Finite Group Databasebeta

← Group #11771453

Character table — Group #11771453

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888888888888888888888881818181818181818363636363636363636363636363636367272
order12224444233466666612121212121212124466661212121212121212121212121212121212121212888888881616161616161616161616161616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1
χ511111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26i−i
χ101111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26i−i
χ111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ii
χ121111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ii
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ii
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ii
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46i−i
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46i−i
χ1722222222-222-22222222222222200-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ1822222222-222-22222222222222200-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-2002222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ202222-2-2-2-2222-2222222-2-2-2-2-2-2-2-2002222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2122-2-22i−2i2i−2i022022-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ470000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41000000
χ2222-2-22i−2i2i−2i022022-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ470000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41000000
χ2322-2-22i−2i2i−2i022022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ470000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41000000
χ2422-2-22i−2i2i−2i022022-2-2-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ470000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41000000
χ2522-2-2−2i2i−2i2i022022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ410000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47000000
χ2622-2-2−2i2i−2i2i022022-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ410000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47000000
χ2722-2-2−2i2i−2i2i022022-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ410000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47000000
χ2822-2-2−2i2i−2i2i022022-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ410000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47000000
χ292-22-22i−2i−2i2i0220-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46000000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ470000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ4100
χ302-22-22i−2i−2i2i0220-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46000000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ470000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ4100
χ312-22-22i−2i−2i2i0220-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46000000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ470000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ4100
χ322-22-22i−2i−2i2i0220-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46000000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ470000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ4100
χ332-22-2−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26000000−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ410000ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ4700
χ342-22-2−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26000000ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ410000−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ4700
χ352-22-2−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26000000−ζ13−ζ25−ζ29−ζ41ζ13+ζ25+ζ29+ζ41ζ13−ζ25+ζ29−ζ41−ζ13+ζ25−ζ29+ζ410000ζ11+ζ31+ζ43+ζ47−ζ11−ζ31−ζ43−ζ47−ζ11+ζ31−ζ43+ζ47ζ11−ζ31+ζ43−ζ4700
χ362-22-2−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26000000ζ13+ζ25+ζ29+ζ41−ζ13−ζ25−ζ29−ζ41−ζ13+ζ25−ζ29+ζ41ζ13−ζ25+ζ29−ζ410000−ζ11−ζ31−ζ43−ζ47ζ11+ζ31+ζ43+ζ47ζ11−ζ31+ζ43−ζ47−ζ11+ζ31−ζ43+ζ4700
χ374444444441-241-21-21-21-21-21-21-24411-2-211-2-21111-2-2-2-21111-2-2-2-200000000000000000000000000
χ384444444441-241-21-21-21-21-21-21-2-4-411-2-211-2-2-1-1-1-12222-1-1-1-1222200000000000000000000000000
χ39444444444-214-21-21-21-21-21-21-2144-2-211-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ40444444444-214-21-21-21-21-21-21-21-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000
χ4144444444-41-2-41-21-21-21-21-21-21-200-1-122-1-12233-3-3000033-3-3000000000000000000000000000000
χ4244444444-41-2-41-21-21-21-21-21-21-200-1-122-1-122-3-3330000-3-333000000000000000000000000000000
χ4344444444-4-21-4-21-21-21-21-21-21-210022-1-122-1-1000033-3-3000033-3-300000000000000000000000000
χ4444444444-4-21-4-21-21-21-21-21-21-210022-1-122-1-10000-3-3330000-3-33300000000000000000000000000
χ454444-4-4-4-441-2-41-21-21-2-12-12-12-120011-2-2-1-12233-3-30000-3-333000000000000000000000000000000
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χ524444-4-4-4-4-4-214-21-21-212-12-12-12-1-4422-1-1-2-2112222-1-1-1-1-2-2-2-2111100000000000000000000000000
χ534-4-4444-4-401-20-12-121-21-2-12-121-2003-3003-3003−33−30023−233−33−30023−2300000000000000000000000000
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χ604-4-4444-4-40-2102-12-1-21-212-12-1-210000-3300-3323−2300−33−3323−2300−33−3300000000000000000000000000
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χ7188-8-88i−8i8i−8i02-402-4-24-242i−4i2i−4i−2i4i−2i4i0000000000000000000000000000000000000000000000000000
χ7288-8-88i−8i8i−8i0-420-424-24-2−4i2i−4i2i4i−2i4i−2i0000000000000000000000000000000000000000000000000000
χ7388-8-8−8i8i−8i8i02-402-4-24-24−2i4i−2i4i2i−4i2i−4i0000000000000000000000000000000000000000000000000000
χ7488-8-8−8i8i−8i8i0-420-424-24-24i−2i4i−2i−4i2i−4i2i0000000000000000000000000000000000000000000000000000
χ758-88-88i−8i−8i8i02-40-242-4-242i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ768-88-88i−8i−8i8i0-4204-2-424-2−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ778-88-8−8i8i8i−8i02-40-242-4-24−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i8i−8i0-4204-2-424-24i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000

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