# Group GAP4(64,222)

Name: (C4 x Q8) : C2
Maximal quotients:GAP4(32,48) GAP4(32,50)
Real polynomial:
```x^64-252*x^62+26556*x^60-1567116*x^58+58991039*x^56-1525289748*x^54+28389328\
152*x^52-392662375560*x^50+4128922151329*x^48-33571596480888*x^46+2138233831\
98552*x^44-1077541665109404*x^42+4329485488229711*x^40-13948506854873700*x^3\
8+36175577455069212*x^36-75704387051836884*x^34+127948564898084641*x^32-1745\
65966491498912*x^30+191923697038513728*x^28-169516889048400000*x^26+11975328\
1468191296*x^24-67259774206428672*x^22+29800011326727168*x^20-10310074341974\
016*x^18+2749027026118144*x^16-555306094878720*x^14+83092292026368*x^12-8938\
573234176*x^10+663622467584*x^8-32075808768*x^6+921698304*x^4-13369344*x^2+6\
5536```
Common denominator of the automorphisms:
```1627292787830529860499476021852160758118986083849190011749433791976723151601\
16905643962531840```
Complex polynomial:
```x^64+56*x^56-392420*x^48+794783624*x^40+22550859334*x^32+23263122824*x^24+63\
26176540*x^16+805793336*x^8+1```
Common denominator of the automorphisms:
`1201285490952686081376681984`

Database of Galois polynomials by Bill Allombert and Igor Schein.