Finite Group Databasebeta

← Group #13025783

Character table — Group #13025783

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222224444444444448888888888888888101010101010101016161616161616162020202020202020202020202020202020202020404040404040404040404040
order12442488882458810202040404040101616161620404080808080808080802244888810204040808080802488161616161616161616161616161616164444888816161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii-1-1-1-1
χ511111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii1111
χ811111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i1111
χ91111111111-1-11-1-11111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-1
χ101111111111-1-11-1-11111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-11-1111-1-1
χ111111111111-1-11-1-11111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-1-111
χ121111111111-1-11-1-11111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-1-111
χ131111111111-1-11-1-111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111
χ141111111111-1-11-1-111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111
χ151111111111-1-11-1-111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i11-1-1
χ161111111111-1-11-1-111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii11-1-1
χ17111111-1-1-1-1111-1-1111-1-1-1-11i−ii−i1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1-11-11i−ii−i
χ18111111-1-1-1-1111-1-1111-1-1-1-11i−ii−i1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i11-1-1−i−iii−i−iii−i−iii−i−iii-11-111-11-1i−ii−i
χ19111111-1-1-1-1111-1-1111-1-1-1-11i−ii−i1-1-1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-1-11111-1-111-1-1-1-111-1-111−iii−ii−i−ii−ii−ii
χ20111111-1-1-1-1111-1-1111-1-1-1-11i−ii−i1-1-1iiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i-1-111-1-111-1-11111-1-111-1-1i−i−ii−iii−i−ii−ii
χ21111111-1-1-1-1111-1-1111-1-1-1-11−ii−ii1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii11-1-1ii−i−iii−i−iii−i−iii−i−i-11-111-11-1−ii−ii
χ22111111-1-1-1-1111-1-1111-1-1-1-11−ii−ii1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii−i−iii1-11-1-11-11−ii−ii
χ23111111-1-1-1-1111-1-1111-1-1-1-11−ii−ii1-1-1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-1-11111-1-111-1-1-1-111-1-111i−i−ii−iii−ii−ii−i
χ24111111-1-1-1-1111-1-1111-1-1-1-11−ii−ii1-1-1−i−i−i−iiiii-1-1-1-1111111-1-1−i−iii-1-111-1-111-1-11111-1-111-1-1−iii−ii−i−iii−ii−i
χ25111111-1-1-1-1-1-1111111-1-1-1-11i−i−ii1-1-1iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-1-111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1i−i−ii
χ26111111-1-1-1-1-1-1111111-1-1-1-11i−i−ii1-1-1iiii−i−i−i−i1111-1-1-1-1-1-111−i−iii-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-11111i−i−ii
χ27111111-1-1-1-1-1-1111111-1-1-1-11i−i−ii1-1-1iiii−i−i−i−i-1-1-1-11111-1-111−i−iii11-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−i−iii−i
χ28111111-1-1-1-1-1-1111111-1-1-1-11i−i−ii1-1-1iiii−i−i−i−i-1-1-1-11111-1-111−i−iii11-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−iii−i
χ29111111-1-1-1-1-1-1111111-1-1-1-11−iii−i1-1-1−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-11111−iii−i
χ30111111-1-1-1-1-1-1111111-1-1-1-11−iii−i1-1-1−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1−iii−i
χ31111111-1-1-1-1-1-1111111-1-1-1-11−iii−i1-1-1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i11-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iiii−i−ii
χ32111111-1-1-1-1-1-1111111-1-1-1-11−iii−i1-1-1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−i11-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−ii−i−ii
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χ342222-2-222-2-2002002222222-20000-2-2-2000000002-22-222-2-20000000000000000−2i2i−2i2i0000−2i2i−2i2i000000000000
χ352222-2-222-2-2002002222222-20000-2-2-200000000-22-22-2-22200000000000000002-22-20000-22-22000000000000
χ362222-2-222-2-2002002222222-20000-2-2-200000000-22-22-2-2220000000000000000-22-2200002-22-2000000000000
χ372222-2-2-2-22200200222-2-2-2-2-20000-222000000002-22-2-2-22200000000000000002-2-2200002-2-22000000000000
χ382222-2-2-2-22200200222-2-2-2-2-20000-222000000002-22-2-2-2220000000000000000-222-20000-222-2000000000000
χ392222-2-2-2-22200200222-2-2-2-2-20000-22200000000-22-2222-2-200000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ402222-2-2-2-22200200222-2-2-2-2-20000-22200000000-22-2222-2-20000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
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χ4322-2-22-22i−2i2i−2i002002-2-22i2i−2i−2i20000-22i−2i00000000-2-222−2i2i−2i2i000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740000000000000000
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χ4722-2-22-2−2i2i−2i2i002002-2-2−2i−2i2i2i20000-2−2i2i00000000-2-2222i−2i2i−2i000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000000000000000
χ4822-2-22-2−2i2i−2i2i002002-2-2−2i−2i2i2i20000-2−2i2i00000000-2-2222i−2i2i−2i0000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ780000000000000000
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χ5022-2-2-222i−2i−2i2i2-222i−2i2-2-22i2i−2i−2i-200002−2i2i00000000-222-2−2i2i2i−2i2-22i−2i00002-2−2i2i0000000000000000000000000000
χ5122-2-2-222i−2i−2i2i-222−2i2i2-2-22i2i−2i−2i-200002−2i2i000000002-2-222i−2i−2i2i-22−2i2i00002-2−2i2i0000000000000000000000000000
χ5222-2-2-222i−2i−2i2i-222−2i2i2-2-22i2i−2i−2i-200002−2i2i00000000-222-2−2i2i2i−2i-22−2i2i0000-222i−2i0000000000000000000000000000
χ5322-2-2-22−2i2i2i−2i2-22−2i2i2-2-2−2i−2i2i2i-2000022i−2i000000002-2-22−2i2i2i−2i2-2−2i2i0000-22−2i2i0000000000000000000000000000
χ5422-2-2-22−2i2i2i−2i2-22−2i2i2-2-2−2i−2i2i2i-2000022i−2i00000000-222-22i−2i−2i2i2-2−2i2i00002-22i−2i0000000000000000000000000000
χ5522-2-2-22−2i2i2i−2i-2222i−2i2-2-2−2i−2i2i2i-2000022i−2i000000002-2-22−2i2i2i−2i-222i−2i00002-22i−2i0000000000000000000000000000
χ5622-2-2-22−2i2i2i−2i-2222i−2i2-2-2−2i−2i2i2i-2000022i−2i00000000-222-22i−2i−2i2i-222i−2i0000-22−2i2i0000000000000000000000000000
χ57444444444444-144-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-100000000000000000000000000000000
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χ798-88i−8i00000000-2002−2i2i2ζ26−2ζ42−2ζ58+2ζ74−2ζ26+2ζ42+2ζ58−2ζ74−2ζ14−2ζ46+2ζ62+2ζ782ζ14+2ζ46−2ζ62−2ζ7800000000−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+ζ79000000000000000000000000000000000000000000000000
χ808-88i−8i00000000-2002−2i2i−2ζ26+2ζ42+2ζ58−2ζ742ζ26−2ζ42−2ζ58+2ζ742ζ14+2ζ46−2ζ62−2ζ78−2ζ14−2ζ46+2ζ62+2ζ7800000000ζ9−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+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+ζ79000000000000000000000000000000000000000000000000
χ818-88i−8i00000000-2002−2i2i−2ζ26+2ζ42+2ζ58−2ζ742ζ26−2ζ42−2ζ58+2ζ742ζ14+2ζ46−2ζ62−2ζ78−2ζ14−2ζ46+2ζ62+2ζ7800000000−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−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−ζ79000000000000000000000000000000000000000000000000
χ828-8−8i8i00000000800-8−8i8i00000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i00000000-20022i−2i−2ζ14−2ζ46+2ζ62+2ζ782ζ14+2ζ46−2ζ62−2ζ782ζ26−2ζ42−2ζ58+2ζ74−2ζ26+2ζ42+2ζ58−2ζ7400000000−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−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−ζ77000000000000000000000000000000000000000000000000
χ848-8−8i8i00000000-20022i−2i−2ζ14−2ζ46+2ζ62+2ζ782ζ14+2ζ46−2ζ62−2ζ782ζ26−2ζ42−2ζ58+2ζ74−2ζ26+2ζ42+2ζ58−2ζ7400000000ζ11−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+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+ζ77000000000000000000000000000000000000000000000000
χ858-8−8i8i00000000-20022i−2i2ζ14+2ζ46−2ζ62−2ζ78−2ζ14−2ζ46+2ζ62+2ζ78−2ζ26+2ζ42+2ζ58−2ζ742ζ26−2ζ42−2ζ58+2ζ7400000000ζ11+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+ζ77000000000000000000000000000000000000000000000000
χ868-8−8i8i00000000-20022i−2i2ζ14+2ζ46−2ζ62−2ζ78−2ζ14−2ζ46+2ζ62+2ζ78−2ζ26+2ζ42+2ζ58−2ζ742ζ26−2ζ42−2ζ58+2ζ7400000000−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−ζ77000000000000000000000000000000000000000000000000

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