# Group GAP4(60,12)

Name: D60
Maximal quotients:GAP4(12,4) GAP4(20,4) GAP4(30,3)
Real polynomial:
```x^60-258*x^58+29889*x^56-2071716*x^54+96472836*x^52-3210683292*x^50+79296024\
042*x^48-1489620178872*x^46+21646629541944*x^44-246195319196340*x^42+2209075\
503295320*x^40-15716698430182632*x^38+88875200520269343*x^36-399415780848830\
913*x^34+1422651006054943785*x^32-3992857276079514762*x^30+87469139130005126\
07*x^28-14744029774909525191*x^26+18733042249019733501*x^24-1742155896607796\
9394*x^22+11380692136474679517*x^20-4940285376167178777*x^18+133728252180447\
5901*x^16-217901977225239060*x^14+20929546743064560*x^12-1170590442453936*x^\
10+38249341091550*x^8-720941916852*x^6+7429840425*x^4-36492282*x^2+59049```
Common denominator of the automorphisms:
```1422433149911869647249140668590765737171773154008539212862847150078161932660\
132897820034505755222543984993233468461039589310460205324529106241```
Complex polynomial:
```x^60+43*x^54+11712*x^48+346266*x^42+3443424*x^36+6801099*x^30+3443424*x^24+3\
46266*x^18+11712*x^12+43*x^6+1```
Common denominator of the automorphisms:
`602091671958`

Database of Galois polynomials by Bill Allombert and Igor Schein.