Finite Group Databasebeta

← Group #73040

Character table — Group #73040

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34
size11222222266888888888888888812121248484848
order124881616161624361212242424244848484848484848816162288
χ11111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1
χ311111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-11-1
χ411111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-11-11
χ522222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12220000
χ622222-2-2-2-222-1-1-1-1-1-1-1-1111111112-2-20000
χ7222-2-20000222222-2-2-2-200000000-2000000
χ8222-2-2000022-1-1-1-111113333−3−3−3−3-2000000
χ9222-2-2000022-1-1-1-11111−3−3−3−33333-2000000
χ1022-20022−2−2-2222-2-2000022−2−222−2−202−20000
χ1122-20022−2−2-22-1-11133−3−3ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ14ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ4602−20000
χ1222-20022−2−2-22-1-111−3−333ζ26−ζ46ζ26−ζ46−ζ26+ζ46−ζ26+ζ46ζ10−ζ14ζ10−ζ14−ζ10+ζ14−ζ10+ζ1402−20000
χ1322-200−2−222-2222-2-20000−2−222−2−2220−220000
χ1422-200−2−222-22-1-11133−3−3−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ14−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ460−220000
χ1522-200−2−222-22-1-111−3−333−ζ26+ζ46−ζ26+ζ46ζ26−ζ46ζ26−ζ46−ζ10+ζ14−ζ10+ζ14ζ10−ζ14ζ10−ζ140−220000
χ16333333333-1-10000000000000000-1-1-111-1-1
χ17333333333-1-10000000000000000-1-1-1-1-111
χ1833333-3-3-3-3-1-10000000000000000-1111-1-11
χ1933333-3-3-3-3-1-10000000000000000-111-111-1
χ204-4022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43001-13−3ζ10−ζ14−ζ10+ζ14−ζ26+ζ46ζ26−ζ46−ζ25+ζ47ζ25−ζ47ζ11−ζ13−ζ11+ζ13−ζ31+ζ41ζ31−ζ41−ζ29+ζ43ζ29−ζ430000000
χ214-4022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43001-1−33ζ26−ζ46−ζ26+ζ46−ζ10+ζ14ζ10−ζ14ζ31−ζ41−ζ31+ζ41−ζ29+ζ43ζ29−ζ43ζ25−ζ47−ζ25+ζ47ζ11−ζ13−ζ11+ζ130000000
χ224-4022−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300-22002−2−22ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ430000000
χ234-4022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43001-13−3ζ10−ζ14−ζ10+ζ14−ζ26+ζ46ζ26−ζ46ζ25−ζ47−ζ25+ζ47−ζ11+ζ13ζ11−ζ13ζ31−ζ41−ζ31+ζ41ζ29−ζ43−ζ29+ζ430000000
χ244-4022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43001-1−33ζ26−ζ46−ζ26+ζ46−ζ10+ζ14ζ10−ζ14−ζ31+ζ41ζ31−ζ41ζ29−ζ43−ζ29+ζ43−ζ25+ζ47ζ25−ζ47−ζ11+ζ13ζ11−ζ130000000
χ254-4022−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300-22002−2−22−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ430000000
χ264-40−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47001-13−3−ζ10+ζ14ζ10−ζ14ζ26−ζ46−ζ26+ζ46ζ11−ζ13−ζ11+ζ13ζ25−ζ47−ζ25+ζ47ζ29−ζ43−ζ29+ζ43−ζ31+ζ41ζ31−ζ410000000
χ274-40−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47001-1−33−ζ26+ζ46ζ26−ζ46ζ10−ζ14−ζ10+ζ14−ζ29+ζ43ζ29−ζ43−ζ31+ζ41ζ31−ζ41−ζ11+ζ13ζ11−ζ13ζ25−ζ47−ζ25+ζ470000000
χ284-40−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700-2200−222−2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ470000000
χ294-40−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47001-13−3−ζ10+ζ14ζ10−ζ14ζ26−ζ46−ζ26+ζ46−ζ11+ζ13ζ11−ζ13−ζ25+ζ47ζ25−ζ47−ζ29+ζ43ζ29−ζ43ζ31−ζ41−ζ31+ζ410000000
χ304-40−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47001-1−33−ζ26+ζ46ζ26−ζ46ζ10−ζ14−ζ10+ζ14ζ29−ζ43−ζ29+ζ43ζ31−ζ41−ζ31+ζ41ζ11−ζ13−ζ11+ζ13−ζ25+ζ47ζ25−ζ470000000
χ314-40−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700-2200−222−2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ470000000
χ32666-6-60000-2-200000000000000002000000
χ3366-6003232−32−322-200000000000000000−220000
χ3466-600−32−3232322-2000000000000000002−20000

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