# Group GAP4(72,44)

Name: A4 x S3
Maximal quotients:GAP4(18,3) GAP4(24,13)
Real polynomial:
```x^72-1260*x^70+552636*x^68-114230940*x^66+13215916980*x^64-941765519940*x^62\
+43753982813026*x^60-1373998799596500*x^58+29891469454489860*x^56-4590698126\
69462060*x^54+5058768009566562732*x^52-40589314794420732060*x^50+24027315866\
6951715695*x^48-1061613710687970208440*x^46+3535488112930559995608*x^44-8944\
281041979693619000*x^42+17289395293405430877192*x^40-25636965823743061600680\
*x^38+29227331222978756381276*x^36-25636965823743061600680*x^34+172893952934\
05430877192*x^32-8944281041979693619000*x^30+3535488112930559995608*x^28-106\
1613710687970208440*x^26+240273158666951715695*x^24-40589314794420732060*x^2\
2+5058768009566562732*x^20-459069812669462060*x^18+29891469454489860*x^16-13\
73998799596500*x^14+43753982813026*x^12-941765519940*x^10+13215916980*x^8-11\
4230940*x^6+552636*x^4-1260*x^2+1```
Common denominator of the automorphisms:
```2615060571350890085784167054291923364521046644539029057108399544417558993949\
59038530687205448089600```
Complex polynomial:
```x^72-300*x^66+36378*x^60-16048476*x^54+2952331983*x^48-12134278872*x^42+6148\
7088012*x^36-109208509848*x^30+239138890623*x^24-11699339004*x^18+238676058*\
x^12-17714700*x^6+531441```
Common denominator of the automorphisms:
`2337432703389771786755712`

Database of Galois polynomials by Bill Allombert and Igor Schein.