# Group GAP4(64,19)

Name: C4 . (C4 x C4)
Maximal quotient:GAP4(32,2)
Real polynomial:
```x^64-544*x^62+112064*x^60-12462496*x^58+869406520*x^56-41287862464*x^54+1404\
112816384*x^52-35381577343296*x^50+676910469887384*x^48-10012890061558144*x^\
46+116131171761206272*x^44-1067850229116864384*x^42+7854365924283392608*x^40\
-46545664129791288576*x^38+223523799423556846592*x^36-873771716489096177408*\
x^34+2789482791653151350288*x^32-7287656507499653466112*x^30+155925154668700\
09140224*x^28-27303780390448315445248*x^26+39042104597761055069696*x^24-4540\
1564797324920897536*x^22+42666993050324744822784*x^20-3211040585658828252774\
4*x^18+19108004736513651808256*x^16-8834284563478520135680*x^14+309678126923\
0681260032*x^12-795152413019162279936*x^10+142256063459979395072*x^8-1645787\
6627521536000*x^6+1100849081085329408*x^4-36573059172270080*x^2+457163239653\
376```
Common denominator of the automorphisms:
```2791761226133522581857381738840167695825275684894841843255961297924249687472\
5024728783258403028788175016947110379520```
Complex polynomial:
```x^64+544*x^62+112064*x^60+12462496*x^58+869406520*x^56+41287862464*x^54+1404\
112816384*x^52+35381577343296*x^50+676910469887384*x^48+10012890061558144*x^\
46+116131171761206272*x^44+1067850229116864384*x^42+7854365924283392608*x^40\
+46545664129791288576*x^38+223523799423556846592*x^36+873771716489096177408*\
x^34+2789482791653151350288*x^32+7287656507499653466112*x^30+155925154668700\
09140224*x^28+27303780390448315445248*x^26+39042104597761055069696*x^24+4540\
1564797324920897536*x^22+42666993050324744822784*x^20+3211040585658828252774\
4*x^18+19108004736513651808256*x^16+8834284563478520135680*x^14+309678126923\
0681260032*x^12+795152413019162279936*x^10+142256063459979395072*x^8+1645787\
6627521536000*x^6+1100849081085329408*x^4+36573059172270080*x^2+457163239653\
376```
Common denominator of the automorphisms:
```2791761226133522581857381738840167695825275684894841843255961297924249687472\
5024728783258403028788175016947110379520```

Database of Galois polynomials by Bill Allombert and Igor Schein.