# Group GAP4(64,22)

Name: (C4 x C2) . D8 = C4 . (C4 x C4)
Maximal quotients:GAP4(32,2) GAP4(32,15)
Real polynomial:
```x^64-1632*x^62+819264*x^60-218714112*x^58+37368330496*x^56-4474178552832*x^5\
4+395542493411328*x^52-26675209536094208*x^50+1401517577557143552*x^48-58143\
021441432911872*x^46+1919717870644456390656*x^44-50622568503696098852864*x^4\
2+1065838310012475192115200*x^40-17848412791745926885539840*x^38+23595879937\
5045371157807104*x^36-2435375205596866734238728192*x^34+19335414522887011760\
978526208*x^32-115996036772790730290492342272*x^30+5161523734256338375610529\
21856*x^28-1680014861159258298197074771968*x^26+3987549312805178342575995617\
280*x^24-6928429923531200209632398147584*x^22+885549370107080308578497383628\
8*x^20-8340885898495083143972790468608*x^18+5766586285144305041685696479232*\
x^16-2891167537393238165729270824960*x^14+1026456564145877929107254149120*x^\
12-247453397265797906705183408128*x^10+37628042822890040581678956544*x^8-314\
5950709470986639163523072*x^6+110094123817241616752574464*x^4-15953446951362\
86490492928*x^2+7669926418924454281216```
Common denominator of the automorphisms:
```5201202135252429890406587393215642066122308821055875696756209199259921270032\
96038288826239328468298379602398543872```
Complex polynomial:
```x^64+1632*x^62+819264*x^60+218714112*x^58+37368330496*x^56+4474178552832*x^5\
4+395542493411328*x^52+26675209536094208*x^50+1401517577557143552*x^48+58143\
021441432911872*x^46+1919717870644456390656*x^44+50622568503696098852864*x^4\
2+1065838310012475192115200*x^40+17848412791745926885539840*x^38+23595879937\
5045371157807104*x^36+2435375205596866734238728192*x^34+19335414522887011760\
978526208*x^32+115996036772790730290492342272*x^30+5161523734256338375610529\
21856*x^28+1680014861159258298197074771968*x^26+3987549312805178342575995617\
280*x^24+6928429923531200209632398147584*x^22+885549370107080308578497383628\
8*x^20+8340885898495083143972790468608*x^18+5766586285144305041685696479232*\
x^16+2891167537393238165729270824960*x^14+1026456564145877929107254149120*x^\
12+247453397265797906705183408128*x^10+37628042822890040581678956544*x^8+314\
5950709470986639163523072*x^6+110094123817241616752574464*x^4+15953446951362\
86490492928*x^2+7669926418924454281216```
Common denominator of the automorphisms:
```5201202135252429890406587393215642066122308821055875696756209199259921270032\
96038288826239328468298379602398543872```

Database of Galois polynomials by Bill Allombert and Igor Schein.