# Group GAP4(64,156)

Name: Q8 : Q8
Maximal quotients:GAP4(32,29) GAP4(32,40) GAP4(32,44)
Real polynomial:
```x^64-960*x^62+378240*x^60-81100800*x^58+10666633200*x^56-924922224000*x^54+5\
5641664224000*x^52-2410505988480000*x^50+77296267825110000*x^48-187222396405\
6800000*x^46+34770065390020800000*x^44-500588498784384000000*x^42+5632121337\
052041000000*x^40-49807048865982840000000*x^38+347613069040884720000000*x^36\
-1919706669223646400000000*x^34+8400601711659383437500000*x^32-2913345016694\
3250000000000*x^30+79980378365349684000000000*x^28-1733659676625254400000000\
00*x^26+295462550729348842500000000*x^24-393500737944026100000000000*x^22+40\
6124120252788200000000000*x^20-321214468365684000000000000*x^18+191836624727\
613937500000000*x^16-84814136568585000000000000*x^14+27014970228570000000000\
000*x^12-5964731071200000000000000*x^10+862491085593750000000000*x^8-7490201\
6250000000000000*x^6+3415000500000000000000*x^4-65610000000000000000*x^2+256\
289062500000000```
Common denominator of the automorphisms:
```1359409882132485825089169089890520888718309692771411736138219988407297657357\
3523968000000000000000```
Complex polynomial:
```x^64+960*x^62+378240*x^60+81100800*x^58+10666633200*x^56+924922224000*x^54+5\
5641664224000*x^52+2410505988480000*x^50+77296267825110000*x^48+187222396405\
6800000*x^46+34770065390020800000*x^44+500588498784384000000*x^42+5632121337\
052041000000*x^40+49807048865982840000000*x^38+347613069040884720000000*x^36\
+1919706669223646400000000*x^34+8400601711659383437500000*x^32+2913345016694\
3250000000000*x^30+79980378365349684000000000*x^28+1733659676625254400000000\
00*x^26+295462550729348842500000000*x^24+393500737944026100000000000*x^22+40\
6124120252788200000000000*x^20+321214468365684000000000000*x^18+191836624727\
613937500000000*x^16+84814136568585000000000000*x^14+27014970228570000000000\
000*x^12+5964731071200000000000000*x^10+862491085593750000000000*x^8+7490201\
6250000000000000*x^6+3415000500000000000000*x^4+65610000000000000000*x^2+256\
289062500000000```
Common denominator of the automorphisms:
```1359409882132485825089169089890520888718309692771411736138219988407297657357\
3523968000000000000000```

Database of Galois polynomials by Bill Allombert and Igor Schein.