Finite Group Databasebeta

← Group #13180943

Character table — Group #13180943

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222224448888889999991616161616161616161818181818181818181818181818182727272727272727363636363636363636545454545454545454545454
order12344461212123336664488881212121212121212122228888881212242424241616161616161616666242424242424161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i
χ4111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii
χ51111111111111111-1-1ii−i−i111111111-1-1-1iii−i−i−i-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-1-1-1iii−i−i−iζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26
χ61111111111111111-1-1ii−i−i111111111-1-1-1iii−i−i−i-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-1-1-1iii−i−i−i−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26
χ71111111111111111-1-1−i−iii111111111-1-1-1−i−i−iiii-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-1-1-1−i−i−iiii−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46
χ81111111111111111-1-1−i−iii111111111-1-1-1−i−i−iiii-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-1-1-1−i−i−iiiiζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46
χ91111-1-111-1-1111111111111111-1-1-1-1-1-11-1-11-1-11-1-1111111111111111-1-11-1-11-1-11-1-11-1-11-1-11-1-1
χ101111-1-111-1-1111111111111111-1-1-1-1-1-11-1-11-1-11-1-1111111-1-1-1-1-1-1-1-11-1-11-1-11-1-1-111-111-111-111
χ111111-1-111-1-111111111-1-1-1-1111-1-1-1-1-1-11-1-1-111-11111-1-1-1-1iiii−i−i−i−i1-1-1-111-111i−i−ii−i−i−iii−iii
χ121111-1-111-1-111111111-1-1-1-1111-1-1-1-1-1-11-1-1-111-11111-1-1-1-1−i−i−i−iiiii1-1-1-111-111−iii−iiii−i−ii−i−i
χ131111-1-111-1-1111111-1-1ii−i−i111-1-1-1-1-1-1-111i−i−i−iii-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-111i−i−i−iiiζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ141111-1-111-1-1111111-1-1ii−i−i111-1-1-1-1-1-1-111i−i−i−iii-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-111i−i−i−iii−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ151111-1-111-1-1111111-1-1−i−iii111-1-1-1-1-1-1-111−iiii−i−i-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-111−iiii−i−i−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ161111-1-111-1-1111111-1-1−i−iii111-1-1-1-1-1-1-111−iiii−i−i-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-111−iiii−i−iζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ17111-11-11-11-1111111111111-1-1-1111-1-1-1-11-1-11-1-11-111111111111111-11-1-11-1-11-1-11-1-11-1-11-1-11-1
χ18111-11-11-11-1111111111111-1-1-1111-1-1-1-11-1-11-1-11-1111111-1-1-1-1-1-1-1-1-11-1-11-1-11-11-111-111-111-11
χ19111-11-11-11-111111111-1-1-1-1-1-1-1111-1-1-1-11-11-111-1111-1-1-1-1iiii−i−i−i−i-11-11-111-11−ii−i−ii−ii−iii−ii
χ20111-11-11-11-111111111-1-1-1-1-1-1-1111-1-1-1-11-11-111-1111-1-1-1-1−i−i−i−iiiii-11-11-111-11i−iii−ii−ii−i−ii−i
χ21111-11-11-11-1111111-1-1ii−i−i-1-1-1111-1-1-11-11−ii−ii−ii-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ261-11−ii−ii−ii−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26
χ22111-11-11-11-1111111-1-1ii−i−i-1-1-1111-1-1-11-11−ii−ii−ii-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ261-11−ii−ii−iiζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26
χ23111-11-11-11-1111111-1-1−i−iii-1-1-1111-1-1-11-11i−ii−ii−i-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ461-11i−ii−ii−iζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46
χ24111-11-11-11-1111111-1-1−i−iii-1-1-1111-1-1-11-11i−ii−ii−i-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ461-11i−ii−ii−i−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46
χ25111-1-111-1-11111111111111-1-1-1-1-1-1111-1-11-1-11-1-1111111111111111-1-11-1-11-1-11-1-11-1-11-1-11-1-11
χ26111-1-111-1-11111111111111-1-1-1-1-1-1111-1-11-1-11-1-11111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111-111-111-111-1
χ27111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1111-1-1111-111-111-1-1-1-1iiii−i−i−i−i-1-1111-111-1−i−ii−i−iiii−iii−i
χ28111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-1111-1-1111-111-111-1-1-1-1−i−i−i−iiiii-1-1111-111-1ii−iii−i−i−ii−i−ii
χ29111-1-111-1-11111111-1-1ii−i−i-1-1-1-1-1-111111-1−i−iiii−i-1-1ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1−i−iiii−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26
χ30111-1-111-1-11111111-1-1ii−i−i-1-1-1-1-1-111111-1−i−iiii−i-1-1ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1−i−iiii−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26
χ31111-1-111-1-11111111-1-1−i−iii-1-1-1-1-1-111111-1ii−i−i−ii-1-1−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1ii−i−i−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46
χ32111-1-111-1-11111111-1-1−i−iii-1-1-1-1-1-111111-1ii−i−i−ii-1-1−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1ii−i−i−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46
χ3322-1222-1-1-1-12-1-12-1-12222222-1-12-1-12-1-1222222222-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1000000000000
χ3422-1222-1-1-1-12-1-12-1-122-2-2-2-22-1-12-1-12-1-1222-2-2-2-2-2-2-1-1111100000000-1-1-1111111000000000000
χ3522-1222-1-1-1-12-1-12-1-1-2-22i2i−2i−2i2-1-12-1-12-1-1-2-2-22i2i2i−2i−2i−2i11−i−iii00000000111−i−i−iiii000000000000
χ3622-1222-1-1-1-12-1-12-1-1-2-2−2i−2i2i2i2-1-12-1-12-1-1-2-2-2−2i−2i−2i2i2i2i11ii−i−i00000000111iii−i−i−i000000000000
χ3722-12-2-2-1-1112-1-12-1-12222222-1-1-211-2112-2-22-2-22-2-2-1-1-1-1-1-100000000-111-111-111000000000000
χ3822-12-2-2-1-1112-1-12-1-122-2-2-2-22-1-1-211-2112-2-2-222-222-1-1111100000000-1111-1-11-1-1000000000000
χ3922-12-2-2-1-1112-1-12-1-1-2-22i2i−2i−2i2-1-1-211-211-2222i−2i−2i−2i2i2i11−i−iii000000001-1-1−iiii−i−i000000000000
χ4022-12-2-2-1-1112-1-12-1-1-2-2−2i−2i2i2i2-1-1-211-211-222−2i2i2i2i−2i−2i11ii−i−i000000001-1-1i−i−i−iii000000000000
χ4122-1-22-2-11-112-1-12-1-1222222-2112-1-1-211-22-2-22-2-22-2-1-1-1-1-1-1000000001-111-111-11000000000000
χ4222-1-22-2-11-112-1-12-1-122-2-2-2-2-2112-1-1-211-22-22-222-22-1-11111000000001-11-11-1-11-1000000000000
χ4322-1-22-2-11-112-1-12-1-1-2-22i2i−2i−2i-2112-1-1-2112-22−2i2i−2i2i−2i2i11−i−iii00000000-11-1i−ii−ii−i000000000000
χ4422-1-22-2-11-112-1-12-1-1-2-2−2i−2i2i2i-2112-1-1-2112-222i−2i2i−2i2i−2i11ii−i−i00000000-11-1−ii−ii−ii000000000000
χ4522-1-2-22-111-12-1-12-1-1222222-211-2112-1-1-2-22-2-22-2-22-1-1-1-1-1-10000000011-111-111-1000000000000
χ4622-1-2-22-111-12-1-12-1-122-2-2-2-2-211-2112-1-1-2-2222-222-2-1-111110000000011-1-1-11-1-11000000000000
χ4722-1-2-22-111-12-1-12-1-1-2-22i2i−2i−2i-211-2112-1-122-2−2i−2i2i2i2i−2i11−i−iii00000000-1-11ii−i−i−ii000000000000
χ4822-1-2-22-111-12-1-12-1-1-2-2−2i−2i2i2i-211-2112-1-122-22i2i−2i−2i−2i2i11ii−i−i00000000-1-11−i−iiii−i000000000000
χ492-22000-2000222-2-2-22i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000000000002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ262ζ11+2ζ43−2ζ11−2ζ43−2ζ31−2ζ472ζ31+2ζ47−2ζ13−2ζ292ζ13+2ζ29−2ζ25−2ζ412ζ25+2ζ41000000000000000000000
χ502-22000-2000222-2-2-22i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000000000002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26−2ζ11−2ζ432ζ11+2ζ432ζ31+2ζ47−2ζ31−2ζ472ζ13+2ζ29−2ζ13−2ζ292ζ25+2ζ41−2ζ25−2ζ41000000000000000000000
χ512-22000-2000222-2-2-22i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000000000002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26−2ζ31−2ζ472ζ31+2ζ47−2ζ11−2ζ432ζ11+2ζ432ζ25+2ζ41−2ζ25−2ζ41−2ζ13−2ζ292ζ13+2ζ29000000000000000000000
χ522-22000-2000222-2-2-22i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000000000002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ262ζ31+2ζ47−2ζ31−2ζ472ζ11+2ζ43−2ζ11−2ζ43−2ζ25−2ζ412ζ25+2ζ412ζ13+2ζ29−2ζ13−2ζ29000000000000000000000
χ532-22000-2000222-2-2-2−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000000000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46−2ζ13−2ζ292ζ13+2ζ292ζ25+2ζ41−2ζ25−2ζ412ζ11+2ζ43−2ζ11−2ζ432ζ31+2ζ47−2ζ31−2ζ47000000000000000000000
χ542-22000-2000222-2-2-2−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000000000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ462ζ13+2ζ29−2ζ13−2ζ29−2ζ25−2ζ412ζ25+2ζ41−2ζ11−2ζ432ζ11+2ζ43−2ζ31−2ζ472ζ31+2ζ47000000000000000000000
χ552-22000-2000222-2-2-2−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000000000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46−2ζ25−2ζ412ζ25+2ζ41−2ζ13−2ζ292ζ13+2ζ292ζ31+2ζ47−2ζ31−2ζ47−2ζ11−2ζ432ζ11+2ζ43000000000000000000000
χ562-22000-2000222-2-2-2−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000000000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ462ζ25+2ζ41−2ζ25−2ζ412ζ13+2ζ29−2ζ13−2ζ29−2ζ31−2ζ472ζ31+2ζ472ζ11+2ζ43−2ζ11−2ζ43000000000000000000000
χ574-4-200020004-2-2-4224i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ26000000000000000000−2i2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000000000000000000000000
χ584-4-200020004-2-2-4224i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ26000000000000000000−2i2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000000000000000000000000
χ594-4-200020004-2-2-422−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ460000000000000000002i−2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000000000000000000000000
χ604-4-200020004-2-2-422−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ460000000000000000002i−2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000000000000000000000000
χ618888888888-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000
χ628888-8-888-8-8-1-1-1-1-1-1000000-1-1-111111100000000000000000000000000000000000000000000
χ63888-88-88-88-8-1-1-1-1-1-1000000111-1-1-111100000000000000000000000000000000000000000000
χ64888-8-888-8-88-1-1-1-1-1-1000000111111-1-1-100000000000000000000000000000000000000000000
χ6588-4888-4-4-4-4-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i32-11−3i321+3i32-11−3i321+3i3200000000000000000000000000000000000000000000
χ6688-4888-4-4-4-4-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i32-11+3i321−3i32-11+3i321−3i3200000000000000000000000000000000000000000000
χ6788-48-8-8-4-444-11−3i321+3i32-11−3i321+3i32000000-11−3i321+3i321−1+3i32−1−3i321−1+3i32−1−3i3200000000000000000000000000000000000000000000
χ6888-48-8-8-4-444-11+3i321−3i32-11+3i321−3i32000000-11+3i321−3i321−1−3i32−1+3i321−1−3i32−1+3i3200000000000000000000000000000000000000000000
χ6988-4-88-8-44-44-11−3i321+3i32-11−3i321+3i320000001−1+3i32−1−3i32-11−3i321+3i321−1+3i32−1−3i3200000000000000000000000000000000000000000000
χ7088-4-88-8-44-44-11+3i321−3i32-11+3i321−3i320000001−1−3i32−1+3i32-11+3i321−3i321−1−3i32−1+3i3200000000000000000000000000000000000000000000
χ7188-4-8-88-444-4-11−3i321+3i32-11−3i321+3i320000001−1+3i32−1−3i321−1+3i32−1−3i32-11−3i321+3i3200000000000000000000000000000000000000000000
χ7288-4-8-88-444-4-11+3i321−3i32-11+3i321−3i320000001−1−3i32−1+3i321−1−3i32−1+3i32-11+3i321−3i3200000000000000000000000000000000000000000000
χ7316-1616000-16000-2-2-222200000000000000000000000000000000000000000000000000000000000
χ7416-16-80008000-21−3i31+3i32−1+3i3−1−3i300000000000000000000000000000000000000000000000000000000000
χ7516-16-80008000-21+3i31−3i32−1−3i3−1+3i300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.