# Group GAP4(64,168)

Name: (C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)
Maximal quotients:GAP4(32,31) GAP4(32,40) GAP4(32,41)
Real polynomial:
```x^64-420*x^62+77052*x^60-8275500*x^58+587852987*x^56-29553496104*x^54+109780\
5320184*x^52-31038489493752*x^50+682390659873187*x^48-11852660016117636*x^46\
+164594826308370492*x^44-1843733006334065292*x^42+16768729106670812009*x^40-\
124402206759568598976*x^38+755074748524447516416*x^36-3755708615027950887936\
*x^34+15314425144721241072640*x^32-51153540302462725079040*x^30+139691271640\
156475817984*x^28-310881052864791761387520*x^26+561250159885585841782784*x^2\
4-816866200058759730954240*x^22+950645688144100897849344*x^20-87530285170421\
6918949888*x^18+629039546827177235316736*x^16-346782134396302141685760*x^14+\
143432263410177496055808*x^12-43236945421899103469568*x^10+91335886996834164\
40832*x^8-1277994372847040987136*x^6+108397772749878067200*x^4-4742290407621\
132288*x^2+72057594037927936```
Common denominator of the automorphisms:
```5606978343930197483672151515636252930121092455141247607828845451504583353012\
48208908706235721951215092166760201579181929382726678365358522368```
Complex polynomial:
```x^64+420*x^62+77052*x^60+8275500*x^58+587852987*x^56+29553496104*x^54+109780\
5320184*x^52+31038489493752*x^50+682390659873187*x^48+11852660016117636*x^46\
+164594826308370492*x^44+1843733006334065292*x^42+16768729106670812009*x^40+\
124402206759568598976*x^38+755074748524447516416*x^36+3755708615027950887936\
*x^34+15314425144721241072640*x^32+51153540302462725079040*x^30+139691271640\
156475817984*x^28+310881052864791761387520*x^26+561250159885585841782784*x^2\
4+816866200058759730954240*x^22+950645688144100897849344*x^20+87530285170421\
6918949888*x^18+629039546827177235316736*x^16+346782134396302141685760*x^14+\
143432263410177496055808*x^12+43236945421899103469568*x^10+91335886996834164\
40832*x^8+1277994372847040987136*x^6+108397772749878067200*x^4+4742290407621\
132288*x^2+72057594037927936```
Common denominator of the automorphisms:
```5606978343930197483672151515636252930121092455141247607828845451504583353012\
48208908706235721951215092166760201579181929382726678365358522368```

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.