# Group GAP4(128,436)

Name: (C2 x C2) . ((C4 x C2 x C2) : C2) = (C4 x C4) . (C2 x C2 x C2)
Maximal quotients:GAP4(64,145) GAP4(64,151) GAP4(64,152)
Real polynomial:
```x^128-800*x^126+305120*x^124-73945920*x^122+12806090800*x^120-1689889544000*\
x^118+176940389698400*x^116-15115464293947200*x^114+1075142220280666800*x^11\
2-64665540573178624000*x^110+3329003230979342312000*x^108-148127051488111769\
456000*x^106+5742749679528214203224000*x^104-195290760811565078374400000*x^1\
02+5858456882735287564948800000*x^100-155787505538414536812917120000*x^98+36\
87657268286113057064508260000*x^96-77986808950492117575721249600000*x^94+147\
8191132808687390451375424800000*x^92-25182376151643686201222803633600000*x^9\
0+386537717067315406531750667468800000*x^88-53574835790270370019229867281760\
00000*x^86+67179166731468844865177444641992000000*x^84-763380850303710094420\
082789917616000000*x^82+7872532347066460810081836299670056000000*x^80-737734\
33274403295468507059442330720000000*x^78+62887002598152816673316318577706416\
0000000*x^76-4880689578136220566258531454616468160000000*x^74+34511887027949\
890526010151019866370320000000*x^72-2224625921914559197540850535345033872000\
00000*x^70+1307694825226550971778033058937816317600000000*x^68-7011396350871\
621147440685505711768491200000000*x^66+3428987152874089823061157586141108640\
8300000000*x^64-152943478894705092128460551338018044688000000000*x^62+621963\
342604538421403582163682812769480000000000*x^60-2304912202483197796630797860\
601938953840000000000*x^58+7778679223489203217469751197391457727840000000000\
*x^56-23885838028950504807587326922215484792800000000000*x^54+66663771276365\
241843543986473087913168720000000000*x^52-1688846567686649677629597776747707\
56120800000000000*x^50+387770753876589144498654710538799768613040000000000*x\
^48-805502880539086218546562725453636400958400000000000*x^46+151066424782892\
3944637941790438913827710400000000000*x^44-255179727714341912139897679413091\
2750870400000000000*x^42+387188899920941062090180486493531045560720000000000\
0*x^40-5260834712133005406878089803016149649104000000000000*x^38+63784125007\
48132635717626123427886971944000000000000*x^36-68731740223944009285156149667\
53274289456000000000000*x^34+65525149506054968827406788961454853940740000000\
00000*x^32-5497989262146469980233572597562619809280000000000000*x^30+4036041\
180806697350822023407920370720240000000000000*x^28-2574436304261621317141455\
581498985230880000000000000*x^26+1415556377482853741365510046586292184400000\
000000000*x^24-664727758693813419020839463311617494400000000000000*x^22+2636\
52142573547438677853362257066091200000000000000*x^20-87155164867297664623791\
490314780297600000000000000*x^18+2361913109580974161817000224103817960000000\
0000000*x^16-5138132127554354930721211026186288000000000000000*x^14+87250731\
1872743626996030582445064000000000000000*x^12-111193155834783462291826692589\
680000000000000000*x^10+10017678905136338300770035178224000000000000000*x^8-\
575918207635335774456135791520000000000000000*x^6+17016553051790306582083548\
240000000000000000*x^4-118431673944891416544854880000000000000000*x^2+162360\
4752801408500010000000000000000```
Common denominator of the automorphisms:
```5961443107013430788002466481488784924735530869808837282359700046196385047149\
4215174404316917565274132070164934319232401954857785478124997386932229483012\
9639940957953136518200085956834336667056613957891476259712470778871452182876\
2470519481871438088722867262764939192768148670255501067766458830900999520707\
9175190319836142309132629579820969327660658288256346709128096067065034086950\
9648704910569318015653630531286261771889718798769071122315030510664368995936\
5742357450430062562730787827055469016963060876069646905437751044615530045613\
1201667861222253429875224265847839208582495477848692520732646579002821683061\
8574197768961403949656985864343835833828146119105145848051966327251504334814\
5057324240301913441764410505882680360857235805474898014742853242333318533972\
30493389891584000000000000000```
Complex polynomial:
```x^128+800*x^126+305120*x^124+73945920*x^122+12806090800*x^120+1689889544000*\
x^118+176940389698400*x^116+15115464293947200*x^114+1075142220280666800*x^11\
2+64665540573178624000*x^110+3329003230979342312000*x^108+148127051488111769\
456000*x^106+5742749679528214203224000*x^104+195290760811565078374400000*x^1\
02+5858456882735287564948800000*x^100+155787505538414536812917120000*x^98+36\
87657268286113057064508260000*x^96+77986808950492117575721249600000*x^94+147\
8191132808687390451375424800000*x^92+25182376151643686201222803633600000*x^9\
0+386537717067315406531750667468800000*x^88+53574835790270370019229867281760\
00000*x^86+67179166731468844865177444641992000000*x^84+763380850303710094420\
082789917616000000*x^82+7872532347066460810081836299670056000000*x^80+737734\
33274403295468507059442330720000000*x^78+62887002598152816673316318577706416\
0000000*x^76+4880689578136220566258531454616468160000000*x^74+34511887027949\
890526010151019866370320000000*x^72+2224625921914559197540850535345033872000\
00000*x^70+1307694825226550971778033058937816317600000000*x^68+7011396350871\
621147440685505711768491200000000*x^66+3428987152874089823061157586141108640\
8300000000*x^64+152943478894705092128460551338018044688000000000*x^62+621963\
342604538421403582163682812769480000000000*x^60+2304912202483197796630797860\
601938953840000000000*x^58+7778679223489203217469751197391457727840000000000\
*x^56+23885838028950504807587326922215484792800000000000*x^54+66663771276365\
241843543986473087913168720000000000*x^52+1688846567686649677629597776747707\
56120800000000000*x^50+387770753876589144498654710538799768613040000000000*x\
^48+805502880539086218546562725453636400958400000000000*x^46+151066424782892\
3944637941790438913827710400000000000*x^44+255179727714341912139897679413091\
2750870400000000000*x^42+387188899920941062090180486493531045560720000000000\
0*x^40+5260834712133005406878089803016149649104000000000000*x^38+63784125007\
48132635717626123427886971944000000000000*x^36+68731740223944009285156149667\
53274289456000000000000*x^34+65525149506054968827406788961454853940740000000\
00000*x^32+5497989262146469980233572597562619809280000000000000*x^30+4036041\
180806697350822023407920370720240000000000000*x^28+2574436304261621317141455\
581498985230880000000000000*x^26+1415556377482853741365510046586292184400000\
000000000*x^24+664727758693813419020839463311617494400000000000000*x^22+2636\
52142573547438677853362257066091200000000000000*x^20+87155164867297664623791\
490314780297600000000000000*x^18+2361913109580974161817000224103817960000000\
0000000*x^16+5138132127554354930721211026186288000000000000000*x^14+87250731\
1872743626996030582445064000000000000000*x^12+111193155834783462291826692589\
680000000000000000*x^10+10017678905136338300770035178224000000000000000*x^8+\
575918207635335774456135791520000000000000000*x^6+17016553051790306582083548\
240000000000000000*x^4+118431673944891416544854880000000000000000*x^2+162360\
4752801408500010000000000000000```
Common denominator of the automorphisms:
```5961443107013430788002466481488784924735530869808837282359700046196385047149\
4215174404316917565274132070164934319232401954857785478124997386932229483012\
9639940957953136518200085956834336667056613957891476259712470778871452182876\
2470519481871438088722867262764939192768148670255501067766458830900999520707\
9175190319836142309132629579820969327660658288256346709128096067065034086950\
9648704910569318015653630531286261771889718798769071122315030510664368995936\
5742357450430062562730787827055469016963060876069646905437751044615530045613\
1201667861222253429875224265847839208582495477848692520732646579002821683061\
8574197768961403949656985864343835833828146119105145848051966327251504334814\
5057324240301913441764410505882680360857235805474898014742853242333318533972\
30493389891584000000000000000```

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.