# Group GAP4(80,20)

Name: C20 x C4
Maximal quotients:GAP4(16,2) GAP4(40,9)
Real polynomial:
```x^80-80*x^78+3080*x^76-76000*x^74+1350500*x^72-18410016*x^70+200271120*x^68-\
1785587520*x^66+13298907050*x^64-83914230400*x^62+453376599104*x^60-21145627\
94240*x^58+8567088967840*x^56-30294642963200*x^54+93834705801600*x^52-255230\
399780352*x^50+610658671349475*x^48-1286317425363600*x^46+2385911353497000*x\
^44-3894861329436000*x^42+5589126007740659*x^40-7037156232506360*x^38+775410\
7886287660*x^36-7452460668735600*x^34+6221473861787800*x^32-4488510596689664\
*x^30+2781342035057920*x^28-1469388240593920*x^26+655976882286125*x^24-24482\
7050579000*x^22+75406699530316*x^20-18864047766320*x^18+3758038063095*x^16-5\
81491602800*x^14+67655781400*x^12-5666214048*x^10+321015355*x^8-11166680*x^6\
+199900*x^4-1200*x^2+1```
Common denominator of the automorphisms:
`1`
Complex polynomial:
```x^80+80*x^78+3080*x^76+76000*x^74+1350500*x^72+18410016*x^70+200271120*x^68+\
1785587520*x^66+13298907050*x^64+83914230400*x^62+453376599104*x^60+21145627\
94240*x^58+8567088967840*x^56+30294642963200*x^54+93834705801600*x^52+255230\
399780352*x^50+610658671349475*x^48+1286317425363600*x^46+2385911353497000*x\
^44+3894861329436000*x^42+5589126007740659*x^40+7037156232506360*x^38+775410\
7886287660*x^36+7452460668735600*x^34+6221473861787800*x^32+4488510596689664\
*x^30+2781342035057920*x^28+1469388240593920*x^26+655976882286125*x^24+24482\
7050579000*x^22+75406699530316*x^20+18864047766320*x^18+3758038063095*x^16+5\
81491602800*x^14+67655781400*x^12+5666214048*x^10+321015355*x^8+11166680*x^6\
+199900*x^4+1200*x^2+1```
Common denominator of the automorphisms:
`1`

Database of Galois polynomials by Bill Allombert and Igor Schein.