# Group GAP4(64,75)

Name: (C2 x ((C4 x C2) : C2)) : C2
Maximal quotients:GAP4(32,27) GAP4(32,28) GAP4(32,30) GAP4(32,31)
Real polynomial:
```x^64-256*x^62+30224*x^60-2191168*x^58+109573392*x^56-4024640768*x^54+1128814\
23808*x^52-2481130451456*x^50+43514914081952*x^48-616782336880640*x^46+71291\
52615938048*x^44-67610817837700096*x^42+528108024211530240*x^40-340378416653\
6249344*x^38+18104232251417072640*x^36-79344581675598311424*x^34+28564659548\
7661576960*x^32-840780029038398701568*x^30+2010613251608263311360*x^28-38748\
18035751850885120*x^26+5957770666350624006144*x^24-7219023650271976751104*x^\
22+6790509174132345749504*x^20-4867504737626424541184*x^18+25976590695087613\
95200*x^16-1001503006329345671168*x^14+267875421082661355520*x^12-4696345964\
3499610112*x^10+4969310506239590400*x^8-281656703740542976*x^6+7428781489258\
496*x^4-71276950454272*x^2+16581197824```
Common denominator of the automorphisms:
```2075056307513679814755375236908447435173765481440351852016386554331664315064\
96892174336```
Complex polynomial:
```x^64-60*x^60+8806*x^56+5400*x^52+117777*x^48+1330680*x^44+1978742*x^40+41023\
80*x^36+78305444*x^32+4102380*x^28+1978742*x^24+1330680*x^20+117777*x^16+540\
0*x^12+8806*x^8-60*x^4+1```
Common denominator of the automorphisms:
`31905779703750426624`

Database of Galois polynomials by Bill Allombert and Igor Schein.