Group GAP4(128,369)
Name: ((C2 x C2) . ((C4 x C2) : C2) = (C4 x C2) . (C4 x C2)) : C2
Maximal quotients:GAP4(64,131) GAP4(64,132) GAP4(64,135)
Real polynomial:
x^128-1600*x^126+1211360*x^124-579049600*x^122+196729149600*x^120-5069716537\
6000*x^118+10326888697056000*x^116-1710805762364800000*x^114+235361178747841\
360000*x^112-27319889467244948800000*x^110+2709334906231937400800000*x^108-2\
31875173282230230832000000*x^106+17267569659364315000740000000*x^104-1126587\
014289875117511840000000*x^102+64766282338218315316280400000000*x^100-329681\
5360487474244274171200000000*x^98+149210117372409337175992990500000000*x^96-\
6025520276827111288525908120000000000*x^94+217769082333076847877703156980000\
000000*x^92-7061959262589121241793648335280000000000*x^90+205938214441298437\
700084826899820000000000*x^88-5410526375724847461884821448472000000000000*x^\
86+128265191315702766865283613819885600000000000*x^84-2747263955252611721423\
860787057904000000000000*x^82+5321802445910332707595005049122149400000000000\
0*x^80-933091872109774669518531226049340600000000000000*x^78+148162757520955\
22579833187859039356340000000000000*x^76-21313220121759724395085118162269132\
0400000000000000*x^74+2777842028594516271916835469262855601900000000000000*x\
^72-32800076563903813160669133452674646044000000000000000*x^70+3507663582296\
78845086862874422997017310000000000000000*x^68-33955343976459334009142153559\
04605863640000000000000000*x^66+29731565156527379992048414921132748592983750\
000000000000*x^64-235242171994704889009966247425737151822200000000000000000*\
x^62+1679802486740596408338723938606272790478500000000000000000*x^60-1080901\
3876799776133631862694747514931142000000000000000000*x^58+625617852549749949\
35752123062326162596131500000000000000000*x^56-32500998216954132151656444691\
3344092604280000000000000000000*x^54+151168816635493261969523863867500387816\
9540000000000000000000*x^52-627690551076875932733035934588629170690600000000\
0000000000000*x^50+231895448675192589672673405461783215284441500000000000000\
00000*x^48-75932565872370367309354174752248675477775000000000000000000000*x^\
46+219396758536731385783079191534148881309678500000000000000000000*x^44-5565\
34384151656155978340253973091728167850000000000000000000000*x^42+12322027413\
08053056745590451772537330845507500000000000000000000*x^40-23653560461012779\
56527279317541683728761100000000000000000000000*x^38+39066203421997079335883\
79356308952155275750000000000000000000000*x^36-55025718323191757291793553733\
70742516023000000000000000000000000*x^34+65430917109588284068235618484432916\
25144062500000000000000000000*x^32-64919042885937794328997137169780769129250\
00000000000000000000000*x^30+53021881773299841028246964574826252455375000000\
00000000000000000*x^28-35090879342998260729218547182308823854500000000000000\
00000000000*x^26+18474213794590327489729697569630480190625000000000000000000\
00000*x^24-756907623607847103468841105516232925000000000000000000000000000*x\
^22+235047051834198849469833810625754685500000000000000000000000000*x^20-535\
71167889461671282748968022542730000000000000000000000000000*x^18+86165768574\
70869044219247378205491250000000000000000000000000*x^16-93350219855122310574\
6520700620025000000000000000000000000000*x^14+647431836526587721948862345925\
37500000000000000000000000000*x^12-27449410867924601703828921177500000000000\
00000000000000000*x^10+66836909267463117081828065062500000000000000000000000\
000*x^8-827356128057650298218292500000000000000000000000000000*x^6+394896656\
9955847699516250000000000000000000000000000*x^4-5862975661631259725000000000\
000000000000000000000*x^2+1966272327300562890625000000000000000000000000
Common denominator of the automorphisms:
1106530990543117387515046870251028660151168332816270824194698966910068735261\
0587880055536182457050967488367982327708901670318170316791487333766647555934\
8284526590638561594525168855445878456992073284451413229048416684320433748548\
7548656167211630266181669583130196470187572610703877417226925080073719784088\
8862595883134279180724776867616516619181783404660123811691413756572797308840\
0703409133200191207767443207947967250581359526151993516437643595247888895053\
4938188124790865837544332149537441135307124635948390920942034446404447955887\
4893635784265710555570532073041406608549783753476860793911222151604537790457\
7812269809746177058225778156026867128972636738629441432028088516400635650213\
0644717496349347224485951361581537647280519999573125083494638559153362628273\
3542199922416135947087923200000000000000000000000000000000000
Complex polynomial:
x^128+1600*x^126+1211360*x^124+579049600*x^122+196729149600*x^120+5069716537\
6000*x^118+10326888697056000*x^116+1710805762364800000*x^114+235361178747841\
360000*x^112+27319889467244948800000*x^110+2709334906231937400800000*x^108+2\
31875173282230230832000000*x^106+17267569659364315000740000000*x^104+1126587\
014289875117511840000000*x^102+64766282338218315316280400000000*x^100+329681\
5360487474244274171200000000*x^98+149210117372409337175992990500000000*x^96+\
6025520276827111288525908120000000000*x^94+217769082333076847877703156980000\
000000*x^92+7061959262589121241793648335280000000000*x^90+205938214441298437\
700084826899820000000000*x^88+5410526375724847461884821448472000000000000*x^\
86+128265191315702766865283613819885600000000000*x^84+2747263955252611721423\
860787057904000000000000*x^82+5321802445910332707595005049122149400000000000\
0*x^80+933091872109774669518531226049340600000000000000*x^78+148162757520955\
22579833187859039356340000000000000*x^76+21313220121759724395085118162269132\
0400000000000000*x^74+2777842028594516271916835469262855601900000000000000*x\
^72+32800076563903813160669133452674646044000000000000000*x^70+3507663582296\
78845086862874422997017310000000000000000*x^68+33955343976459334009142153559\
04605863640000000000000000*x^66+29731565156527379992048414921132748592983750\
000000000000*x^64+235242171994704889009966247425737151822200000000000000000*\
x^62+1679802486740596408338723938606272790478500000000000000000*x^60+1080901\
3876799776133631862694747514931142000000000000000000*x^58+625617852549749949\
35752123062326162596131500000000000000000*x^56+32500998216954132151656444691\
3344092604280000000000000000000*x^54+151168816635493261969523863867500387816\
9540000000000000000000*x^52+627690551076875932733035934588629170690600000000\
0000000000000*x^50+231895448675192589672673405461783215284441500000000000000\
00000*x^48+75932565872370367309354174752248675477775000000000000000000000*x^\
46+219396758536731385783079191534148881309678500000000000000000000*x^44+5565\
34384151656155978340253973091728167850000000000000000000000*x^42+12322027413\
08053056745590451772537330845507500000000000000000000*x^40+23653560461012779\
56527279317541683728761100000000000000000000000*x^38+39066203421997079335883\
79356308952155275750000000000000000000000*x^36+55025718323191757291793553733\
70742516023000000000000000000000000*x^34+65430917109588284068235618484432916\
25144062500000000000000000000*x^32+64919042885937794328997137169780769129250\
00000000000000000000000*x^30+53021881773299841028246964574826252455375000000\
00000000000000000*x^28+35090879342998260729218547182308823854500000000000000\
00000000000*x^26+18474213794590327489729697569630480190625000000000000000000\
00000*x^24+756907623607847103468841105516232925000000000000000000000000000*x\
^22+235047051834198849469833810625754685500000000000000000000000000*x^20+535\
71167889461671282748968022542730000000000000000000000000000*x^18+86165768574\
70869044219247378205491250000000000000000000000000*x^16+93350219855122310574\
6520700620025000000000000000000000000000*x^14+647431836526587721948862345925\
37500000000000000000000000000*x^12+27449410867924601703828921177500000000000\
00000000000000000*x^10+66836909267463117081828065062500000000000000000000000\
000*x^8+827356128057650298218292500000000000000000000000000000*x^6+394896656\
9955847699516250000000000000000000000000000*x^4+5862975661631259725000000000\
000000000000000000000*x^2+1966272327300562890625000000000000000000000000
Common denominator of the automorphisms:
1106530990543117387515046870251028660151168332816270824194698966910068735261\
0587880055536182457050967488367982327708901670318170316791487333766647555934\
8284526590638561594525168855445878456992073284451413229048416684320433748548\
7548656167211630266181669583130196470187572610703877417226925080073719784088\
8862595883134279180724776867616516619181783404660123811691413756572797308840\
0703409133200191207767443207947967250581359526151993516437643595247888895053\
4938188124790865837544332149537441135307124635948390920942034446404447955887\
4893635784265710555570532073041406608549783753476860793911222151604537790457\
7812269809746177058225778156026867128972636738629441432028088516400635650213\
0644717496349347224485951361581537647280519999573125083494638559153362628273\
3542199922416135947087923200000000000000000000000000000000000
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.