# Group GAP4(48,31)

Name: C4 x A4
Maximal quotients:GAP4(12,2) GAP4(24,13)
Real polynomial:
```x^48-96*x^46+4320*x^44-121088*x^42+2369441*x^40-34382416*x^38+383600016*x^36\
-3366917760*x^34+23592656480*x^32-133171124224*x^30+608330340352*x^28-225106\
5802752*x^26+6731655334817*x^24-16174768598576*x^22+30933341030896*x^20-4643\
9143595904*x^18+53682183870337*x^16-46530387292192*x^14+29153475551648*x^12-\
12541277965056*x^10+3437261780000*x^8-534061056512*x^6+37741378048*x^4-60224\
7168*x^2+246016```
Common denominator of the automorphisms:
`302043669999616`
Complex polynomial:
```x^48-2*x^47-2*x^46+7*x^45+x^44-8*x^43-6*x^42+7*x^41+11*x^40+3*x^39-44*x^38+5\
2*x^37+50*x^36-228*x^35+71*x^34+387*x^33-196*x^32-521*x^31+523*x^30+97*x^29-\
236*x^28-11*x^27+9*x^26+217*x^25-339*x^24+217*x^23+9*x^22-11*x^21-236*x^20+9\
7*x^19+523*x^18-521*x^17-196*x^16+387*x^15+71*x^14-228*x^13+50*x^12+52*x^11-\
44*x^10+3*x^9+11*x^8+7*x^7-6*x^6-8*x^5+x^4+7*x^3-2*x^2-2*x+1```
Common denominator of the automorphisms:
`16529441375`

Database of Galois polynomials by Bill Allombert and Igor Schein.