# Group GAP4(64,43)

Name: C2 . ((C8 x C2) : C2) = C8 . (C4 x C2)
Maximal quotient:GAP4(32,9)
Real polynomial:
```x^64-816*x^62+205020*x^60-26404128*x^58+2099107572*x^56-113332319136*x^54+44\
02835538192*x^52-127905159154752*x^50+2855250088824096*x^48-4996779049263398\
4*x^46+695914123373075520*x^44-7801687316806133760*x^42+71009452956033605952\
*x^40-528055139250384321024*x^38+3222446788986194780928*x^36-161811755742011\
78446848*x^34+66934922050797615383040*x^32-228017415605728413984768*x^30+638\
503148866185939336192*x^28-1464770586965154598895616*x^26+273895396314672260\
1268224*x^24-4145460920755816926633984*x^22+5031703746647430163329024*x^20-4\
839278106938734200176640*x^18+3630568999567815889293312*x^16-208152893711365\
8115719168*x^14+887263577936543360581632*x^12-270656618625827727998976*x^10+\
55906045968076151980032*x^8-7186938456875408031744*x^6+503970185283612180480\
*x^4-16107187752394555392*x^2+147097605044699136```
Common denominator of the automorphisms:
```4931501601565445297366458423788290368071756229000244160977413885568730138500\
4800736338846481958322067110087888139054678540288```
Complex polynomial:
```x^64+816*x^62+205020*x^60+26404128*x^58+2099107572*x^56+113332319136*x^54+44\
02835538192*x^52+127905159154752*x^50+2855250088824096*x^48+4996779049263398\
4*x^46+695914123373075520*x^44+7801687316806133760*x^42+71009452956033605952\
*x^40+528055139250384321024*x^38+3222446788986194780928*x^36+161811755742011\
78446848*x^34+66934922050797615383040*x^32+228017415605728413984768*x^30+638\
503148866185939336192*x^28+1464770586965154598895616*x^26+273895396314672260\
1268224*x^24+4145460920755816926633984*x^22+5031703746647430163329024*x^20+4\
839278106938734200176640*x^18+3630568999567815889293312*x^16+208152893711365\
8115719168*x^14+887263577936543360581632*x^12+270656618625827727998976*x^10+\
55906045968076151980032*x^8+7186938456875408031744*x^6+503970185283612180480\
*x^4+16107187752394555392*x^2+147097605044699136```
Common denominator of the automorphisms:
```4931501601565445297366458423788290368071756229000244160977413885568730138500\
4800736338846481958322067110087888139054678540288```

Database of Galois polynomials by Bill Allombert and Igor Schein.