Group GAP4(128,222)
Name: (C4 x (C8 : C2)) : C2
Maximal quotients:GAP4(64,88) GAP4(64,99) GAP4(64,101)
Real polynomial:
x^128-960*x^126+441120*x^124-129332480*x^122+27213504480*x^120-4382466128000\
*x^118+562514869982400*x^116-59176868427404800*x^114+5207197142058037600*x^1\
12-389219740918637920000*x^110+25013367575281940048000*x^108-139553108358360\
7708800000*x^106+68127869312298577032656000*x^104-29292889214241727330307200\
00*x^102+111537208136571931964205280000*x^100-377825697765871708801105280000\
0*x^98+114305035873136318052978593880000*x^96-309866486831993162957131714240\
0000*x^94+75480882396106319018244821390400000*x^92-1656094908107493981612712\
657369600000*x^90+32793755195589980272338480117905600000*x^88-58706276304870\
2038851917963681184000000*x^86+9514112543047971517677110318209904000000*x^84\
-139743149346331295863762770657701760000000*x^82+186189092454757202047772837\
0176238696000000*x^80-22517742853118324737209653954912693440000000*x^78+2473\
06905090438879307151983596927212960000000*x^76-24671477329949477118710608412\
67948990720000000*x^74+22357563947610482600331274009317627355680000000*x^72-\
184020118612762463403592141464699504963200000000*x^70+1375238164322061627247\
954672431552260030400000000*x^68-9326995363451787928528402964599909448998400\
000000*x^66+57365976389530124915702824490974898862128600000000*x^64-31969020\
2070972098985146091477896085318944000000000*x^62+161247437665158535568755094\
2727199782089968000000000*x^60-735155810396007983122795845020815437915584000\
0000000*x^58+30250043083521295969814760791648135498265616000000000*x^56-1121\
41059496037073199994457970588005320676800000000000*x^54+37377761616745173341\
7170343224506277946086560000000000*x^52-111754353201935636359010894338164195\
8322474240000000000*x^50+298931378278938951692412683115380799093099048000000\
0000*x^48-7132336172003375633860799868803361754309840000000000000*x^46+15127\
463229259717501874121686311917842889342400000000000*x^44-2841144982859403729\
9813868434759353694969587200000000000*x^42+470435383559442895387551579968370\
54483956273600000000000*x^40-68328411685739418626752854668106211912816736000\
000000000*x^38+86555512145062819805667340142692870782863120000000000000*x^36\
-94994883917675197847009063094943212319578240000000000000*x^34+8963678917307\
8787384419834300207642046053756000000000000*x^32-720735924483507878455198352\
48869003745532480000000000000*x^30+48868479599940505025534267638088578710208\
480000000000000*x^28-2759866083573129533907055657273632098663296000000000000\
0*x^26+12793561671058067886984559875209415374712480000000000000*x^24-4783365\
933637480989736920340447936736918400000000000000*x^22+1412473181139704158486\
727639078137611310400000000000000*x^20-3211810295897121058208439871207858739\
84000000000000000*x^18+54564915178949545035508592563981722389600000000000000\
*x^16-6683960983588951473978187244049098656000000000000000*x^14+567015981127\
217837381225821246308400000000000000000*x^12-3192214555872277750410045730505\
9200000000000000000*x^10+1145779340608699140397446378623600000000000000000*x\
^8-25091380567952503900820099448000000000000000000*x^6+312383134201440275758\
290580000000000000000000*x^4-1905008657896371340208800000000000000000000*x^2\
+3729999008662354141506250000000000000000
Common denominator of the automorphisms:
4483377731531662794924481731651893886605085860007856945849691099915405964553\
8373070525822790018852910170715167825501064832502233564299452849027880745659\
0486749768149486448434158134181549409298897160552135200881955430961658162546\
4598825268824023395720146403521101293159444984497225789679480609887186403037\
0010987287526148129798306312755512890057112228575511427885090098321942287718\
2272997853717065613253785167598142852496299929456161020523912393132855001401\
4530531338432501651129995942673903179461062979524406610461563289600000000000\
00000000
Complex polynomial:
x^128+960*x^126+441120*x^124+129332480*x^122+27213504480*x^120+4382466128000\
*x^118+562514869982400*x^116+59176868427404800*x^114+5207197142058037600*x^1\
12+389219740918637920000*x^110+25013367575281940048000*x^108+139553108358360\
7708800000*x^106+68127869312298577032656000*x^104+29292889214241727330307200\
00*x^102+111537208136571931964205280000*x^100+377825697765871708801105280000\
0*x^98+114305035873136318052978593880000*x^96+309866486831993162957131714240\
0000*x^94+75480882396106319018244821390400000*x^92+1656094908107493981612712\
657369600000*x^90+32793755195589980272338480117905600000*x^88+58706276304870\
2038851917963681184000000*x^86+9514112543047971517677110318209904000000*x^84\
+139743149346331295863762770657701760000000*x^82+186189092454757202047772837\
0176238696000000*x^80+22517742853118324737209653954912693440000000*x^78+2473\
06905090438879307151983596927212960000000*x^76+24671477329949477118710608412\
67948990720000000*x^74+22357563947610482600331274009317627355680000000*x^72+\
184020118612762463403592141464699504963200000000*x^70+1375238164322061627247\
954672431552260030400000000*x^68+9326995363451787928528402964599909448998400\
000000*x^66+57365976389530124915702824490974898862128600000000*x^64+31969020\
2070972098985146091477896085318944000000000*x^62+161247437665158535568755094\
2727199782089968000000000*x^60+735155810396007983122795845020815437915584000\
0000000*x^58+30250043083521295969814760791648135498265616000000000*x^56+1121\
41059496037073199994457970588005320676800000000000*x^54+37377761616745173341\
7170343224506277946086560000000000*x^52+111754353201935636359010894338164195\
8322474240000000000*x^50+298931378278938951692412683115380799093099048000000\
0000*x^48+7132336172003375633860799868803361754309840000000000000*x^46+15127\
463229259717501874121686311917842889342400000000000*x^44+2841144982859403729\
9813868434759353694969587200000000000*x^42+470435383559442895387551579968370\
54483956273600000000000*x^40+68328411685739418626752854668106211912816736000\
000000000*x^38+86555512145062819805667340142692870782863120000000000000*x^36\
+94994883917675197847009063094943212319578240000000000000*x^34+8963678917307\
8787384419834300207642046053756000000000000*x^32+720735924483507878455198352\
48869003745532480000000000000*x^30+48868479599940505025534267638088578710208\
480000000000000*x^28+2759866083573129533907055657273632098663296000000000000\
0*x^26+12793561671058067886984559875209415374712480000000000000*x^24+4783365\
933637480989736920340447936736918400000000000000*x^22+1412473181139704158486\
727639078137611310400000000000000*x^20+3211810295897121058208439871207858739\
84000000000000000*x^18+54564915178949545035508592563981722389600000000000000\
*x^16+6683960983588951473978187244049098656000000000000000*x^14+567015981127\
217837381225821246308400000000000000000*x^12+3192214555872277750410045730505\
9200000000000000000*x^10+1145779340608699140397446378623600000000000000000*x\
^8+25091380567952503900820099448000000000000000000*x^6+312383134201440275758\
290580000000000000000000*x^4+1905008657896371340208800000000000000000000*x^2\
+3729999008662354141506250000000000000000
Common denominator of the automorphisms:
4483377731531662794924481731651893886605085860007856945849691099915405964553\
8373070525822790018852910170715167825501064832502233564299452849027880745659\
0486749768149486448434158134181549409298897160552135200881955430961658162546\
4598825268824023395720146403521101293159444984497225789679480609887186403037\
0010987287526148129798306312755512890057112228575511427885090098321942287718\
2272997853717065613253785167598142852496299929456161020523912393132855001401\
4530531338432501651129995942673903179461062979524406610461563289600000000000\
00000000
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.