Group GAP4(80,23)

x^80-x^79-80*x^78+79*x^77+3080*x^76-3001*x^75-76001*x^74+73000*x^73+1350574*\
x^72-1277574*x^71-18412642*x^70+17135068*x^69+200330620*x^68-183195552*x^67-\
1786554464*x^66+1603358912*x^65+13310909897*x^64-11707550985*x^63-8403257692\
8*x^62+72325025943*x^61+454328208865*x^60-382003182922*x^59-2120920516005*x^\
58+1738917333083*x^57+8602866619464*x^56-6863949286381*x^55-30465961098651*x\
^54+23602011812270*x^53+94538070338919*x^52-70936058526649*x^51-257720394299\
648*x^50+186784335772999*x^49+618290606512725*x^48-431506270739726*x^47-1306\
627172190229*x^46+875120901450503*x^45+2432915689851183*x^44-155779478840068\
0*x^43-3989535127786787*x^42+2431740339386107*x^41+5755034763976401*x^40-332\
3294424590293*x^39-7289825548388096*x^38+3966531123797762*x^37+8087826198760\
712*x^36-4121295074962171*x^35-7833561936705177*x^34+3712266861733904*x^33+6\
596255142034594*x^32-2883988280227505*x^31-4804260564552963*x^30+19202722838\
96106*x^29+3007766571139215*x^28-1087494285341693*x^27-1606490318631420*x^26\
+518996026802543*x^25+725389242122201*x^24-206393198069646*x^23-273857853829\
953*x^22+67464619822782*x^21+85288707308825*x^20-17824028826728*x^19-2155163\
1735567*x^18+3727528251529*x^17+4328627382295*x^16-601025760651*x^15-6733047\
63692*x^14+72224177021*x^13+78435457322*x^12-6180821401*x^11-6545739783*x^10\
+352734822*x^9+368063102*x^8-11977801*x^7-12744919*x^6+175857*x^5+234730*x^4\
+1110*x^3-1720*x^2-40*x+1

1

x^80-x^79+x^77-x^76+x^74-x^73+x^71-x^70+x^68-x^67+x^65-x^64+x^62-x^61+x^59-x\
^58+x^56-x^55+x^53-x^52+x^50-x^49+x^47-x^46+x^44-x^43+x^41-x^40+x^39-x^37+x^\
36-x^34+x^33-x^31+x^30-x^28+x^27-x^25+x^24-x^22+x^21-x^19+x^18-x^16+x^15-x^1\
3+x^12-x^10+x^9-x^7+x^6-x^4+x^3-x+1

1