# Group GAP4(64,129)

Name: (C2 x C2 x Q8) : C2
Maximal quotients:GAP4(32,27) GAP4(32,40) GAP4(32,44)
Real polynomial:
```x^64-144*x^62+9480*x^60-380832*x^58+10511184*x^56-212721840*x^54+3288466800*\
x^52-39929664240*x^50+388462445280*x^48-3072390065280*x^46+19969218223920*x^\
44-107511905867040*x^42+482222441666592*x^40-1808923369910688*x^38+568820508\
6130560*x^36-15007151372452704*x^34+33204838208697288*x^32-61509305540335680\
*x^30+95107327105128480*x^28-122218364237431680*x^26+129777171617597760*x^24\
-113030286102394560*x^22+80006408817059520*x^20-45503170721311680*x^18+20503\
774672016256*x^16-7192646180642304*x^14+1921129516589760*x^12-37952640283507\
2*x^10+53300446775424*x^8-5020342830720*x^6+288054144000*x^4-8293104000*x^2+\
65610000```
Common denominator of the automorphisms:
`3913459249975941560492064342332420804456823362427218287823040000`
Complex polynomial:
```x^64-168*x^56+62748*x^48-46872*x^40-7762554*x^32-3796632*x^24+411689628*x^16\
-89282088*x^8+43046721```
Common denominator of the automorphisms:
`348407073570816`

Database of Galois polynomials by Bill Allombert and Igor Schein.