# Group GAP4(64,68)

Name: (C4 : C4) : C4
Maximal quotients:GAP4(32,24) GAP4(32,25) GAP4(32,26) GAP4(32,29) GAP4(32,30) GAP4(32,32) GAP4(32,33)
Real polynomial:
```x^64-208*x^62+19856*x^60-1157552*x^58+46263304*x^56-1349055840*x^54+29826509\
808*x^52-512931586752*x^50+6984403955088*x^48-76262888053152*x^46+6738156849\
98208*x^44-4848085881626208*x^42+28525786740433328*x^40-137601126225807488*x\
^38+544688460421233952*x^36-1768678527013218112*x^34+4703205334469262920*x^3\
2-10211509396338457152*x^30+18023966171751671616*x^28-25711709283037960128*x\
^26+29418618583400246304*x^24-26735350735554784128*x^22+19059589214530721472\
*x^20-10490081074066758912*x^18+4366522855030425664*x^16-1338125822007858304\
*x^14+291335611291408640*x^12-42958844295645056*x^10+4018354966649536*x^8-21\
7410107079168*x^6+5936654395008*x^4-61766012160*x^2+100881936```
Common denominator of the automorphisms:
```5967849810696039113049970644387220545168455083133877661157486070567142917876\
219694080```
Complex polynomial:
```x^64-24*x^62+356*x^60-4248*x^58+44986*x^56-386544*x^54+2815348*x^52-18071880\
*x^50+103440035*x^48-513224160*x^46+2252078036*x^44-8823886032*x^42+30461574\
500*x^40-89466108456*x^38+231342312592*x^36-533985903768*x^34+1090058069077*\
x^32-1927767284616*x^30+3036834179728*x^28-4217703582648*x^26+4969962661220*\
x^24-4752486079344*x^22+4022799358484*x^20-2772974603040*x^18+1233948585635*\
x^16-82171946520*x^14+4433664052*x^12-222877392*x^10+10282426*x^8-205896*x^6\
+4004*x^4-72*x^2+1```
Common denominator of the automorphisms:
`188782827845097478420130604643418390170423231892595992563600`

Database of Galois polynomials by Bill Allombert and Igor Schein.