Finite Group Databasebeta

← Group #11720249

Character table — Group #11720249

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49
size112222222222266661212121212121212121212121212181818181818181818181818727272727272
order123468812122424242433663612121212242424242424242416161616484848484848484824661212
χ11111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ522222222222222-1-12-1-1-12-1-122-1-1-1-1-1-100000000000020-1-100
χ622222222222222-1-12-1-1-12-1-122-1-1-1-1-1-1000000000000-201100
χ72222222222222-122-1-1-12-1-1-1-1-122-1-1-1-10000000000000200-1-1
χ82222222222222-122-1-1-12-1-1-1-1-122-1-1-1-10000000000000-20011
χ922222-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000
χ1022222-2-222-2-2-2-22-1-12-1-1-12-1-1-2-211111100000000000000−i3i300
χ1122222-2-222-2-2-2-22-1-12-1-1-12-1-1-2-211111100000000000000i3−i300
χ1222222-2-222-2-2-2-2-122-1-1-12-1-1-111-2-211110000000000000000−i3i3
χ1322222-2-222-2-2-2-2-122-1-1-12-1-1-111-2-211110000000000000000i3−i3
χ14222-2200-2-20000222222-2-2-2-20000000022−2−22222−2−2−2−2000000
χ15222-2200-2-20000222222-2-2-2-200000000−2−222−2−2−2−22222000000
χ162-220-22−20022−2−222-2-22-200002−22−222−2−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43000000
χ172-220-22−20022−2−222-2-22-200002−22−222−2−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43000000
χ182-220-2−2200−2−22222-2-22-20000−22−22−2−222ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47000000
χ192-220-2−2200−2−22222-2-22-20000−22−22−2−222−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47000000
χ204444444444444-2-2-2-211-2-211-2-2-2-21111000000000000000000
χ2144444-4-444-4-4-4-4-2-2-2-211-2-2112222-1-1-1-1000000000000000000
χ22444-4400-4-400004-2-24-2-22-42200000000000000000000000000
χ23444-4400-4-40000-244-2-2-2-422200000000000000000000000000
χ24444-4400-4-40000-2-2-2-21122-1-100003i−3i3i−3i000000000000000000
χ25444-4400-4-40000-2-2-2-21122-1-10000−3i3i−3i3i000000000000000000
χ264-440-422−22002222−22−224-22-4-22000022−22−22−2−222000000000000000000
χ274-440-422−22002222−22−22-24-42-220000−2222−22−2−222000000000000000000
χ284-440-422−22002222−22−22-2-2221-1003i−3i−22−22−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ462ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46000000000000000000
χ294-440-422−22002222−22−22-2-2221-100−3i3i−22−22ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46000000000000000000
χ304-440-4−222200−22−2222224-22-4-220000−22222−222−2−2000000000000000000
χ314-440-4−222200−22−222222-24-42-2200002−2−222222−2−2000000000000000000
χ324-440-4−222200−22−222222-2-2221-1003i−3i2−22−22ζ10+ζ14+2ζ26+ζ46−ζ10−2ζ14−ζ26−2ζ46−2ζ10−ζ14−2ζ26−ζ46ζ10+2ζ14+ζ26+2ζ46000000000000000000
χ334-440-4−222200−22−222222-2-2221-100−3i3i2−22−2−ζ10−2ζ14−ζ26−2ζ462ζ10+ζ14+2ζ26+ζ46ζ10+2ζ14+ζ26+2ζ46−2ζ10−ζ14−2ζ26−ζ46000000000000000000
χ3466-36-366-3-3-3-3-3-30000000000000000002222-1-1-1-1-1-1-1-1000000
χ3566-36-366-3-3-3-3-3-3000000000000000000-2-2-2-211111111000000
χ3666-36-3-6-6-3-3333300000000000000000000003−33−33−33−3000000
χ3766-36-3-6-6-3-333330000000000000000000000−33−33−33−33000000
χ3866-3-6-3003333−3333−3300000000000000000022−2−2ζ10−ζ14ζ26−ζ46ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46000000
χ3966-3-6-3003333−3333−33000000000000000000−2−222−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46ζ10−ζ14ζ26−ζ46000000
χ4066-3-6-30033−3333−333300000000000000000022−2−2ζ26−ζ46ζ10−ζ14ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14000000
χ4166-3-6-30033−3333−3333000000000000000000−2−222−ζ26+ζ46−ζ10+ζ14−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14ζ26−ζ46ζ10−ζ14000000
χ426-6-30332−3233−333ζ10−3ζ143ζ26−3ζ46−3ζ10+3ζ14−3ζ26+3ζ46000000000000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ47ζ31+ζ41−ζ25−ζ47−ζ31−ζ41−ζ11−ζ13−ζ29−ζ43ζ11+ζ13ζ29+ζ43000000
χ436-6-30332−3233−333ζ10−3ζ143ζ26−3ζ46−3ζ10+3ζ14−3ζ26+3ζ46000000000000000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ47−ζ31−ζ41ζ25+ζ47ζ31+ζ41ζ11+ζ13ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000
χ446-6-30332−32−33333ζ26−3ζ463ζ10−3ζ14−3ζ26+3ζ46−3ζ10+3ζ14000000000000000000−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ31+ζ41ζ25+ζ47−ζ31−ζ41−ζ25−ζ47−ζ29−ζ43−ζ11−ζ13ζ29+ζ43ζ11+ζ13000000
χ456-6-30332−32−33333ζ26−3ζ463ζ10−3ζ14−3ζ26+3ζ46−3ζ10+3ζ14000000000000000000ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ31−ζ41−ζ25−ζ47ζ31+ζ41ζ25+ζ47ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13000000
χ466-6-303−323233−33−3ζ10+3ζ14−3ζ26+3ζ463ζ10−3ζ143ζ26−3ζ46000000000000000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13ζ29+ζ43−ζ25−ζ47−ζ31−ζ41ζ25+ζ47ζ31+ζ41000000
χ476-6-303−323233−33−3ζ10+3ζ14−3ζ26+3ζ463ζ10−3ζ143ζ26−3ζ46000000000000000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ47ζ31+ζ41−ζ25−ζ47−ζ31−ζ41000000
χ486-6-303−3232−3333−3ζ26+3ζ46−3ζ10+3ζ143ζ26−3ζ463ζ10−3ζ14000000000000000000ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ29−ζ43−ζ11−ζ13ζ29+ζ43ζ11+ζ13−ζ31−ζ41−ζ25−ζ47ζ31+ζ41ζ25+ζ47000000
χ496-6-303−3232−3333−3ζ26+3ζ46−3ζ10+3ζ143ζ26−3ζ463ζ10−3ζ14000000000000000000−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13ζ31+ζ41ζ25+ζ47−ζ31−ζ41−ζ25−ζ47000000

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