Finite Group Databasebeta

← Group #64845

Character table — Group #64845

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size1111224444444444444444441010101020202020202020202020
order1244885101616202040404040808080808080808024884488161616161616
χ111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1i−ii−i-1-1ii−i−i
χ4111111111111111111111111-1-1-1-1−ii−ii-1-1−i−iii
χ511111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ611111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i11−i−iii
χ811111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii11ii−i−i
χ91111-1-111i−i11-1-1-1-1iiii−i−i−i−i11-1-111-1-1i−ii−ii−i
χ101111-1-111i−i11-1-1-1-1iiii−i−i−i−i11-1-1-1-111i−i−ii−ii
χ111111-1-111i−i11-1-1-1-1iiii−i−i−i−i-1-111i−i−ii−ii-111-1
χ121111-1-111i−i11-1-1-1-1iiii−i−i−i−i-1-111−iii−i−ii1-1-11
χ131111-1-111−ii11-1-1-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii−ii
χ141111-1-111−ii11-1-1-1-1−i−i−i−iiiii11-1-1-1-111−iii−ii−i
χ151111-1-111−ii11-1-1-1-1−i−i−i−iiiii-1-111i−i−iii−i1-1-11
χ161111-1-111−ii11-1-1-1-1−i−i−i−iiiii-1-111−iii−ii−i-111-1
χ1722-2-22i−2i2200-2-22i2i−2i−2i000000002-22i−2i0000000000
χ1822-2-22i−2i2200-2-22i2i−2i−2i00000000-22−2i2i0000000000
χ1922-2-2−2i2i2200-2-2−2i−2i2i2i000000002-2−2i2i0000000000
χ2022-2-2−2i2i2200-2-2−2i−2i2i2i00000000-222i−2i0000000000
χ21444444-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22444444-1-1-4-4-1-1-1-1-1-11111111100000000000000
χ234444-4-4-1-14i−4i-1-11111−i−i−i−iiiii00000000000000
χ244444-4-4-1-1−4i4i-1-11111iiii−i−i−i−i00000000000000
χ2544-4-44i−4i-1-10011−i−iiiζ26−ζ42−ζ58+ζ74ζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74−ζ26+ζ42+ζ58−ζ74−ζ14−ζ46+ζ62+ζ78−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78ζ14+ζ46−ζ62−ζ7800000000000000
χ2644-4-44i−4i-1-10011−i−iii−ζ26+ζ42+ζ58−ζ74−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74ζ26−ζ42−ζ58+ζ74ζ14+ζ46−ζ62−ζ78ζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78−ζ14−ζ46+ζ62+ζ7800000000000000
χ2744-4-4−4i4i-1-10011ii−i−i−ζ14−ζ46+ζ62+ζ78−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78ζ14+ζ46−ζ62−ζ78ζ26−ζ42−ζ58+ζ74ζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74−ζ26+ζ42+ζ58−ζ7400000000000000
χ2844-4-4−4i4i-1-10011ii−i−iζ14+ζ46−ζ62−ζ78ζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78−ζ14−ζ46+ζ62+ζ78−ζ26+ζ42+ζ58−ζ74−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74ζ26−ζ42−ζ58+ζ7400000000000000
χ294-44i−4i004-4004i−4i00000000000000000000000000
χ304-44i−4i00-1100−iiζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78ζ9+ζ13−ζ41−ζ77−ζ9−ζ13+ζ41+ζ77−ζ29−ζ57+ζ61+ζ73ζ29+ζ57−ζ61−ζ73ζ27+ζ31−ζ43−ζ79−ζ27−ζ31+ζ43+ζ79ζ11−ζ47−ζ59+ζ63−ζ11+ζ47+ζ59−ζ6300000000000000
χ314-44i−4i00-1100−iiζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78−ζ9−ζ13+ζ41+ζ77ζ9+ζ13−ζ41−ζ77ζ29+ζ57−ζ61−ζ73−ζ29−ζ57+ζ61+ζ73−ζ27−ζ31+ζ43+ζ79ζ27+ζ31−ζ43−ζ79−ζ11+ζ47+ζ59−ζ63ζ11−ζ47−ζ59+ζ6300000000000000
χ324-44i−4i00-1100−ii−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74ζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78−ζ29−ζ57+ζ61+ζ73ζ29+ζ57−ζ61−ζ73−ζ9−ζ13+ζ41+ζ77ζ9+ζ13−ζ41−ζ77−ζ11+ζ47+ζ59−ζ63ζ11−ζ47−ζ59+ζ63ζ27+ζ31−ζ43−ζ79−ζ27−ζ31+ζ43+ζ7900000000000000
χ334-44i−4i00-1100−ii−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74ζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78ζ29+ζ57−ζ61−ζ73−ζ29−ζ57+ζ61+ζ73ζ9+ζ13−ζ41−ζ77−ζ9−ζ13+ζ41+ζ77ζ11−ζ47−ζ59+ζ63−ζ11+ζ47+ζ59−ζ63−ζ27−ζ31+ζ43+ζ79ζ27+ζ31−ζ43−ζ7900000000000000
χ344-4−4i4i004-400−4i4i00000000000000000000000000
χ354-4−4i4i00-1100i−i−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78ζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74ζ27+ζ31−ζ43−ζ79−ζ27−ζ31+ζ43+ζ79−ζ11+ζ47+ζ59−ζ63ζ11−ζ47−ζ59+ζ63ζ9+ζ13−ζ41−ζ77−ζ9−ζ13+ζ41+ζ77ζ29+ζ57−ζ61−ζ73−ζ29−ζ57+ζ61+ζ7300000000000000
χ364-4−4i4i00-1100i−i−ζ14−ζ46+ζ62+ζ78ζ14+ζ46−ζ62−ζ78ζ26−ζ42−ζ58+ζ74−ζ26+ζ42+ζ58−ζ74−ζ27−ζ31+ζ43+ζ79ζ27+ζ31−ζ43−ζ79ζ11−ζ47−ζ59+ζ63−ζ11+ζ47+ζ59−ζ63−ζ9−ζ13+ζ41+ζ77ζ9+ζ13−ζ41−ζ77−ζ29−ζ57+ζ61+ζ73ζ29+ζ57−ζ61−ζ7300000000000000
χ374-4−4i4i00-1100i−iζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74ζ11−ζ47−ζ59+ζ63−ζ11+ζ47+ζ59−ζ63ζ27+ζ31−ζ43−ζ79−ζ27−ζ31+ζ43+ζ79ζ29+ζ57−ζ61−ζ73−ζ29−ζ57+ζ61+ζ73−ζ9−ζ13+ζ41+ζ77ζ9+ζ13−ζ41−ζ7700000000000000
χ384-4−4i4i00-1100i−iζ14+ζ46−ζ62−ζ78−ζ14−ζ46+ζ62+ζ78−ζ26+ζ42+ζ58−ζ74ζ26−ζ42−ζ58+ζ74−ζ11+ζ47+ζ59−ζ63ζ11−ζ47−ζ59+ζ63−ζ27−ζ31+ζ43+ζ79ζ27+ζ31−ζ43−ζ79−ζ29−ζ57+ζ61+ζ73ζ29+ζ57−ζ61−ζ73ζ9+ζ13−ζ41−ζ77−ζ9−ζ13+ζ41+ζ7700000000000000

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