Group GAP4(72,26)
Name: C3 x (C3 : Q8)
Maximal quotients:GAP4(24,4) GAP4(24,11) GAP4(36,12)
Real polynomial:
x^72-600*x^70+156600*x^68-24012000*x^66+2452808250*x^64-178976250000*x^62+97\
51693140000*x^60-409045671450000*x^58+13504421787328125*x^56-356779413770625\
000*x^54+7639751191798125000*x^52-133915034711306250000*x^50+193658471853695\
8593750*x^48-23246352490604343750000*x^46+232724193213223828125000*x^44-1950\
075217868610937500000*x^42+13712036957614612792968750*x^40-81043466145168023\
437500000*x^38+402956607559047591796875000*x^36-1685501314329927480468750000\
*x^34+5926322560297534497070312500*x^32-17487182171938012207031250000*x^30+4\
3195833915098787597656250000*x^28-89010613981649487304687500000*x^26+1523144\
36862257400054931640625*x^24-215189802160655328369140625000*x^22+24918840571\
1513488769531250000*x^20-234383196855970458984375000000*x^18+177053655191069\
641113281250000*x^16-105892840225085449218750000000*x^14+4923292948132324218\
7500000000*x^12-17369094377197265625000000000*x^10+4498254810791015625000000\
000*x^8-815159399414062500000000000*x^6+95894824218750000000000000*x^4-64072\
26562500000000000000*x^2+177978515625000000000000
Common denominator of the automorphisms:
8569646340098782721596726207578168513363702028679431454603396732108888973366\
193477378857421875000000000000
Complex polynomial:
x^72+600*x^70+156600*x^68+24012000*x^66+2452808250*x^64+178976250000*x^62+97\
51693140000*x^60+409045671450000*x^58+13504421787328125*x^56+356779413770625\
000*x^54+7639751191798125000*x^52+133915034711306250000*x^50+193658471853695\
8593750*x^48+23246352490604343750000*x^46+232724193213223828125000*x^44+1950\
075217868610937500000*x^42+13712036957614612792968750*x^40+81043466145168023\
437500000*x^38+402956607559047591796875000*x^36+1685501314329927480468750000\
*x^34+5926322560297534497070312500*x^32+17487182171938012207031250000*x^30+4\
3195833915098787597656250000*x^28+89010613981649487304687500000*x^26+1523144\
36862257400054931640625*x^24+215189802160655328369140625000*x^22+24918840571\
1513488769531250000*x^20+234383196855970458984375000000*x^18+177053655191069\
641113281250000*x^16+105892840225085449218750000000*x^14+4923292948132324218\
7500000000*x^12+17369094377197265625000000000*x^10+4498254810791015625000000\
000*x^8+815159399414062500000000000*x^6+95894824218750000000000000*x^4+64072\
26562500000000000000*x^2+177978515625000000000000
Common denominator of the automorphisms:
8569646340098782721596726207578168513363702028679431454603396732108888973366\
193477378857421875000000000000
Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
Copyleft © 2002-2008 the PARI group.