Finite Group Databasebeta

← Group #13014107

Character table — Group #13014107

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111224444448888888888888888888888888888888888882020202040404040404040404040808080808080
order12442424510202022244410101010101010101010101010101020202020202020202020202020202088888816161616161616164416161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ51111111111111-1-11-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ61111111111111-1-11-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111111-1-11-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ81111111111111-1-11-1-11111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911-1-11-1-1111-1-111-1-11-111111-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1ii−i−ii−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
χ1011-1-11-1-1111-1-111-1-11-111111-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1ii−i−ii−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
χ1111-1-11-1-1111-1-111-1-11-111111-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1−i−iii−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
χ1211-1-11-1-1111-1-111-1-11-111111-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1−i−iii−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
χ1311-1-11-1-1111-1-11-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111ii−i−ii−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
χ1411-1-11-1-1111-1-11-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111ii−i−ii−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
χ1511-1-11-1-1111-1-11-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111−i−iii−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
χ1611-1-11-1-1111-1-11-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111−i−iii−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
χ17222222222222-200-2002-2-2-2-22200000000222-2-2-2-2000000002222-2-200000000000000
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χ2022-2-22-2-2222-2-2-2002002-2-2-2-2-2-20000000022-2222200000000−2i−2i2i2i2i−2i00000000000000
χ2144444444-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
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χ594-44i−4i00004-44i−4i000000000000000000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800−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
χ604-44i−4i00004-44i−4i000000000000000000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800ζ11+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
χ614-44i−4i00004-44i−4i0000000000000000000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800−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
χ624-44i−4i00004-44i−4i0000000000000000000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800ζ11+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
χ634-4−4i4i00004-4−4i4i000000000000000000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400−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
χ644-4−4i4i00004-4−4i4i000000000000000000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400ζ9−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
χ654-4−4i4i00004-4−4i4i0000000000000000000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400ζ9+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
χ664-4−4i4i00004-4−4i4i0000000000000000000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400−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
χ6716-1616i−16i0000-44−4i4i00000000000000000000000000000000000000000000000000000000
χ6816-16−16i16i0000-444i−4i00000000000000000000000000000000000000000000000000000000

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