Finite Group Databasebeta

← Group #64932

Character table — Group #64932

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size111122444444555588888810101010101010101010202020202020
order12442424510202088881010102020208816161616161616168816161616
χ111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111-1-1-1-1111111-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111-1-1-1-1111111-1-1−i−i−i−iiiii-1-1−i−iii
χ5111111-1-1111111111-1-11-1-11111111111-1-1-1-1-1-1
χ6111111-1-1111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-11111
χ7111111-1-11111-1-1-1-11-1-11-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111-1-11111-1-1-1-11-1-11-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911-1-1-111-111-1-1ii−i−i-1111-1-1i−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+ζ78i−i−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78
χ1011-1-1-111-111-1-1ii−i−i-1111-1-1i−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−ζ78i−iζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78
χ1111-1-1-111-111-1-1−i−iii-1111-1-1−ii−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−ii−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74
χ1211-1-1-111-111-1-1−i−iii-1111-1-1−iiζ14+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−iiζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74
χ1311-1-1-11-1111-1-1ii−i−i-1-1-1111i−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−iiζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78
χ1411-1-1-11-1111-1-1ii−i−i-1-1-1111i−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−ii−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78
χ1511-1-1-11-1111-1-1−i−iii-1-1-1111−ii−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+ζ74i−iζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74
χ1611-1-1-11-1111-1-1−i−iii-1-1-1111−iiζ14+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−ζ74i−i−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74
χ172222-2-20022222222-200-200-2-200000000000000
χ182222-2-2002222-2-2-2-2-200-2002200000000000000
χ1922-2-22-20022-2-22i2i−2i−2i200-200−2i2i00000000000000
χ2022-2-22-20022-2-2−2i−2i2i2i200-2002i−2i00000000000000
χ212-22i−2i00002-22i−2i−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77000000
χ222-22i−2i00002-22i−2i−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77000000
χ232-22i−2i00002-22i−2i2ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77000000
χ242-22i−2i00002-22i−2i2ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77000000
χ252-2−2i2i00002-2−2i2i−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79000000
χ262-2−2i2i00002-2−2i2i−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79000000
χ272-2−2i2i00002-2−2i2i2ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79000000
χ282-2−2i2i00002-2−2i2i2ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79000000
χ2944444444-1-1-1-10000-1-1-1-1-1-10000000000000000
χ30444444-4-4-1-1-1-10000-111-1110000000000000000
χ314444-4-400-1-1-1-1000015−515−50000000000000000
χ324444-4-400-1-1-1-100001−551−550000000000000000
χ3344-4-44-400-1-1110000-15−51−550000000000000000
χ3444-4-44-400-1-1110000-1−5515−50000000000000000
χ3544-4-4-444-4-1-11100001-1-1-1110000000000000000
χ3644-4-4-44-44-1-1110000111-1-1-10000000000000000
χ378-88i−8i0000-22−2i2i00000000000000000000000000
χ388-8−8i8i0000-222i−2i00000000000000000000000000

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