Finite Group Databasebeta

← Group #11771454

Character table — Group #11771454

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888888888888888888888881818181818181818363636363636363636363636363636367272
order12224444233466666612121212121212126666881212121224242424242424242424242424242424888888881616161616161616161616161616161644
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
χ5111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ8111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ91111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ461-1
χ101111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ461-1
χ111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-11
χ121111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-11
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-11
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-11
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ261-1
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ261-1
χ1722222222-222-222222222222222-2-2-2-200-2-2-2-2000000000000000022-2-222-2-2000000000000000000
χ1822222222-222-222222222222222-2-2-2-200-2-2-2-20000000000000000-2-222-2-222000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-2222200-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ202222-2-2-2-2222-2222222-2-2-2-2-2-2-2-2222200-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ212-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−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
χ222-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−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
χ232-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−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
χ242-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−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
χ252-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002ζ14+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
χ262-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002ζ14+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
χ272-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+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
χ282-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2ζ14−2ζ462ζ14+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
χ292-2-222i−2i−2i2i0220-2-222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46000000−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
χ302-2-222i−2i−2i2i0220-2-222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46000000ζ13+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
χ312-2-222i−2i−2i2i0220-2-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46000000−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
χ322-2-222i−2i−2i2i0220-2-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ46000000ζ13−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
χ332-2-22−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26000000ζ11+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
χ342-2-22−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ26000000−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
χ352-2-22−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26000000ζ11−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
χ362-2-22−2i2i2i−2i0220-2-222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26000000−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
χ374444444441-241-21-21-21-21-21-21-211-2-24411-2-21111-2-2-2-21111-2-2-2-200000000000000000000000000
χ384444444441-241-21-21-21-21-21-21-211-2-2-4-411-2-2-1-1-1-12222-1-1-1-1222200000000000000000000000000
χ39444444444-214-21-21-21-21-21-21-21-2-21144-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000
χ40444444444-214-21-21-21-21-21-21-21-2-211-4-4-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000
χ4144444444-41-2-41-21-21-21-21-21-21-2-1-12200-1-12233-3-3000033-3-3000000000000000000000000000000
χ4244444444-41-2-41-21-21-21-21-21-21-2-1-12200-1-122-3-3330000-3-333000000000000000000000000000000
χ4344444444-4-21-4-21-21-21-21-21-21-2122-1-10022-1-1000033-3-3000033-3-300000000000000000000000000
χ4444444444-4-21-4-21-21-21-21-21-21-2122-1-10022-1-10000-3-3330000-3-33300000000000000000000000000
χ454444-4-4-4-441-2-41-21-21-2-12-12-12-1211-2-200-1-1223i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ464444-4-4-4-441-2-41-21-21-2-12-12-12-1211-2-200-1-122−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ474444-4-4-4-44-21-4-21-21-212-12-12-12-1-2-2110022-1-100003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000
χ484444-4-4-4-44-21-4-21-21-212-12-12-12-1-2-2110022-1-10000−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000
χ494444-4-4-4-4-41-241-21-21-2-12-12-12-12-1-1224i−4i11-2-2iiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i00000000000000000000000000
χ504444-4-4-4-4-41-241-21-21-2-12-12-12-12-1-122−4i4i11-2-2−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i00000000000000000000000000
χ514444-4-4-4-4-4-214-21-21-212-12-12-12-122-1-14i−4i-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i00000000000000000000000000
χ524444-4-4-4-4-4-214-21-21-212-12-12-12-122-1-1−4i4i-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii00000000000000000000000000
χ5344-4-444-4-401-20-12-121-21-21-2-12-123-300003-3003−33−30023−233−33−30023−2300000000000000000000000000
χ5444-4-444-4-401-20-12-121-21-21-2-12-123-300003-300−33−3300−2323−33−3300−232300000000000000000000000000
χ5544-4-444-4-401-20-12-121-21-21-2-12-12-330000-33003−3−3323−23003−3−3323−230000000000000000000000000000
χ5644-4-444-4-401-20-12-121-21-21-2-12-12-330000-3300−333−3−232300−333−3−23230000000000000000000000000000
χ5744-4-444-4-40440-4-4-4-4444444-4-4-4-40000000000000000000000000000000000000000000000000000
χ5844-4-444-4-40-2102-12-1-21-21-212-12-1003-300003-30023−233−3−330023−233−3−3300000000000000000000000000
χ5944-4-444-4-40-2102-12-1-21-21-212-12-1003-300003-300−2323−333−300−2323−333−300000000000000000000000000
χ6044-4-444-4-40-2102-12-1-21-21-212-12-100-330000-3323−2300−33−3323−2300−33−3300000000000000000000000000
χ6144-4-444-4-40-2102-12-1-21-21-212-12-100-330000-33−2323003−33−3−2323003−33−300000000000000000000000000
χ6244-4-4-4-44401-20-12-121-2-12-121-21-23-30000-3300−i3i3i3−i3−2i32i300i3−i3−i3i32i3−2i30000000000000000000000000000
χ6344-4-4-4-44401-20-12-121-2-12-121-21-23-30000-3300i3−i3−i3i32i3−2i300−i3i3i3−i3−2i32i30000000000000000000000000000
χ6444-4-4-4-44401-20-12-121-2-12-121-21-2-3300003-300−i3i3−i3i300−2i32i3i3−i3i3−i3002i3−2i300000000000000000000000000
χ6544-4-4-4-44401-20-12-121-2-12-121-21-2-3300003-300i3−i3i3−i3002i3−2i3−i3i3−i3i300−2i32i300000000000000000000000000
χ6644-4-4-4-4440440-4-4-4-444-4-4-4-444440000000000000000000000000000000000000000000000000000
χ6744-4-4-4-4440-2102-12-1-212-12-1-21-21003-30000-33−2i32i300i3−i3i3−i32i3−2i300−i3i3−i3i300000000000000000000000000
χ6844-4-4-4-4440-2102-12-1-212-12-1-21-21003-30000-332i3−2i300−i3i3−i3i3−2i32i300i3−i3i3−i300000000000000000000000000
χ6944-4-4-4-4440-2102-12-1-212-12-1-21-2100-3300003-300−2i32i3−i3i3i3−i3002i3−2i3i3−i3−i3i300000000000000000000000000
χ7044-4-4-4-4440-2102-12-1-212-12-1-21-2100-3300003-3002i3−2i3i3−i3−i3i300−2i32i3−i3i3i3−i300000000000000000000000000
χ718-88-88i−8i8i−8i02-402-4-24-242i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ728-88-88i−8i8i−8i0-420-424-24-2−4i2i4i−2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ738-88-8−8i8i−8i8i02-402-4-24-24−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i−8i8i0-420-424-24-24i−2i−4i2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ758-8-888i−8i−8i8i02-40-242-4-242i−4i−2i4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ768-8-888i−8i−8i8i0-4204-2-424-2−4i2i4i−2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ778-8-88−8i8i8i−8i02-40-242-4-24−2i4i2i−4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i8i−8i0-4204-2-424-24i−2i−4i2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000

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