Finite Group Databasebeta

← Group #13025777

Character table — Group #13025777

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222224444444444444444444444444444888888888888888888888888101010101010101020202020202020202020202040404040404040404040404040404040
order12442488882458810161616161616161620204040404080808080808080801010102020204040404040408080808080808080808080802244888824881616161616161616444488881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii
χ51111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiiiii−i−i−i−i
χ91111111111-1-11-1-111111-1-1-1-1111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ101111111111-1-11-1-111111-1-1-1-1111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11-11-11-1-111-1-111
χ111111111111-1-11-1-111111-1-1-1-1111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111i−i−iii−i−iiii−i−i−i−iii
χ121111111111-1-11-1-111111-1-1-1-1111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i
χ131111111111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-11-11-11-1-1-111-1-111
χ141111111111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-11-11-11-1111-1-111-1-1
χ151111111111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1i−i−iii−i−ii−i−iiiii−i−i
χ161111111111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−iii−i−iii−iii−i−i−i−iii
χ17111111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i1-11-1-11-11i−ii−ii−ii−i
χ18111111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i-11-111-11-1−ii−ii−ii−ii
χ19111111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iiii−i−ii−iii−i-11-111-11-1
χ20111111-1-1-1-1111-1-11ii−i−iii−i−i11-1-1-1-1iiii−i−i−i−i111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii−iii−ii−i−ii1-11-1-11-11
χ21111111-1-1-1-1111-1-11−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii1-11-1-11-11−ii−ii−ii−ii
χ22111111-1-1-1-1111-1-11−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii-11-111-11-1i−ii−ii−ii−i
χ23111111-1-1-1-1111-1-11−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−ii−i−ii−iii−i1-11-1-11-11
χ24111111-1-1-1-1111-1-11−i−iii−i−iii11-1-1-1-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−i−iii−ii−i−ii-11-111-11-1
χ25111111-1-1-1-1-1-11111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii1111-1-1-1-1i−i−iii−i−ii
χ26111111-1-1-1-1-1-11111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-11111ii−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111−iii−i−iii−i
χ27111111-1-1-1-1-1-11111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ28111111-1-1-1-1-1-11111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-11111ii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
χ29111111-1-1-1-1-1-11111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i1111-1-1-1-1−iii−i−iii−i
χ30111111-1-1-1-1-1-11111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-11111−i−iiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111i−i−iii−i−ii
χ31111111-1-1-1-1-1-11111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ32111111-1-1-1-1-1-11111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-11111−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ332222-2-222-2-20020022i−2i2i−2i000022-2-2-2-22i2i2i2i−2i−2i−2i−2i-200-200220000−2i−2i2i2i000000002-22-222-2-200002i−2i2i−2i00000000000000000000
χ342222-2-222-2-20020022i−2i2i−2i000022-2-2-2-22i2i2i2i−2i−2i−2i−2i-200-200220000−2i−2i2i2i00000000-22-22-2-2220000−2i2i−2i2i00000000000000000000
χ352222-2-222-2-2002002−2i2i−2i2i000022-2-2-2-2−2i−2i−2i−2i2i2i2i2i-200-2002200002i2i−2i−2i000000002-22-222-2-20000−2i2i−2i2i00000000000000000000
χ362222-2-222-2-2002002−2i2i−2i2i000022-2-2-2-2−2i−2i−2i−2i2i2i2i2i-200-2002200002i2i−2i−2i00000000-22-22-2-22200002i−2i2i−2i00000000000000000000
χ372222-2-2-2-2220020022-2-22000022222222222222-200-200-2-20000-2-2-2-2000000002-22-2-2-22200002-2-2200000000000000000000
χ382222-2-2-2-2220020022-2-22000022222222222222-200-200-2-20000-2-2-2-200000000-22-2222-2-20000-222-200000000000000000000
χ392222-2-2-2-222002002-222-20000222222-2-2-2-2-2-2-2-2-200-200-2-200002222000000002-22-2-2-2220000-222-200000000000000000000
χ402222-2-2-2-222002002-222-20000222222-2-2-2-2-2-2-2-2-200-200-2-20000222200000000-22-2222-2-200002-2-2200000000000000000000
χ4122-2-22-22i−2i2i−2i0020020000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78-2-22i2i−2i−2i00000000200-2002i−2i00000000−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ7822-2-22i−2i2i−2i00000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000000000000000
χ4222-2-22-22i−2i2i−2i0020020000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78-2-22i2i−2i−2i00000000200-2002i−2i00000000−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78-2-222−2i2i−2i2i000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ780000000000000000
χ4322-2-22-22i−2i2i−2i00200200002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78-2-22i2i−2i−2i00000000200-2002i−2i000000002ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ7822-2-22i−2i2i−2i000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ780000000000000000
χ4422-2-22-22i−2i2i−2i00200200002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78-2-22i2i−2i−2i00000000200-2002i−2i000000002ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ78-2-222−2i2i−2i2i00000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000000000000000
χ4522-2-22-2−2i2i−2i2i0020020000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74-2-2−2i−2i2i2i00000000200-200−2i2i00000000−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ7422-2-2−2i2i−2i2i00000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740000000000000000
χ4622-2-22-2−2i2i−2i2i0020020000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74-2-2−2i−2i2i2i00000000200-200−2i2i00000000−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74-2-2222i−2i2i−2i000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ740000000000000000
χ4722-2-22-2−2i2i−2i2i00200200002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74-2-2−2i−2i2i2i00000000200-200−2i2i000000002ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ7422-2-2−2i2i−2i2i000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ740000000000000000
χ4822-2-22-2−2i2i−2i2i00200200002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74-2-2−2i−2i2i2i00000000200-200−2i2i000000002ζ14+2ζ46+2ζ62+2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74−2ζ26−2ζ42−2ζ58−2ζ74-2-2222i−2i2i−2i00000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740000000000000000
χ4922-2-2-222i−2i−2i2i2-222i−2i200000000-2-2−2i−2i2i2i00000000-2222-2-22i−2i2i2i−2i−2i0000000000002-2-222i−2i−2i2i2-22i−2i000000000000000000000000
χ5022-2-2-222i−2i−2i2i2-222i−2i200000000-2-2−2i−2i2i2i00000000-2222-2-22i−2i2i2i−2i−2i000000000000-222-2−2i2i2i−2i-22−2i2i000000000000000000000000
χ5122-2-2-222i−2i−2i2i-222−2i2i200000000-2-2−2i−2i2i2i00000000-2-2-22222i−2i−2i−2i2i2i0000000000002-2-222i−2i−2i2i-22−2i2i000000000000000000000000
χ5222-2-2-222i−2i−2i2i-222−2i2i200000000-2-2−2i−2i2i2i00000000-2-2-22222i−2i−2i−2i2i2i000000000000-222-2−2i2i2i−2i2-22i−2i000000000000000000000000
χ5322-2-2-22−2i2i2i−2i2-22−2i2i200000000-2-22i2i−2i−2i00000000-2222-2-2−2i2i−2i−2i2i2i0000000000002-2-22−2i2i2i−2i2-2−2i2i000000000000000000000000
χ5422-2-2-22−2i2i2i−2i2-22−2i2i200000000-2-22i2i−2i−2i00000000-2222-2-2−2i2i−2i−2i2i2i000000000000-222-22i−2i−2i2i-222i−2i000000000000000000000000
χ5522-2-2-22−2i2i2i−2i-2222i−2i200000000-2-22i2i−2i−2i00000000-2-2-2222−2i2i2i2i−2i−2i0000000000002-2-22−2i2i2i−2i-222i−2i000000000000000000000000
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χ57444444444444-144-144444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ58444444444444-144-1-4-4-4-4-4-4-4-4-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000000000000000
χ594444444444-4-4-1-4-4-14444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-111111111000000000000000000000000000000000000
χ604444444444-4-4-1-4-4-1-4-4-4-44444-1-1-1-1-1-111111111-111-111-1-111111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ61444444-4-4-4-444-1-4-4-14i4i−4i−4i4i4i−4i−4i-1-11111−i−i−i−iiiii-1-1-1-1-1-1111111−i−iii−i−i−i−iiiii000000000000000000000000000000000000
χ62444444-4-4-4-444-1-4-4-1−4i−4i4i4i−4i−4i4i4i-1-11111iiii−i−i−i−i-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i000000000000000000000000000000000000
χ63444444-4-4-4-4-4-4-144-14i4i−4i−4i−4i−4i4i4i-1-11111−i−i−i−iiiii-111-11111-1-1-1-1−i−iiiiiii−i−i−i−i000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.