# Group GAP4(64,127)

Name: C8 : Q8
Maximal quotients:GAP4(32,26) GAP4(32,37) GAP4(32,38)
Real polynomial:
```x^64-216*x^62+20400*x^60-1133568*x^58+41945904*x^56-1107128304*x^54+21774389\
760*x^52-328838390496*x^50+3897004231512*x^48-36830422713024*x^46+2810111368\
98240*x^44-1747144191456000*x^42+8914253301337536*x^40-37519431054897600*x^3\
8+130746946153193856*x^36-378097877075735808*x^34+908276815127824560*x^32-18\
12122047604577024*x^30+2998414927860712704*x^28-4103461537381969920*x^26+462\
5641302486103296*x^24-4270480389185736960*x^22+3204671068399403520*x^20-1935\
738568150391808*x^18+929437157349286272*x^16-349061645352043008*x^14+1004128\
84890593280*x^12-21517663180382208*x^10+3306448562264064*x^8-344968845871104\
*x^6+22480719575040*x^4-793437161472*x^2+11019960576```
Common denominator of the automorphisms:
`2711562558176448247190234397148781820870178572988720738337054278470260736`
Complex polynomial:
```x^64+216*x^62+20400*x^60+1133568*x^58+41945904*x^56+1107128304*x^54+21774389\
760*x^52+328838390496*x^50+3897004231512*x^48+36830422713024*x^46+2810111368\
98240*x^44+1747144191456000*x^42+8914253301337536*x^40+37519431054897600*x^3\
8+130746946153193856*x^36+378097877075735808*x^34+908276815127824560*x^32+18\
12122047604577024*x^30+2998414927860712704*x^28+4103461537381969920*x^26+462\
5641302486103296*x^24+4270480389185736960*x^22+3204671068399403520*x^20+1935\
738568150391808*x^18+929437157349286272*x^16+349061645352043008*x^14+1004128\
84890593280*x^12+21517663180382208*x^10+3306448562264064*x^8+344968845871104\
*x^6+22480719575040*x^4+793437161472*x^2+11019960576```
Common denominator of the automorphisms:
`2711562558176448247190234397148781820870178572988720738337054278470260736`

Database of Galois polynomials by Bill Allombert and Igor Schein.