Finite Group Databasebeta

← Group #10623955

Character table — Group #10623955

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size11448888888888993636454545454545454545454545
order1251036151515153030303044202088881616161616161616
χ1111111111111111111111111111111
χ21111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1iiii−i−i−i−i
χ4111111111111111111-1-1-1-1−i−i−i−iiiii
χ511111111111111-1-1-1-1ii−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
χ611111111111111-1-1-1-1ii−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
χ711111111111111-1-1-1-1−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
χ811111111111111-1-1-1-1−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
χ91-11-11-11111-1-1-1-1i−ii−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
χ101-11-11-11111-1-1-1-1i−ii−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
χ111-11-11-11111-1-1-1-1i−ii−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
χ121-11-11-11111-1-1-1-1i−ii−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
χ131-11-11-11111-1-1-1-1−ii−ii−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
χ141-11-11-11111-1-1-1-1−ii−ii−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
χ151-11-11-11111-1-1-1-1−ii−iiζ14+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
χ161-11-11-11111-1-1-1-1−ii−iiζ14+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
χ1744-1-144-1-1-1-1-1-1-1-144-1-1000000000000
χ1844-1-144-1-1-1-1-1-1-1-1-4-411000000000000
χ194-4-114-4-1-1-1-111114i−4i−ii000000000000
χ204-4-114-4-1-1-1-11111−4i4ii−i000000000000
χ218888-1-1-1-1-1-1-1-1-1-10000000000000000
χ2288-2-2-1-1−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ72−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ720000000000000000
χ2388-2-2-1-1ζ8+ζ24−2ζ56+ζ72ζ8+ζ24+ζ56−2ζ72−2ζ8+ζ24+ζ56+ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72ζ8+ζ24+ζ56−2ζ72−2ζ8+ζ24+ζ56+ζ72ζ8−2ζ24+ζ56+ζ720000000000000000
χ2488-2-2-1-1ζ8−2ζ24+ζ56+ζ72−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ72ζ8+ζ24−2ζ56+ζ72ζ8−2ζ24+ζ56+ζ72−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ72ζ8+ζ24−2ζ56+ζ720000000000000000
χ2588-2-2-1-1ζ8+ζ24+ζ56−2ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72−2ζ8+ζ24+ζ56+ζ720000000000000000
χ268-88-8-11-1-1-1-111110000000000000000
χ278-8-22-11−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ722ζ8−ζ24−ζ56−ζ72−ζ8−ζ24+2ζ56−ζ72−ζ8+2ζ24−ζ56−ζ72−ζ8−ζ24−ζ56+2ζ720000000000000000
χ288-8-22-11ζ8+ζ24−2ζ56+ζ72ζ8+ζ24+ζ56−2ζ72−2ζ8+ζ24+ζ56+ζ72ζ8−2ζ24+ζ56+ζ72−ζ8−ζ24+2ζ56−ζ72−ζ8−ζ24−ζ56+2ζ722ζ8−ζ24−ζ56−ζ72−ζ8+2ζ24−ζ56−ζ720000000000000000
χ298-8-22-11ζ8−2ζ24+ζ56+ζ72−2ζ8+ζ24+ζ56+ζ72ζ8+ζ24+ζ56−2ζ72ζ8+ζ24−2ζ56+ζ72−ζ8+2ζ24−ζ56−ζ722ζ8−ζ24−ζ56−ζ72−ζ8−ζ24−ζ56+2ζ72−ζ8−ζ24+2ζ56−ζ720000000000000000
χ308-8-22-11ζ8+ζ24+ζ56−2ζ72ζ8−2ζ24+ζ56+ζ72ζ8+ζ24−2ζ56+ζ72−2ζ8+ζ24+ζ56+ζ72−ζ8−ζ24−ζ56+2ζ72−ζ8+2ζ24−ζ56−ζ72−ζ8−ζ24+2ζ56−ζ722ζ8−ζ24−ζ56−ζ720000000000000000

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