# Group GAP4(54,4)

Name: C9 x S3
Maximal quotients:GAP4(18,2) GAP4(18,3)
Real polynomial:
```x^54-216*x^52+20925*x^50-1210734*x^48+46996524*x^46-1302656904*x^44+26785523\
556*x^42-418857453432*x^40+5064626429982*x^38-47877786064656*x^36+3563125380\
88758*x^34-2095256114251524*x^32+9744746824623780*x^30-35793045185342544*x^2\
8+103441621996115316*x^26-233796266999200152*x^24+409767223918764969*x^22-55\
0671748924365144*x^20+559143537333137397*x^18-420824822309236926*x^16+228844\
151262255528*x^14-86821787166646248*x^12+21870445892558400*x^10-340533526016\
2752*x^8+295457081333184*x^6-12234605119488*x^4+205705930752*x^2-816293376```
Common denominator of the automorphisms:
```5365384417250087144904196329337388676561734888887826428895669772847523797401\
6```
Complex polynomial:
```x^54-18*x^51+153*x^48-867*x^45+3771*x^42-12519*x^39+31839*x^36-54963*x^33+39\
519*x^30+50348*x^27-136908*x^24+30933*x^21+145077*x^18+53019*x^15+9351*x^12+\
348*x^9-45*x^6-9*x^3+1```
Common denominator of the automorphisms:
`19490985117370794210147`

Database of Galois polynomials by Bill Allombert and Igor Schein.