Group GAP4(50,2)

x^50+x^49-49*x^48-48*x^47+1128*x^46+1081*x^45-16215*x^44-15180*x^43+163185*x\
^42+148995*x^41-1221759*x^40-1086008*x^39+7059052*x^38+6096454*x^37-32224114\
*x^36-26978328*x^35+118030185*x^34+95548245*x^33-350343565*x^32-273438880*x^\
31+847660528*x^30+635745396*x^29-1676056044*x^28-1203322288*x^27+2707475148*\
x^26+1852482996*x^25-3562467300*x^24-2310789600*x^23+3796297200*x^22+2319959\
400*x^21-3247943160*x^20-1855967520*x^19+2203961430*x^18+1166803110*x^17-116\
6803110*x^16-565722720*x^15+471435600*x^14+206253075*x^13-141120525*x^12-546\
27300*x^11+30045015*x^10+10015005*x^9-4292145*x^8-1184040*x^7+376740*x^6+807\
30*x^5-17550*x^4-2600*x^3+325*x^2+25*x-1

1

x^50+100*x^48+4550*x^46+125000*x^44+2320575*x^42+30877270*x^40+304850350*x^3\
8+2281609875*x^36+13117034375*x^34+58362686750*x^32+201612776975*x^30+540448\
376625*x^28+1119657810000*x^26+1778847312500*x^24+2141335293750*x^22+1919715\
531375*x^20+1251780369375*x^18+575482249625*x^16+179504919375*x^14+364451723\
75*x^12+4636678800*x^10+354065375*x^8+15186750*x^6+321250*x^4+2500*x^2+5

152322616089151948536225216109479080763050827224473778262926264007146234443