Group GAP4(128,913)
Name: (C16 : C4) : C2
Maximal quotient:GAP4(64,123)
Real polynomial:
x^128-6720*x^126+11940320*x^124-10150183680*x^122+5026566248800*x^120-160699\
6801320960*x^118+354782142020776960*x^116-56743799989271162880*x^114+6810220\
678882595543040*x^112-629715947549593344921600*x^110+45774794272650138557568\
000*x^108-2657271952313616999195340800*x^106+124742263998067602086706841600*\
x^104-4784012514210149580514955673600*x^102+15117209373200685768526483107840\
0*x^100-3964711390626131530239298530508800*x^98+8684924299255702784899782528\
0358400*x^96-1597975870086309880180330879524864000*x^94+24819584375381712680\
203039798231040000*x^92-326870496071515776483922503044677632000*x^90+3664670\
619681056899236001102167044096000*x^88-3509850799345786809966167286247587840\
0000*x^86+288043208234553142926727513760703578112000*x^84-203084240945864755\
6111824521540224942080000*x^82+12328295339004775359529106685386937073664000*\
x^80-64555561323995509859501718665307783168000000*x^78+292021765103336404584\
928324648505673646080000*x^76-1142515851128335683604982657389657765969920000\
*x^74+3869664825127540430633906173130827356569600000*x^72-113539767807682104\
11940268439276253484154880000*x^70+28873672113920880389932574010674898314199\
040000*x^68-63662121902735638063720377911522387243827200000*x^66+12172256879\
0336752515961268709742987152588800000*x^64-201838569825088440150161456805067\
075721625600000*x^62+290242031761609370602311147534559669859123200000*x^60-3\
61879977442595494955656950458736817943347200000*x^58+39109297367642935859848\
9910245201326427340800000*x^56-366182926892612820491017346425912183436083200\
000*x^54+296843152434339252165223308977757924150476800000*x^52-2081517526919\
02270686173677000859720456601600000*x^50+12611429848727028540439793992597915\
7128806400000*x^48-65928234456735226142595478473377725808640000000*x^46+2968\
7288633354615292347170360272479059968000000*x^44-114922143249532556946466544\
27400681553920000000*x^42+3815785702056596442545470770943784648704000000*x^4\
0-1083912834073455023166895809541806489600000000*x^38+2626555625283824642455\
19417647432728576000000*x^36-54122300483638787585336552420775297024000000*x^\
34+9449966064378750993506736012708020224000000*x^32-139265174159751413175282\
2181671731200000000*x^30+172461800245685954852077767523041280000000*x^28-178\
56056726036832033295118358282240000000*x^26+15366095801985404249440140237209\
60000000*x^24-109143218797891310991350735831040000000*x^22+63451116581001331\
25472429015040000000*x^20-298847889765295050186974822400000000*x^18+11260790\
183746157250284093440000000*x^16-334217029616191176651571200000000*x^14+7662\
659408578877377740800000000*x^12-132419738414821775769600000000*x^10+1670992\
054114582528000000000*x^8-14748862718882611200000000*x^6+8535989802762240000\
0000*x^4-288621802291200000000*x^2+429496729600000000
Common denominator of the automorphisms:
9662370753719170852876366925858570242972242424737625111113900342010860589119\
4771696317409016484983964541348313365698382735270459301014320908040538193855\
6999192637437262829603071636241652270600261423562519471925453677182417281002\
4842609831318314670306133107927681412650707785981325972675872036709648031112\
0891060814239832556680322058437106073372241504421717807019877940221404711442\
5753670417194094767659597557892507278035936434458166611187129670936541365602\
8743797955206299090420970291200000000
Complex polynomial:
x^128+6720*x^126+11940320*x^124+10150183680*x^122+5026566248800*x^120+160699\
6801320960*x^118+354782142020776960*x^116+56743799989271162880*x^114+6810220\
678882595543040*x^112+629715947549593344921600*x^110+45774794272650138557568\
000*x^108+2657271952313616999195340800*x^106+124742263998067602086706841600*\
x^104+4784012514210149580514955673600*x^102+15117209373200685768526483107840\
0*x^100+3964711390626131530239298530508800*x^98+8684924299255702784899782528\
0358400*x^96+1597975870086309880180330879524864000*x^94+24819584375381712680\
203039798231040000*x^92+326870496071515776483922503044677632000*x^90+3664670\
619681056899236001102167044096000*x^88+3509850799345786809966167286247587840\
0000*x^86+288043208234553142926727513760703578112000*x^84+203084240945864755\
6111824521540224942080000*x^82+12328295339004775359529106685386937073664000*\
x^80+64555561323995509859501718665307783168000000*x^78+292021765103336404584\
928324648505673646080000*x^76+1142515851128335683604982657389657765969920000\
*x^74+3869664825127540430633906173130827356569600000*x^72+113539767807682104\
11940268439276253484154880000*x^70+28873672113920880389932574010674898314199\
040000*x^68+63662121902735638063720377911522387243827200000*x^66+12172256879\
0336752515961268709742987152588800000*x^64+201838569825088440150161456805067\
075721625600000*x^62+290242031761609370602311147534559669859123200000*x^60+3\
61879977442595494955656950458736817943347200000*x^58+39109297367642935859848\
9910245201326427340800000*x^56+366182926892612820491017346425912183436083200\
000*x^54+296843152434339252165223308977757924150476800000*x^52+2081517526919\
02270686173677000859720456601600000*x^50+12611429848727028540439793992597915\
7128806400000*x^48+65928234456735226142595478473377725808640000000*x^46+2968\
7288633354615292347170360272479059968000000*x^44+114922143249532556946466544\
27400681553920000000*x^42+3815785702056596442545470770943784648704000000*x^4\
0+1083912834073455023166895809541806489600000000*x^38+2626555625283824642455\
19417647432728576000000*x^36+54122300483638787585336552420775297024000000*x^\
34+9449966064378750993506736012708020224000000*x^32+139265174159751413175282\
2181671731200000000*x^30+172461800245685954852077767523041280000000*x^28+178\
56056726036832033295118358282240000000*x^26+15366095801985404249440140237209\
60000000*x^24+109143218797891310991350735831040000000*x^22+63451116581001331\
25472429015040000000*x^20+298847889765295050186974822400000000*x^18+11260790\
183746157250284093440000000*x^16+334217029616191176651571200000000*x^14+7662\
659408578877377740800000000*x^12+132419738414821775769600000000*x^10+1670992\
054114582528000000000*x^8+14748862718882611200000000*x^6+8535989802762240000\
0000*x^4+288621802291200000000*x^2+429496729600000000
Common denominator of the automorphisms:
9662370753719170852876366925858570242972242424737625111113900342010860589119\
4771696317409016484983964541348313365698382735270459301014320908040538193855\
6999192637437262829603071636241652270600261423562519471925453677182417281002\
4842609831318314670306133107927681412650707785981325972675872036709648031112\
0891060814239832556680322058437106073372241504421717807019877940221404711442\
5753670417194094767659597557892507278035936434458166611187129670936541365602\
8743797955206299090420970291200000000
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.