# Group GAP4(64,117)

Name: (C8 x C4) : C2
Maximal quotients:GAP4(32,25) GAP4(32,37) GAP4(32,38)
Real polynomial:
```x^64-528*x^62+114224*x^60-13718496*x^58+1047272908*x^56-54923874720*x^54+208\
0648758848*x^52-58954480857888*x^50+1281738956624324*x^48-21800238410415168*\
x^46+294471721089501824*x^44-3196680916952339520*x^42+28151397319181933104*x\
^40-202601272468729643520*x^38+1198367955516760268416*x^36-58502795139253764\
92160*x^34+23641356399772320007744*x^32-79219501363150618322688*x^30+2202507\
56981766197854464*x^28-507807364251957230951424*x^26+96925017811028809624288\
0*x^24-1526964417692562418082304*x^22+1976708029133561565422592*x^20-2089705\
562420735375052288*x^18+1789083743249831884846144*x^16-122673829458428715320\
8320*x^14+663756549199370163587072*x^12-277768933250059566560256*x^10+874238\
80088465676870400*x^8-19864719870736674041856*x^6+3054136517593881409536*x^4\
-282315140281787357184*x^2+11763130845074473216```
Common denominator of the automorphisms:
`2291363971253615895405156852149838643461160960`
Complex polynomial:
`x^64-380*x^48+36102*x^32+150148*x^16+1`
Common denominator of the automorphisms:
`8777216`

Database of Galois polynomials by Bill Allombert and Igor Schein.