Group GAP4(136,9)

Name: C68 x C2
Maximal quotients:GAP4(8,2) GAP4(68,2) GAP4(68,5)
Real polynomial:
x^136-270*x^134+35644*x^132-3066448*x^130+193324560*x^128-9523284992*x^126+3\
81658368000*x^124-12793524019200*x^122+366003879014400*x^120-907384616723200\
0*x^118+197281134149299200*x^116-3797590663133696000*x^114+65227417229984362\
496*x^112-1006088400748344410112*x^110+14010452874532693934080*x^108-1769451\
29418688318144512*x^106+2034503399204546467921920*x^104-21366274913999119376\
842752*x^102+205523215839420100672487424*x^100-1815057838367760032700825600*\
x^98+14746957103866604163123118080*x^96-110420565506784425260823347200*x^94+\
763080303288782170458591068160*x^92-4873004042054679123630300856320*x^90+287\
85222991783170929409078067200*x^88-157414048017922826168254215487488*x^86+79\
7433604304238294726221978664960*x^84-3743910497783938983724727027105792*x^82\
+16295578981835467057601334806052864*x^80-6576504416679447752493003574345728\
0*x^78+246096483031630923373663423473647616*x^76-853773556470052503487450708\
338278400*x^74+2745288542887633109428100432406773760*x^72-817827216272819373\
8576019469967032320*x^70+22559140231854469307436992598481305600*x^68-5757951\
9829876169279934419203742760960*x^66+135872464285021323548360098121043148800\
*x^64-296128527566057284619993467904889716736*x^62+5954056838143692984757125\
44187290222592*x^60-1102949304397104822922042075574572154880*x^58+1879562062\
029293064216634588582234816512*x^56-2941591032037714754973188278878700830720\
*x^54+4219966683554856956758528748947790364672*x^52-553753173913284544746344\
2969920603684864*x^50+6630964203751452270911747446874623180800*x^48-72267899\
72784191460471933449347415408640*x^46+71473746983579915543129012136403009536\
00*x^44-6393774434654052019271871913100448890880*x^42+5154531636926159914412\
997862527609077760*x^40-3729624004454920902822020716856711577600*x^38+241096\
6138052238523847246495586453553152*x^36-138523362241031488374260400567210737\
6640*x^34+703272454454467556361629725956608360448*x^32-313408030017444661235\
730767362513698816*x^30+121671122764469814937566161358941061120*x^28-4079085\
0913498527757339254096389996544*x^26+11690499600429472240860015503815475200*\
x^24-2830331482209240647787161648292167680*x^22+5707608663381358268344254393\
32597760*x^20-94258639377875538547188903496908800*x^18+124862093721341622491\
08140463226880*x^16-1292791306864624219062102550118400*x^14+1011991474620910\
14137334479192064*x^12-5730711053194343142912119799808*x^10+2207893813302615\
08074525163520*x^8-5283848442091728398364704768*x^6+676549096298556773158092\
80*x^4-346208492775380864729088*x^2+295147905179352825856
Common denominator of the automorphisms:
147573952589676412928
Complex polynomial:
x^136+135*x^134+8911*x^132+383306*x^130+12082785*x^128+297602656*x^126+59634\
12000*x^124+99949406400*x^122+1429702652400*x^120+17722355795375*x^118+19265\
7357567675*x^116+1854292315983250*x^114+15924662409664151*x^112+122813525481\
975636*x^110+855130180330364620*x^108+5399936810873056584*x^106+310440582154\
01404845*x^104+163011740982048945441*x^102+784008849485092547121*x^100+34619\
48086486358704950*x^98+14063794235102276003955*x^96+52652628663437092428600*\
x^94+181932521650500815024040*x^92+580907349831423654989040*x^90+17157329912\
05642874801700*x^88+4691304207382286374814934*x^86+1188268667912838302144739\
0*x^84+27894306911408446607922964*x^82+60705762288851540750270094*x^80+12249\
6940506239379802588440*x^78+229195210180832933051198184*x^76+397569293375151\
466339570800*x^74+639187298456121494394750435*x^72+9520761858122648832593135\
85*x^70+1313114785115145455780264025*x^68+1675784582908852295948146470*x^66+\
1977204582144932989443770175*x^64+2154618614921181030658724688*x^62+21660732\
59338624842623949168*x^60+2006253097346606997092825760*x^58+1709451737069041\
941337340712*x^56+1337680729210530787428610110*x^54+959509335087854414441273\
718*x^52+629544472205093989880815908*x^50+376926675684868102445747550*x^48+2\
05397724721029574666088520*x^46+101570303433476163296417400*x^44+45430499786\
320780368042960*x^42+18312575054317505569702710*x^40+66251431087048489537885\
50*x^38+2141368094445751179086598*x^36+615167304833936727234180*x^34+1561578\
54303999323067138*x^32+34795281102777926433648*x^30+6754104096255420793680*x\
^28+1132173546955454128608*x^26+162238272822099908200*x^24+19639369867938409\
940*x^22+1980224548011249540*x^20+163512674542432600*x^18+10830060261901380*\
x^16+560658857389200*x^14+21944067106416*x^12+621324937376*x^10+11969016345*\
x^8+143218999*x^6+916895*x^4+2346*x^2+1
Common denominator of the automorphisms:
1

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.