687265926250*x^96-59410338\
25000*x^88-59713243750000*x^80+24049114375000*x^72+2107683232421875*x^64+601\
227859375000*x^56-37320777343750000*x^48-92828653515625000*x^40+659088252441\
406250*x^32+69131230468750000*x^24+7016625976562500*x^16+33447265625000*x^8+\
152587890625
Common denominator of the automorphisms:
45524333099442055789340436000000000000000

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.