Group GAP4(128,1745)

Name: (C2 x (Q8 : C4)) : C2
Maximal quotients:GAP4(64,202) GAP4(64,258) GAP4(64,259)
Real polynomial:
x^128-544*x^126+141440*x^124-23430912*x^122+2781714688*x^120-252383960960*x^\
118+18223717151424*x^116-1076776966248832*x^114+53127364035447424*x^112-2222\
654888547117568*x^110+79796434346795421184*x^108-2482004027089923663360*x^10\
6+67406553365349780470528*x^104-1608651222385925806949376*x^102+339153531952\
89412941885440*x^100-634524002403188494560307200*x^98+1057441684899201651721\
2551680*x^96-157474258472119609531991764992*x^94+210128084714585388297611687\
1168*x^92-25181176988665104410474398785536*x^90+2715344827062506557436088412\
32384*x^88-2638963728207776959119659844354048*x^86+2314630626571849758396558\
6043707392*x^84-183417233849682781557547850226778112*x^82+131425148812760363\
2021443322814144512*x^80-8520658501196826080931109499207024640*x^78+50004940\
434658012140796451412578336768*x^76-265706863978349734629811381321062612992*\
x^74+1278400009361872970942089697934447312896*x^72-5568643455500390551992851\
703135432736768*x^70+21954125813482908190886850836544739868672*x^68-78298370\
537351067427647930329904724049920*x^66+2524431814728538075198793914912241678\
74560*x^64-735139369048750171153768054179110982254592*x^62+19315432722776783\
75102156222991897289818112*x^60-4573092678856744094002821929417877416312832*\
x^58+9741628233263183000700180088275313309515776*x^56-1863850157931391044328\
9075560605660244606976*x^54+31965348568126126104341048868913590725246976*x^5\
2-49028486043932550528517741528299676580708352*x^50+670810832054268799164929\
50568104337459904512*x^48-81634720203367727104407169905934397656268800*x^46+\
88076310327683784728327109574278062062698496*x^44-83939968528108325613691442\
269645346189606912*x^42+70377261702918185882856755415313612447678464*x^40-51\
673734085405780991912618157980239997698048*x^38+3305740656975556222984598795\
9554953139191808*x^36-18321264775318964289457559205454811251081216*x^34+8740\
978398124018766563924945974000971939840*x^32-3564292143980170885081378940712\
424409399296*x^30+1232227564037607520163111480407519844630528*x^28-357882414\
425124229179411028483391688278016*x^26+8641348141660566768188326436527292180\
0704*x^24-17138387492126183764954791598906740310016*x^22+2752752840656426744\
465346087977775792128*x^20-352109279512530271346286053214639882240*x^18+3514\
6774619713916880703803522038104064*x^16-267032815043059117022863554036052787\
2*x^14+149699239246057973227878047230722048*x^12-595415345515867870241012372\
7339520*x^10+159820334367089449065796092297216*x^8-2712735250020668836208908\
959744*x^6+26662273622296886165416968192*x^4-131237046186871048202354688*x^2\
+236325252060460777209856
Common denominator of the automorphisms:
5268946354583298255331923673111018236428412443688625622388209498053621422099\
9075034350911683228472046405464392557402343360244653494221473789630512244801\
6210542900492986148630427131808658527232330455106268148385436524243209123326\
5515464423107818566006739015166660302620994539161576601234570690613835896993\
8601773169649357311835674938089760183161514684669971593364335043154489285867\
8533443142284548792295899037292502062711360235328691234230351150354776310423\
430696193680330297885087716944682338118575720220727241863208297815867392
Complex polynomial:
x^128-120*x^124+2137500*x^120-15768000*x^116+607432466250*x^112-187318919250\
00*x^108+30466797927750000*x^104-1562296056688125000*x^100+24580121998588242\
1875*x^96-10285474785925359375000*x^92+388244288998577812500000*x^88-1481307\
882861420703125000*x^84+966966626627843893066406250*x^80+2490565216750561511\
7187500000*x^76+468761288646035702416992187500*x^72+428780776615733001049804\
6875000*x^68+214440640940705185405426025390625*x^64+130101095213464896287841\
7968750000*x^60+24252493382978587784362792968750000*x^56+3555412568876323687\
93945312500000000*x^52+4147723369701665665933227539062500000*x^48+1600632086\
1356037668334960937500000000*x^44+175947859627640495903320312500000000000*x^\
40+570566063031444849353027343750000000000*x^36+2937167280124367070602416992\
187500000000*x^32-6710760570131264542236328125000000000000*x^28+391898493924\
28591772460937500000000000000*x^24+93349339915399331176757812500000000000000\
*x^20+756041407875088981018066406250000000000000*x^16+6970272701120929687500\
00000000000000000000*x^12+1696490651414649353027343750000000000000000*x^8-22\
61987535219532470703125000000000000000000*x^4+282748441902441558837890625000\
0000000000000
Common denominator of the automorphisms:
1947234797145133234902016130687173991241878478520971922035974130633256670626\
606868914211971003017233674279533293916402154541015625000000000000000000000

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.