Finite Group Databasebeta

← Group #87765

Character table — Group #87765

Order 400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1111444444444444444444444444252525252525252525252525
order124455555510101010101020202020202020202020202088881616161616161616
χ11111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111-1-1-1-1−i−i−i−iiiii
χ511-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78
χ611-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78
χ711-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74
χ811-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74
χ91-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ13+ζ29+ζ61+ζ77−ζ13−ζ29−ζ61−ζ77−ζ9−ζ41−ζ57−ζ73ζ9+ζ41+ζ57+ζ73−ζ31−ζ47−ζ63−ζ79ζ31+ζ47+ζ63+ζ79−ζ11−ζ27−ζ43−ζ59ζ11+ζ27+ζ43+ζ59
χ101-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ13−ζ29−ζ61−ζ77ζ13+ζ29+ζ61+ζ77ζ9+ζ41+ζ57+ζ73−ζ9−ζ41−ζ57−ζ73ζ31+ζ47+ζ63+ζ79−ζ31−ζ47−ζ63−ζ79ζ11+ζ27+ζ43+ζ59−ζ11−ζ27−ζ43−ζ59
χ111-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ9−ζ41−ζ57−ζ73ζ9+ζ41+ζ57+ζ73−ζ13−ζ29−ζ61−ζ77ζ13+ζ29+ζ61+ζ77−ζ11−ζ27−ζ43−ζ59ζ11+ζ27+ζ43+ζ59ζ31+ζ47+ζ63+ζ79−ζ31−ζ47−ζ63−ζ79
χ121-1i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ9+ζ41+ζ57+ζ73−ζ9−ζ41−ζ57−ζ73ζ13+ζ29+ζ61+ζ77−ζ13−ζ29−ζ61−ζ77ζ11+ζ27+ζ43+ζ59−ζ11−ζ27−ζ43−ζ59−ζ31−ζ47−ζ63−ζ79ζ31+ζ47+ζ63+ζ79
χ131-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ31−ζ47−ζ63−ζ79ζ31+ζ47+ζ63+ζ79−ζ11−ζ27−ζ43−ζ59ζ11+ζ27+ζ43+ζ59−ζ13−ζ29−ζ61−ζ77ζ13+ζ29+ζ61+ζ77ζ9+ζ41+ζ57+ζ73−ζ9−ζ41−ζ57−ζ73
χ141-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ31+ζ47+ζ63+ζ79−ζ31−ζ47−ζ63−ζ79ζ11+ζ27+ζ43+ζ59−ζ11−ζ27−ζ43−ζ59ζ13+ζ29+ζ61+ζ77−ζ13−ζ29−ζ61−ζ77−ζ9−ζ41−ζ57−ζ73ζ9+ζ41+ζ57+ζ73
χ151-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiiiζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ11−ζ27−ζ43−ζ59ζ11+ζ27+ζ43+ζ59ζ31+ζ47+ζ63+ζ79−ζ31−ζ47−ζ63−ζ79ζ9+ζ41+ζ57+ζ73−ζ9−ζ41−ζ57−ζ73ζ13+ζ29+ζ61+ζ77−ζ13−ζ29−ζ61−ζ77
χ161-1−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiiiζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ11+ζ27+ζ43+ζ59−ζ11−ζ27−ζ43−ζ59−ζ31−ζ47−ζ63−ζ79ζ31+ζ47+ζ63+ζ79−ζ9−ζ41−ζ57−ζ73ζ9+ζ41+ζ57+ζ73−ζ13−ζ29−ζ61−ζ77ζ13+ζ29+ζ61+ζ77
χ1744444-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1000000000000
χ184444-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1000000000000
χ194444-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5000000000000
χ204444-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52000000000000
χ214444-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52000000000000
χ224444-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5000000000000
χ2344-4-44-1-1-1-1-14-1-1-1-1-1-411111-411111000000000000
χ2444-4-4-14-1-1-1-1-14-1-1-1-11-411111-41111000000000000
χ2544-4-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+5000000000000
χ2644-4-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−52000000000000
χ2744-4-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+52000000000000
χ2844-4-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−5000000000000
χ294-44i−4i4-1-1-1-1-1-4111114i−i−i−i−i−i−4iiiiii000000000000
χ304-44i−4i-14-1-1-1-11-41111−i4i−i−i−i−ii−4iiiii000000000000
χ314-44i−4i-1-1−1+53−523+52−1−5111−5−3+52−3−521+5−i−i−2ζ44−2ζ76ζ12+ζ28+2ζ44+2ζ762ζ12+2ζ28+ζ44+ζ76−2ζ12−2ζ28ii2ζ44+2ζ76−ζ12−ζ28−2ζ44−2ζ76−2ζ12−2ζ28−ζ44−ζ762ζ12+2ζ28000000000000
χ324-44i−4i-1-13−52−1−5−1+53+5211−3+521+51−5−3−52−i−iζ12+ζ28+2ζ44+2ζ76−2ζ12−2ζ28−2ζ44−2ζ762ζ12+2ζ28+ζ44+ζ76ii−ζ12−ζ28−2ζ44−2ζ762ζ12+2ζ282ζ44+2ζ76−2ζ12−2ζ28−ζ44−ζ76000000000000
χ334-44i−4i-1-13+52−1+5−1−53−5211−3−521−51+5−3+52−i−i2ζ12+2ζ28+ζ44+ζ76−2ζ44−2ζ76−2ζ12−2ζ28ζ12+ζ28+2ζ44+2ζ76ii−2ζ12−2ζ28−ζ44−ζ762ζ44+2ζ762ζ12+2ζ28−ζ12−ζ28−2ζ44−2ζ76000000000000
χ344-44i−4i-1-1−1−53+523−52−1+5111+5−3−52−3+521−5−i−i−2ζ12−2ζ282ζ12+2ζ28+ζ44+ζ76ζ12+ζ28+2ζ44+2ζ76−2ζ44−2ζ76ii2ζ12+2ζ28−2ζ12−2ζ28−ζ44−ζ76−ζ12−ζ28−2ζ44−2ζ762ζ44+2ζ76000000000000
χ354-4−4i4i4-1-1-1-1-1-411111−4iiiiii4i−i−i−i−i−i000000000000
χ364-4−4i4i-14-1-1-1-11-41111i−4iiiii−i4i−i−i−i−i000000000000
χ374-4−4i4i-1-1−1+53−523+52−1−5111−5−3+52−3−521+5ii2ζ44+2ζ76−ζ12−ζ28−2ζ44−2ζ76−2ζ12−2ζ28−ζ44−ζ762ζ12+2ζ28−i−i−2ζ44−2ζ76ζ12+ζ28+2ζ44+2ζ762ζ12+2ζ28+ζ44+ζ76−2ζ12−2ζ28000000000000
χ384-4−4i4i-1-13−52−1−5−1+53+5211−3+521+51−5−3−52ii−ζ12−ζ28−2ζ44−2ζ762ζ12+2ζ282ζ44+2ζ76−2ζ12−2ζ28−ζ44−ζ76−i−iζ12+ζ28+2ζ44+2ζ76−2ζ12−2ζ28−2ζ44−2ζ762ζ12+2ζ28+ζ44+ζ76000000000000
χ394-4−4i4i-1-13+52−1+5−1−53−5211−3−521−51+5−3+52ii−2ζ12−2ζ28−ζ44−ζ762ζ44+2ζ762ζ12+2ζ28−ζ12−ζ28−2ζ44−2ζ76−i−i2ζ12+2ζ28+ζ44+ζ76−2ζ44−2ζ76−2ζ12−2ζ28ζ12+ζ28+2ζ44+2ζ76000000000000
χ404-4−4i4i-1-1−1−53+523−52−1+5111+5−3−52−3+521−5ii2ζ12+2ζ28−2ζ12−2ζ28−ζ44−ζ76−ζ12−ζ28−2ζ44−2ζ762ζ44+2ζ76−i−i−2ζ12−2ζ282ζ12+2ζ28+ζ44+ζ76ζ12+ζ28+2ζ44+2ζ76−2ζ44−2ζ76000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.