Group GAP4(128,644)
Name: (C2 x (C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2))) : C2
Maximal quotient:GAP4(64,67)
Real polynomial:
x^128-1024*x^126+496064*x^124-151622528*x^122+32903987104*x^120-540926791833\
6*x^118+701898394879104*x^116-73959118843455744*x^114+6461497208848684128*x^\
112-475563214434125871104*x^110+29858140052085557357312*x^108-16154390797604\
34998875648*x^106+75945450064009779025840512*x^104-3123949231325215078711601\
152*x^102+113091514362669344377492601344*x^100-36210110254871447282302562437\
12*x^98+102976587926321584936524696314816*x^96-26105222427004657461211440150\
28224*x^94+59175731162968425975878742112971776*x^92-120265326651288049467554\
6701088577536*x^90+21963477122639220676402982355042314752*x^88-3611252364542\
55912228008858411639791616*x^86+5354350233624719474804531237064049993728*x^8\
4-71683588678471130701355685769315486748672*x^82+867468277160936359481943445\
482405125872128*x^80-9496367228010863790100674205679866342965248*x^78+940975\
48748076822253743851910089693289967616*x^76-84423742547544328884485727176253\
7169984544768*x^74+6859133597283044909975618399736996735006316544*x^72-50460\
426976440214759117404810364045147646099456*x^70+3360270569116684774459165440\
12768920228166967296*x^68-2024460006549363926971375055037892528009228992512*\
x^66+11026285839372816492694621624619060075167362377216*x^64-542386103023628\
95165156902087799069867061633351680*x^62+24066789594510061749355126062506020\
4196394833100800*x^60-961880404087715681861446495850300218799419592704000*x^\
58+3456736451185858159402044435251543702391285332172800*x^56-111476029496249\
51240144373178136649196922142277632000*x^54+32185842626320087164486035368672\
888523271221964800000*x^52-8298035112013744584458855516637797661457073680384\
0000*x^50+190467591647593956708247792559801072050887152378880000*x^48-387925\
135176587097750267534324662849880811538022400000*x^46+6984325381900050443541\
27319674701811375309923328000000*x^44-11069474719911150633673482634462787120\
44395513856000000*x^42+15371711396597853745178686914205634576841460495360000\
00*x^40-1860578573941150106545408997057200477830576332800000000*x^38+1951606\
198368388621460190373838821403543052646400000000*x^36-1762657158071127873635\
201255393337494296524288000000000*x^34+1361081314093062918754885662964966083\
475412576000000000*x^32-8914746338256837267282919770688480855944396800000000\
00*x^30+490931552981643497102388069969325791774353920000000000*x^28-22508241\
3769583002006562791155617593438622720000000000*x^26+849656019133131708995705\
44743952812827554560000000000*x^24-26074859672859303006966146071958158941900\
800000000000*x^22+6411048207938776204882445175895621350272000000000000*x^20-\
1241500382284591351743684269442106689280000000000000*x^18+185562823607172432\
912274723688951054688000000000000*x^16-2089192392912369322952061124691254272\
0000000000000*x^14+1719123329151895273840999628334777600000000000000*x^12-99\
411823682769541552833882732710400000000000000*x^10+3821383705495745182869422\
571932800000000000000*x^8-89209491414696968515038417664000000000000000*x^6+1\
057212123172918013073014720000000000000000*x^4-38755499868353310561401600000\
00000000000*x^2+4217199457458350395210000000000000000
Common denominator of the automorphisms:
4638568705798209753565274694255909693409994494894185504918089540680937789855\
9962195943782092802837302930034105948133963598829404669451454038255273989786\
7851406100704718966410867040703694913180630143554777525325295252532289148252\
6083301866152262795874247339166456925389665892602571406748570699841845361821\
0004074018926193460412086956800091564851383268693549408468492047515092731497\
7796505024299102144942234451932029959349906666329273688186987694609083856044\
3026427004717583454826219171195326748627731283254415000335077325625927246513\
5793746594406102779340951772522032272705046053476649875648830401076821073812\
2387398838646736696310558569581431171560032687446586949239089924284572003786\
8764055850305497102969872489967526549211635285061384062005228336820334144704\
5902982278461876318786773796581253901050572304487350920249699352601895799384\
7001802871711009396016681436671412582237632417140601373196807464269331167117\
6998384749869895373804095189223156828527382598288715966267135098880000000000\
0000000
Complex polynomial:
x^128+1024*x^126+496064*x^124+151622528*x^122+32903987104*x^120+540926791833\
6*x^118+701898394879104*x^116+73959118843455744*x^114+6461497208848684128*x^\
112+475563214434125871104*x^110+29858140052085557357312*x^108+16154390797604\
34998875648*x^106+75945450064009779025840512*x^104+3123949231325215078711601\
152*x^102+113091514362669344377492601344*x^100+36210110254871447282302562437\
12*x^98+102976587926321584936524696314816*x^96+26105222427004657461211440150\
28224*x^94+59175731162968425975878742112971776*x^92+120265326651288049467554\
6701088577536*x^90+21963477122639220676402982355042314752*x^88+3611252364542\
55912228008858411639791616*x^86+5354350233624719474804531237064049993728*x^8\
4+71683588678471130701355685769315486748672*x^82+867468277160936359481943445\
482405125872128*x^80+9496367228010863790100674205679866342965248*x^78+940975\
48748076822253743851910089693289967616*x^76+84423742547544328884485727176253\
7169984544768*x^74+6859133597283044909975618399736996735006316544*x^72+50460\
426976440214759117404810364045147646099456*x^70+3360270569116684774459165440\
12768920228166967296*x^68+2024460006549363926971375055037892528009228992512*\
x^66+11026285839372816492694621624619060075167362377216*x^64+542386103023628\
95165156902087799069867061633351680*x^62+24066789594510061749355126062506020\
4196394833100800*x^60+961880404087715681861446495850300218799419592704000*x^\
58+3456736451185858159402044435251543702391285332172800*x^56+111476029496249\
51240144373178136649196922142277632000*x^54+32185842626320087164486035368672\
888523271221964800000*x^52+8298035112013744584458855516637797661457073680384\
0000*x^50+190467591647593956708247792559801072050887152378880000*x^48+387925\
135176587097750267534324662849880811538022400000*x^46+6984325381900050443541\
27319674701811375309923328000000*x^44+11069474719911150633673482634462787120\
44395513856000000*x^42+15371711396597853745178686914205634576841460495360000\
00*x^40+1860578573941150106545408997057200477830576332800000000*x^38+1951606\
198368388621460190373838821403543052646400000000*x^36+1762657158071127873635\
201255393337494296524288000000000*x^34+1361081314093062918754885662964966083\
475412576000000000*x^32+8914746338256837267282919770688480855944396800000000\
00*x^30+490931552981643497102388069969325791774353920000000000*x^28+22508241\
3769583002006562791155617593438622720000000000*x^26+849656019133131708995705\
44743952812827554560000000000*x^24+26074859672859303006966146071958158941900\
800000000000*x^22+6411048207938776204882445175895621350272000000000000*x^20+\
1241500382284591351743684269442106689280000000000000*x^18+185562823607172432\
912274723688951054688000000000000*x^16+2089192392912369322952061124691254272\
0000000000000*x^14+1719123329151895273840999628334777600000000000000*x^12+99\
411823682769541552833882732710400000000000000*x^10+3821383705495745182869422\
571932800000000000000*x^8+89209491414696968515038417664000000000000000*x^6+1\
057212123172918013073014720000000000000000*x^4+38755499868353310561401600000\
00000000000*x^2+4217199457458350395210000000000000000
Common denominator of the automorphisms:
4638568705798209753565274694255909693409994494894185504918089540680937789855\
9962195943782092802837302930034105948133963598829404669451454038255273989786\
7851406100704718966410867040703694913180630143554777525325295252532289148252\
6083301866152262795874247339166456925389665892602571406748570699841845361821\
0004074018926193460412086956800091564851383268693549408468492047515092731497\
7796505024299102144942234451932029959349906666329273688186987694609083856044\
3026427004717583454826219171195326748627731283254415000335077325625927246513\
5793746594406102779340951772522032272705046053476649875648830401076821073812\
2387398838646736696310558569581431171560032687446586949239089924284572003786\
8764055850305497102969872489967526549211635285061384062005228336820334144704\
5902982278461876318786773796581253901050572304487350920249699352601895799384\
7001802871711009396016681436671412582237632417140601373196807464269331167117\
6998384749869895373804095189223156828527382598288715966267135098880000000000\
0000000
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.