# Group GAP4(64,7)

Name: Q8 : C8
Maximal quotients:GAP4(32,5) GAP4(32,10) GAP4(32,11)
Real polynomial:
```x^64-204*x^62+16848*x^60-775404*x^58+22841651*x^56-464982164*x^54+6859729236\
*x^52-75691076760*x^50+638471007301*x^48-4181693655920*x^46+21506504167820*x\
^44-87573825073300*x^42+284052972532915*x^40-737182276262588*x^38+1535615605\
495368*x^36-2573025250342444*x^34+3471835619664021*x^32-3773147000287848*x^3\
0+3299886086304388*x^28-2317713759837824*x^26+1302954668055324*x^24-58344727\
9135072*x^22+206744233315040*x^20-57482990274496*x^18+12406847537552*x^16-20\
51102530816*x^14+255423378048*x^12-23456183296*x^10+1544418752*x^8-70058496*\
x^6+2056448*x^4-34816*x^2+256```
Common denominator of the automorphisms:
```6452926917285974818090721049411682427051518243346966791635521721116059171890\
6842989790675853444096```
Complex polynomial:
```x^64+204*x^62+16848*x^60+775404*x^58+22841651*x^56+464982164*x^54+6859729236\
*x^52+75691076760*x^50+638471007301*x^48+4181693655920*x^46+21506504167820*x\
^44+87573825073300*x^42+284052972532915*x^40+737182276262588*x^38+1535615605\
495368*x^36+2573025250342444*x^34+3471835619664021*x^32+3773147000287848*x^3\
0+3299886086304388*x^28+2317713759837824*x^26+1302954668055324*x^24+58344727\
9135072*x^22+206744233315040*x^20+57482990274496*x^18+12406847537552*x^16+20\
51102530816*x^14+255423378048*x^12+23456183296*x^10+1544418752*x^8+70058496*\
x^6+2056448*x^4+34816*x^2+256```
Common denominator of the automorphisms:
```6452926917285974818090721049411682427051518243346966791635521721116059171890\
6842989790675853444096```

Database of Galois polynomials by Bill Allombert and Igor Schein.