# Group GAP4(50,1)

Name: D50
Maximal quotient:GAP4(10,1)
Real polynomial:
```x^50-494*x^48+109423*x^46-14434928*x^44+1271555367*x^42-79564235862*x^40+367\
6245174161*x^38-128816520439948*x^36+3489861318005736*x^34-74149041705437696\
*x^32+1248410034193778032*x^30-16773428814256131392*x^28+1805740103387464135\
68*x^26-1559391264376620400128*x^24+10782744653526740029184*x^22-59399593366\
760928293888*x^20+258409191467394799716352*x^18-876051027930620266397696*x^1\
6+2270738528904565865549824*x^14-4381280643889736459927552*x^12+606188875295\
6419924033536*x^10-5707451787668187614543872*x^8+3394031098668839581253632*x\
^6-1136982171447521362051072*x^4+168053191607992604164096*x^2-30127260891774\
88162816```
Common denominator of the automorphisms:
```5581218580982985964040118567308137226770434070696990042977941295791210069400\
5721583987525363172188764870924112211893634964150599931710004464308295925225\
364121335103488```
Complex polynomial:
```x^50-5*x^49+9*x^48-31*x^47+132*x^46-267*x^45+485*x^44-1435*x^43+3379*x^42-61\
29*x^41+12657*x^40-30790*x^39+62387*x^38-106119*x^37+212648*x^36-407574*x^35\
+614705*x^34-982302*x^33+1604826*x^32-2152959*x^31+2856367*x^30-3857017*x^29\
+4546479*x^28-5144013*x^27+5693425*x^26-5831477*x^25+5693425*x^24-5144013*x^\
23+4546479*x^22-3857017*x^21+2856367*x^20-2152959*x^19+1604826*x^18-982302*x\
^17+614705*x^16-407574*x^15+212648*x^14-106119*x^13+62387*x^12-30790*x^11+12\
657*x^10-6129*x^9+3379*x^8-1435*x^7+485*x^6-267*x^5+132*x^4-31*x^3+9*x^2-5*x\
+1```
Common denominator of the automorphisms:
`43666588149150165198264715358441`

Database of Galois polynomials by Bill Allombert and Igor Schein.