# Group GAP4(64,76)

Name: (C4 x C2) : Q8
Maximal quotients:GAP4(32,27) GAP4(32,29) GAP4(32,35)
Real polynomial:
```x^64-176*x^62+14240*x^60-705968*x^58+24105072*x^56-603879328*x^54+1154343529\
6*x^52-172847242240*x^50+2065008038240*x^48-19945643270656*x^46+157244934093\
440*x^44-1018671252529280*x^42+5447255202755328*x^40-24106977091399424*x^38+\
88374261450276096*x^36-268178003475256320*x^34+672095508952173952*x^32-13855\
10688581243904*x^30+2335666417714612224*x^28-3194144718875386880*x^26+350629\
8029549153280*x^24-3047303156476246016*x^22+2059603316794849280*x^20-1057461\
313559142400*x^18+399747651926853632*x^16-106634156171296768*x^14+1893096919\
1735296*x^12-2068676388216832*x^10+128023878696960*x^8-4336745332736*x^6+789\
97864448*x^4-720896000*x^2+2560000```
Common denominator of the automorphisms:
```1581016866905290410424032438612900675993832051956835815409511563725484223332\
4747423735808000```
Complex polynomial:
```x^64+176*x^62+14240*x^60+705968*x^58+24105072*x^56+603879328*x^54+1154343529\
6*x^52+172847242240*x^50+2065008038240*x^48+19945643270656*x^46+157244934093\
440*x^44+1018671252529280*x^42+5447255202755328*x^40+24106977091399424*x^38+\
88374261450276096*x^36+268178003475256320*x^34+672095508952173952*x^32+13855\
10688581243904*x^30+2335666417714612224*x^28+3194144718875386880*x^26+350629\
8029549153280*x^24+3047303156476246016*x^22+2059603316794849280*x^20+1057461\
313559142400*x^18+399747651926853632*x^16+106634156171296768*x^14+1893096919\
1735296*x^12+2068676388216832*x^10+128023878696960*x^8+4336745332736*x^6+789\
97864448*x^4+720896000*x^2+2560000```
Common denominator of the automorphisms:
```1581016866905290410424032438612900675993832051956835815409511563725484223332\
4747423735808000```

Database of Galois polynomials by Bill Allombert and Igor Schein.