# Group GAP4(64,79)

Name: (C2 x C2 x C2) . (C2 x C2 x C2)
Maximal quotients:GAP4(32,28) GAP4(32,29) GAP4(32,30) GAP4(32,32) GAP4(32,35)
Real polynomial:
```x^64-380*x^62+62390*x^60-5865336*x^58+353522400*x^56-14515153056*x^54+421349\
071656*x^52-8863644277440*x^50+137552591334576*x^48-1597239152365696*x^46+14\
051986811441696*x^44-94765939668079616*x^42+495377057692404736*x^40-20279957\
15329415936*x^38+6562171449667154816*x^36-16915907218037838336*x^34+34960669\
904305157376*x^32-58209042124108179456*x^30+78328268476957669376*x^28-853167\
39736463589376*x^26+75204991600830447616*x^24-53534413651670204416*x^22+3064\
2573008273801216*x^20-14006670059903123456*x^18+5061622766440022016*x^16-142\
5714061969981440*x^14+306898007821910016*x^12-49110239429001216*x^10+5614990\
597816320*x^8-432225644445696*x^6+20355460628480*x^4-493921239040*x^2+429496\
7296```
Common denominator of the automorphisms:
```6386911320015159752566609251438922731234383204102656550023651538364932237096\
13122251653120000000```
Complex polynomial:
```x^64+380*x^62+62390*x^60+5865336*x^58+353522400*x^56+14515153056*x^54+421349\
071656*x^52+8863644277440*x^50+137552591334576*x^48+1597239152365696*x^46+14\
051986811441696*x^44+94765939668079616*x^42+495377057692404736*x^40+20279957\
15329415936*x^38+6562171449667154816*x^36+16915907218037838336*x^34+34960669\
904305157376*x^32+58209042124108179456*x^30+78328268476957669376*x^28+853167\
39736463589376*x^26+75204991600830447616*x^24+53534413651670204416*x^22+3064\
2573008273801216*x^20+14006670059903123456*x^18+5061622766440022016*x^16+142\
5714061969981440*x^14+306898007821910016*x^12+49110239429001216*x^10+5614990\
597816320*x^8+432225644445696*x^6+20355460628480*x^4+493921239040*x^2+429496\
7296```
Common denominator of the automorphisms:
```6386911320015159752566609251438922731234383204102656550023651538364932237096\
13122251653120000000```

Database of Galois polynomials by Bill Allombert and Igor Schein.