# Group GAP4(54,9)

Name: C18 x C3
Maximal quotients:GAP4(18,2) GAP4(18,5) GAP4(27,2)
Real polynomial:
```x^54-54*x^52+1377*x^50-22050*x^48+248724*x^46+x^45-2101464*x^44-45*x^43+1380\
5451*x^42+945*x^41-72258318*x^40-12300*x^39+306312435*x^38+111150*x^37-10633\
95762*x^36-740259*x^35+3045178773*x^34+3764565*x^33-7223447322*x^32-14945040\
*x^31+14217578856*x^30+46955700*x^29-23206929840*x^28-117679101*x^27+3132935\
5284*x^26+236030679*x^25-34810394760*x^24-378659124*x^23+31604174190*x^22+48\
3844077*x^21-23213240820*x^20-488504520*x^19+13612702949*x^18+384974694*x^17\
-6263890362*x^16-232746048*x^15+2210784705*x^14+105410727*x^13-580609614*x^1\
2-34619481*x^11+108863118*x^10+7884305*x^9-13739868*x^8-1169388*x^7+1067409*\
x^6+103005*x^5-43686*x^4-4614*x^3+648*x^2+72*x+1```
Common denominator of the automorphisms:
`1`
Complex polynomial:
```x^54-x^53+3*x^52-4*x^51+9*x^50-14*x^49+28*x^48-47*x^47+89*x^46-155*x^45+286*\
x^44-507*x^43+924*x^42-1652*x^41+2993*x^40-5373*x^39+9707*x^38-17460*x^37+31\
501*x^36+15506*x^35+30036*x^34+32477*x^33+43101*x^32+51889*x^31+66790*x^30+8\
0089*x^29+105380*x^28+121588*x^27+169261*x^26+179295*x^25+280815*x^24+247036\
*x^23+493889*x^22+280998*x^21+953816*x^20+102069*x^19+2086561*x^18-928607*x^\
17+413269*x^16-183922*x^15+81853*x^14-36428*x^13+16212*x^12-7215*x^11+3211*x\
^10-1429*x^9+636*x^8-283*x^7+126*x^6-56*x^5+25*x^4-11*x^3+5*x^2-2*x+1```
Common denominator of the automorphisms:
`49515279841`

Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
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