# Group GAP4(64,243)

Name: ((C2 x C2) . (C2 x C2 x C2)) : C2
Maximal quotients:GAP4(32,49) GAP4(32,50)
Real polynomial:
```x^64-144*x^62+9096*x^60-337176*x^58+8276978*x^56-143791008*x^54+1842783072*x\
^52-17916774720*x^50+134799275649*x^48-796202463288*x^46+3731644045104*x^44-\
13987171384824*x^42+42165188200306*x^40-102611466261120*x^38+202001630153832\
*x^36-321859063554984*x^34+414701950742852*x^32-431091864745512*x^30+3602301\
21589608*x^28-240762455236320*x^26+127881045121906*x^24-53551688815512*x^22+\
17508465047856*x^20-4415886984216*x^18+846480631809*x^16-121041813360*x^14+1\
2609733728*x^12-928662576*x^10+46519538*x^8-1505448*x^6+29064*x^4-288*x^2+1```
Common denominator of the automorphisms:
`21016462384267555237865732611244367357760332018172154733886968416000`
Complex polynomial:
```x^64-36*x^60+1376*x^56-21672*x^52+173890*x^48-882540*x^44+3133280*x^40-68490\
36*x^36+8890099*x^32-6849036*x^28+3133280*x^24-882540*x^20+173890*x^16-21672\
*x^12+1376*x^8-36*x^4+1```
Common denominator of the automorphisms:
`75858088992552000`

Database of Galois polynomials by Bill Allombert and Igor Schein.