Finite Group Databasebeta

← Group #72341930

Character table — Group #72341930

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size112222222661212121212121212121212121212121212121216161616323232323232323232323232323232329696128128128128
order12488161616162422448888816161616161616161616336624121224242424484848484848484844661212
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ5111111111111111111111111111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ6111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ711111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1111111-1-1-1-1-1-1-1-11-111-1-1
χ811111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-11111111-1-1-1-1-1-1-1-1-11-1-111
χ911111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1−1−i32−1+i321+i321−i32
χ1011111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-111+i321−i32−1−i32−1+i32
χ1111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1−1+i32−1−i321−i321+i32
χ1211111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-111−i321+i32−1+i32−1−i32
χ13222-2-20000222222-2-2-2-2-2000000000022220022-2-2-2-200000000000000
χ14222-2-20000222222-2-2-2-2-20000000000−1−i3−1+i3−1−i3−1+i300−1−i3−1+i31+i31+i31−i31−i300000000000000
χ15222-2-20000222222-2-2-2-2-20000000000−1+i3−1−i3−1+i3−1−i300−1+i3−1−i31−i31−i31+i31+i300000000000000
χ1622-20022−2−22-22-22-20000022222−2−2−2−2−2222200-2-2000022−2−222−2−2000000
χ1722-20022−2−22-22-22-20000022222−2−2−2−2−2−1−i3−1+i3−1−i3−1+i3001+i31−i30000−ζ14+ζ26−ζ14+ζ26ζ14−ζ26ζ14−ζ26ζ10−ζ46ζ10−ζ46−ζ10+ζ46−ζ10+ζ46000000
χ1822-20022−2−22-22-22-20000022222−2−2−2−2−2−1+i3−1−i3−1+i3−1−i3001−i31+i30000ζ10−ζ46ζ10−ζ46−ζ10+ζ46−ζ10+ζ46−ζ14+ζ26−ζ14+ζ26ζ14−ζ26ζ14−ζ26000000
χ1922-200−2−2222-22-22-200000−2−2−2−2−222222222200-2-20000−2−222−2−222000000
χ2022-200−2−2222-22-22-200000−2−2−2−2−222222−1−i3−1+i3−1−i3−1+i3001+i31−i30000ζ14−ζ26ζ14−ζ26−ζ14+ζ26−ζ14+ζ26−ζ10+ζ46−ζ10+ζ46ζ10−ζ46ζ10−ζ46000000
χ2122-200−2−2222-22-22-200000−2−2−2−2−222222−1+i3−1−i3−1+i3−1−i3001−i31+i30000−ζ10+ζ46−ζ10+ζ46ζ10−ζ46ζ10−ζ46ζ14−ζ26ζ14−ζ26−ζ14+ζ26−ζ14+ζ26000000
χ2233333333333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-100003300000000000000-1-10000
χ2333333333333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-10000-3-300000000000000110000
χ2433333-3-3-3-333-1-1-1-13-1-1-1-1-31111-3111100003-300000000000000-110000
χ2533333-3-3-3-333-1-1-1-13-1-1-1-1-31111-311110000-33000000000000001-10000
χ26666666666-2-22-2-22-222-2-2-222-2-2-222-2-200000000000000000000000000
χ27666666666-2-2-222-2-2-2-222-2-2-222-2-2-22200000000000000000000000000
χ2866666-6-6-6-6-2-22-2-22-222-2-22-2-2222-2-22200000000000000000000000000
χ2966666-6-6-6-6-2-2-222-2-2-2-222222-2-2222-2-200000000000000000000000000
χ30666-6-6000066-2-2-2-2-62222000000000000000000000000000000000000
χ31666-6-60000-2-22-2-222-2-22204i−4i0004i−4i0000000000000000000000000000
χ32666-6-60000-2-22-2-222-2-2220−4i4i000−4i4i0000000000000000000000000000
χ33666-6-60000-2-2-222-2222-2-20004i−4i0004i−4i00000000000000000000000000
χ34666-6-60000-2-2-222-2222-2-2000−4i4i000−4i4i00000000000000000000000000
χ3566-6003232−32−326-6-22-220000032−2−2−2−2−32222200000000000000000000000000
χ3666-6003232−32−32-2222-2-204i−4i00−2−3ζ10−ζ14−3ζ26−ζ46ζ10+3ζ14+ζ26+3ζ46−2−223ζ10+ζ14+3ζ26+ζ46−ζ10−3ζ14−ζ26−3ζ462200000000000000000000000000
χ3766-6003232−32−32-2222-2-20−4i4i00−2ζ10+3ζ14+ζ26+3ζ46−3ζ10−ζ14−3ζ26−ζ46−2−22−ζ10−3ζ14−ζ26−3ζ463ζ10+ζ14+3ζ26+ζ462200000000000000000000000000
χ3866-6003232−32−32-22-2-2220004i−4i−2−2−2−3ζ10−ζ14−3ζ26−ζ46ζ10+3ζ14+ζ26+3ζ462223ζ10+ζ14+3ζ26+ζ46−ζ10−3ζ14−ζ26−3ζ4600000000000000000000000000
χ3966-6003232−32−32-22-2-222000−4i4i−2−2−2ζ10+3ζ14+ζ26+3ζ46−3ζ10−ζ14−3ζ26−ζ46222−ζ10−3ζ14−ζ26−3ζ463ζ10+ζ14+3ζ26+ζ4600000000000000000000000000
χ4066-600−32−3232326-6-22-2200000−32222232−2−2−2−200000000000000000000000000
χ4166-600−32−323232-2222-2-204i−4i0023ζ10+ζ14+3ζ26+ζ46−ζ10−3ζ14−ζ26−3ζ4622−2−3ζ10−ζ14−3ζ26−ζ46ζ10+3ζ14+ζ26+3ζ46−2−200000000000000000000000000
χ4266-600−32−323232-2222-2-20−4i4i002−ζ10−3ζ14−ζ26−3ζ463ζ10+ζ14+3ζ26+ζ4622−2ζ10+3ζ14+ζ26+3ζ46−3ζ10−ζ14−3ζ26−ζ46−2−200000000000000000000000000
χ4366-600−32−323232-22-2-2220004i−4i2223ζ10+ζ14+3ζ26+ζ46−ζ10−3ζ14−ζ26−3ζ46−2−2−2−3ζ10−ζ14−3ζ26−ζ46ζ10+3ζ14+ζ26+3ζ4600000000000000000000000000
χ4466-600−32−323232-22-2-222000−4i4i222−ζ10−3ζ14−ζ26−3ζ463ζ10+ζ14+3ζ26+ζ46−2−2−2ζ10+3ζ14+ζ26+3ζ46−3ζ10−ζ14−3ζ26−ζ4600000000000000000000000000
χ458-8042−42−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ474ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ4300000000000000000000022-2-200002−22−2−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43000000
χ468-8042−42−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ474ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ43000000000000000000000−1−i3−1+i31+i31−i30000−ζ14+ζ26ζ14−ζ26ζ10−ζ46−ζ10+ζ46ζ41+ζ47−ζ41−ζ47−ζ11−ζ29ζ11+ζ29ζ25+ζ31−ζ25−ζ31−ζ13−ζ43ζ13+ζ43000000
χ478-8042−42−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ474ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ43000000000000000000000−1+i3−1−i31−i31+i30000ζ10−ζ46−ζ10+ζ46−ζ14+ζ26ζ14−ζ26ζ25+ζ31−ζ25−ζ31−ζ13−ζ43ζ13+ζ43ζ41+ζ47−ζ41−ζ47−ζ11−ζ29ζ11+ζ29000000
χ488-8042−424ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ47−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ4300000000000000000000022-2-200002−22−2ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43000000
χ498-8042−424ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ47−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ43000000000000000000000−1−i3−1+i31+i31−i30000−ζ14+ζ26ζ14−ζ26ζ10−ζ46−ζ10+ζ46−ζ41−ζ47ζ41+ζ47ζ11+ζ29−ζ11−ζ29−ζ25−ζ31ζ25+ζ31ζ13+ζ43−ζ13−ζ43000000
χ508-8042−424ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ47−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ43000000000000000000000−1+i3−1−i31−i31+i30000ζ10−ζ46−ζ10+ζ46−ζ14+ζ26ζ14−ζ26−ζ25−ζ31ζ25+ζ31ζ13+ζ43−ζ13−ζ43−ζ41−ζ47ζ41+ζ47ζ11+ζ29−ζ11−ζ29000000
χ518-80−42424ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ434ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ4700000000000000000000022-2-20000−22−22ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47000000
χ528-80−42424ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ434ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ47000000000000000000000−1−i3−1+i31+i31−i30000ζ14−ζ26−ζ14+ζ26−ζ10+ζ46ζ10−ζ46−ζ11−ζ29ζ11+ζ29−ζ41−ζ47ζ41+ζ47−ζ13−ζ43ζ13+ζ43−ζ25−ζ31ζ25+ζ31000000
χ538-80−42424ζ11+4ζ13+4ζ29+4ζ43−4ζ11−4ζ13−4ζ29−4ζ434ζ25+4ζ31+4ζ41+4ζ47−4ζ25−4ζ31−4ζ41−4ζ47000000000000000000000−1+i3−1−i31−i31+i30000−ζ10+ζ46ζ10−ζ46ζ14−ζ26−ζ14+ζ26−ζ13−ζ43ζ13+ζ43−ζ25−ζ31ζ25+ζ31−ζ11−ζ29ζ11+ζ29−ζ41−ζ47ζ41+ζ47000000
χ548-80−4242−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ43−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ4700000000000000000000022-2-20000−22−22−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47000000
χ558-80−4242−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ43−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ47000000000000000000000−1−i3−1+i31+i31−i30000ζ14−ζ26−ζ14+ζ26−ζ10+ζ46ζ10−ζ46ζ11+ζ29−ζ11−ζ29ζ41+ζ47−ζ41−ζ47ζ13+ζ43−ζ13−ζ43ζ25+ζ31−ζ25−ζ31000000
χ568-80−4242−4ζ11−4ζ13−4ζ29−4ζ434ζ11+4ζ13+4ζ29+4ζ43−4ζ25−4ζ31−4ζ41−4ζ474ζ25+4ζ31+4ζ41+4ζ47000000000000000000000−1+i3−1−i31−i31+i30000−ζ10+ζ46ζ10−ζ46ζ14−ζ26−ζ14+ζ26ζ13+ζ43−ζ13−ζ43ζ25+ζ31−ζ25−ζ31ζ11+ζ29−ζ11−ζ29ζ41+ζ47−ζ41−ζ47000000

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