# Group GAP4(64,204)

Name: C2 x ((C2 x Q8) : C2)
Maximal quotients:GAP4(32,29) GAP4(32,46) GAP4(32,47) GAP4(32,48)
Real polynomial:
```x^64-360*x^62+49680*x^60-3726000*x^58+175046148*x^56-5562474120*x^54+1255076\
33760*x^52-2079848965320*x^50+25949400766506*x^48-248361192398880*x^46+18497\
14046532720*x^44-10837754179210440*x^42+50374126677907728*x^40-1869083596070\
79480*x^38+556137949189232880*x^36-1331119195863766560*x^34+2567534642660492\
019*x^32-3993357587591299680*x^30+5005241542703095920*x^28-50465257093911459\
60*x^26+4080304260910525968*x^24-2633574265548136920*x^22+134844153992235288\
0*x^20-543165927776350560*x^18+170254018429045866*x^16-40937667184393560*x^1\
4+7411100265894240*x^12-985375602935640*x^10+93026699939268*x^8-594044749800\
0*x^6+237617899920*x^4-5165606520*x^2+43046721```
Common denominator of the automorphisms:
`9208300696512479836773137781077476254110400`
Complex polynomial:
```x^64+1316*x^56+14026*x^48+2910992*x^40+6601171*x^32+2910992*x^24+14026*x^16+\
1316*x^8+1```
Common denominator of the automorphisms:
`530474541315264`

Database of Galois polynomials by Bill Allombert and Igor Schein.