Finite Group Databasebeta

← Group #13166223

Character table — Group #13166223

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244448888889999991616161616161616161818181818181818183636363636363636363636365454545454545454108108108108
order123462661233366644888866666612121228812122424242446881212242424242424161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111-1-1ii−i−i111111111-1i−i-1-1ii−i−i-1-1i−i-1-1iii−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ6111111111111111-1-1ii−i−i111111111-1i−i-1-1ii−i−i-1-1i−i-1-1iii−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ7111111111111111-1-1−i−iii111111111-1−ii-1-1−i−iii-1-1−ii-1-1−i−i−iiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ8111111111111111-1-1−i−iii111111111-1−ii-1-1−i−iii-1-1−ii-1-1−i−i−iiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ911111-1-1-11111111111111-1-1-1-1-1-1111111111111-11-1-1-1-11-1-11-1-111111111-1-1-1-1
χ1011111-1-1-11111111111111-1-1-1-1-1-1111111111111-11-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ1111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1111-1-1-111-111iiii−i−i−i−i−i−iii
χ1211111-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1111-1-1-111-111−i−i−i−iiiiiii−i−i
χ1311111-1-1-11111111-1-1ii−i−i-1-1-1-1-1-1111-1i−i-1-1ii−i−i1-1−ii11i−i−i−iiiζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1411111-1-1-11111111-1-1ii−i−i-1-1-1-1-1-1111-1i−i-1-1ii−i−i1-1−ii11i−i−i−iii−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1511111-1-1-11111111-1-1−i−iii-1-1-1-1-1-1111-1−ii-1-1−i−iii1-1i−i11−iiii−i−i−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1611111-1-1-11111111-1-1−i−iii-1-1-1-1-1-1111-1−ii-1-1−i−iii1-1i−i11−iiii−i−iζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ17222-22000-2222222222222000000-2-2-2-2-2-22222220-20000-200-200000000000000
χ18222-22000-222222222-2-2-2-2000000-2-2-2-22222-2-2-2-20-20000200200000000000000
χ19222-22000-2222222-2-22i2i−2i−2i000000-2-2-22−2i2i-2-22i2i−2i−2i020000−2i002i00000000000000
χ20222-22000-2222222-2-2−2i−2i2i2i000000-2-2-222i−2i-2-2−2i−2i2i2i0200002i00−2i00000000000000
χ2122-12-12-1-1-12-1-12-1-122222222-1-1-1-12-1-1222-1-1-1-1-1-12-122-1-1-1-1-1-1-1-1000000000000
χ2222-12-12-1-1-12-1-12-1-122-2-2-2-222-1-1-1-12-1-12-2-2-1-111112-1-2-2-1-1111111000000000000
χ2322-12-12-1-1-12-1-12-1-1-2-22i2i−2i−2i22-1-1-1-12-1-1-22i−2i11−i−iii-212i−2i11−i−i−iiii000000000000
χ2422-12-12-1-1-12-1-12-1-1-2-2−2i−2i2i2i22-1-1-1-12-1-1-2−2i2i11ii−i−i-21−2i2i11iii−i−i−i000000000000
χ2522-12-1-211-12-1-12-1-1222222-2-211112-1-1222-1-1-1-1-1-1-2-1-2-211-111-111000000000000
χ2622-12-1-211-12-1-12-1-122-2-2-2-2-2-211112-1-12-2-2-1-11111-2-122111-1-11-1-1000000000000
χ2722-12-1-211-12-1-12-1-1-2-22i2i−2i−2i-2-211112-1-1-22i−2i11−i−iii21−2i2i-1-1−iiii−i−i000000000000
χ2822-12-1-211-12-1-12-1-1-2-2−2i−2i2i2i-2-211112-1-1-2−2i2i11ii−i−i212i−2i-1-1i−i−i−iii000000000000
χ2922-1-2-10−i3i312-1-12-1-122222200−i3−i3i3i3-211-2-2-2-1-1-1-1-1-10100−i3i31−i3i31−i3i3000000000000
χ3022-1-2-10−i3i312-1-12-1-122-2-2-2-200−i3−i3i3i3-211-222-1-111110100−i3i3-1i3−i3-1i3−i3000000000000
χ3122-1-2-10−i3i312-1-12-1-1-2-22i2i−2i−2i00−i3−i3i3i3-2112−2i2i11−i−iii0-100i3−i3i3−3−i−33000000000000
χ3222-1-2-10−i3i312-1-12-1-1-2-2−2i−2i2i2i00−i3−i3i3i3-21122i−2i11ii−i−i0-100i3−i3−i−33i3−3000000000000
χ3322-1-2-10i3−i312-1-12-1-122222200i3i3−i3−i3-211-2-2-2-1-1-1-1-1-10100i3−i31i3−i31i3−i3000000000000
χ3422-1-2-10i3−i312-1-12-1-122-2-2-2-200i3i3−i3−i3-211-222-1-111110100i3−i3-1−i3i3-1−i3i3000000000000
χ3522-1-2-10i3−i312-1-12-1-1-2-22i2i−2i−2i00i3i3−i3−i3-2112−2i2i11−i−iii0-100−i3i3i−33−i3−3000000000000
χ3622-1-2-10i3−i312-1-12-1-1-2-2−2i−2i2i2i00i3i3−i3−i3-21122i−2i11ii−i−i0-100−i3i3−i3−3i−33000000000000
χ372-220-20000222-2-2-22i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26000000000000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ470000
χ382-220-20000222-2-2-22i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000000000002i−2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26000000000000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ470000
χ392-220-20000222-2-2-22i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26000000000000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ470000
χ402-220-20000222-2-2-22i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000000000002i−2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26000000000000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ470000
χ412-220-20000222-2-2-2−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ410000
χ422-220-20000222-2-2-2−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000−2i2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ410000
χ432-220-20000222-2-2-2−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ410000
χ442-220-20000222-2-2-2−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000−2i2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ410000
χ454-4-20200004-2-2-4224i−4i4ζ14+4ζ46−4ζ14−4ζ46−4ζ10−4ζ264ζ10+4ζ26000000000000−2i2i−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ26000000000000000000000000
χ464-4-20200004-2-2-4224i−4i−4ζ14−4ζ464ζ14+4ζ464ζ10+4ζ26−4ζ10−4ζ26000000000000−2i2i2ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26000000000000000000000000
χ474-4-20200004-2-2-422−4i4i−4ζ10−4ζ264ζ10+4ζ264ζ14+4ζ46−4ζ14−4ζ460000000000002i−2i2ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46000000000000000000000000
χ484-4-20200004-2-2-422−4i4i4ζ10+4ζ26−4ζ10−4ζ26−4ζ14−4ζ464ζ14+4ζ460000000000002i−2i−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ46000000000000000000000000
χ49888888888-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ5088888-8-8-88-1-1-1-1-1-1000000111111-1-1-1000000000000000000000000000000000
χ51888-88000-8-1-1-1-1-1-10000003-33-33-3111000000000000000000000000000000000
χ52888-88000-8-1-1-1-1-1-1000000-33-33-33111000000000000000000000000000000000
χ5388-48-48-4-4-4-11−3i321+3i32-11−3i321+3i32000000-1-11−3i321+3i321+3i321−3i32-11−3i321+3i32000000000000000000000000000000000
χ5488-48-48-4-4-4-11+3i321−3i32-11+3i321−3i32000000-1-11+3i321−3i321−3i321+3i32-11+3i321−3i32000000000000000000000000000000000
χ5588-48-4-844-4-11−3i321+3i32-11−3i321+3i3200000011−1+3i32−1−3i32−1−3i32−1+3i32-11−3i321+3i32000000000000000000000000000000000
χ5688-48-4-844-4-11+3i321−3i32-11+3i321−3i3200000011−1−3i32−1+3i32−1+3i32−1−3i32-11+3i321−3i32000000000000000000000000000000000
χ5788-4-8-40−4i34i34-11−3i321+3i32-11−3i321+3i320000003-3−3+i323+i32−3−i323−i321−1+3i32−1−3i32000000000000000000000000000000000
χ5888-4-8-40−4i34i34-11+3i321−3i32-11+3i321−3i32000000-333+i32−3+i323−i32−3−i321−1−3i32−1+3i32000000000000000000000000000000000
χ5988-4-8-404i3−4i34-11−3i321+3i32-11−3i321+3i32000000-333−i32−3−i323+i32−3+i321−1+3i32−1−3i32000000000000000000000000000000000
χ6088-4-8-404i3−4i34-11+3i321−3i32-11+3i321−3i320000003-3−3−i323−i32−3+i323+i321−1−3i32−1+3i32000000000000000000000000000000000
χ6116-16160-160000-2-2-2222000000000000000000000000000000000000000000000000
χ6216-16-8080000-21−3i31+3i32−1+3i3−1−3i3000000000000000000000000000000000000000000000000
χ6316-16-8080000-21+3i31−3i32−1−3i3−1+3i3000000000000000000000000000000000000000000000000

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