# Group GAP4(64,24)

Name: (C8 : C2) : C4
Maximal quotients:GAP4(32,2) GAP4(32,7) GAP4(32,8)
Real polynomial:
```x^64-256*x^62+31232*x^60-2416640*x^58+133156864*x^56-5560991744*x^54+1829374\
52544*x^52-4863660392448*x^50+106392571090642*x^48-1939568812170624*x^46+297\
40055203700480*x^44-386059588879781888*x^42+4261504082414516224*x^40-4010827\
8060381569024*x^38+322241457258083254272*x^36-2209657242460341927936*x^34+12\
912705121322597399649*x^32-64127400334503656173696*x^30+26952293720197222570\
3168*x^28-953274316916739664637952*x^26+2816575651903646701086720*x^24-68874\
37185350787812229120*x^22+13776382973117991052247040*x^20-222104532142030264\
21579776*x^18+28329654043364811244771856*x^16-27916259950601940261831680*x^1\
4+20606533769090146664802304*x^12-10940936585849929538568192*x^10+3961234565\
669821793517568*x^8-914934415293517625032704*x^6+125450125318672555704320*x^\
4-9168113265739158257664*x^2+272488302620241362944```
Common denominator of the automorphisms:
`2513777042098235130139580990907530715136000`
Complex polynomial:
```x^64+256*x^62+31232*x^60+2416640*x^58+133156864*x^56+5560991744*x^54+1829374\
52544*x^52+4863660392448*x^50+106392571090642*x^48+1939568812170624*x^46+297\
40055203700480*x^44+386059588879781888*x^42+4261504082414516224*x^40+4010827\
8060381569024*x^38+322241457258083254272*x^36+2209657242460341927936*x^34+12\
912705121322597399649*x^32+64127400334503656173696*x^30+26952293720197222570\
3168*x^28+953274316916739664637952*x^26+2816575651903646701086720*x^24+68874\
37185350787812229120*x^22+13776382973117991052247040*x^20+222104532142030264\
21579776*x^18+28329654043364811244771856*x^16+27916259950601940261831680*x^1\
4+20606533769090146664802304*x^12+10940936585849929538568192*x^10+3961234565\
669821793517568*x^8+914934415293517625032704*x^6+125450125318672555704320*x^\
4+9168113265739158257664*x^2+272488302620241362944```
Common denominator of the automorphisms:
`2513777042098235130139580990907530715136000`

Database of Galois polynomials by Bill Allombert and Igor Schein.