Finite Group Databasebeta

← Group #13157204

Character table — Group #13157204

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222244444444444444444444444444444444888888888888888888888888888888888888999918181818181836363636363636365454545454545454108108108108
order124423461212333333666666688121212121212121212121212122424242466666612121212121224242424242424242424242424242424242424242424242488888824242424246612122424161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1
χ611111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−iii
χ811111111111111111111111-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiiiii−i−i
χ911-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−ii−iii−i−i1-111-1-1i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ1011-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−ii−iii−i−i1-111-1-1i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1111-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iii−ii−i−iii-11-1-111−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1211-1-1-1111-1-1111111-1111111i−i1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−iii−ii−i−iii-11-1-111−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1311-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−ii−iii−i−i-11-1-111i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46
χ1411-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiii−i−ii−iii−i−i-11-1-111i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46
χ1511-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−ii−i−iii1-111-1-1−ii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26
χ1611-1-1-1111-1-1111111-1111111−ii1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−ii−i−iii1-111-1-1−iiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26
χ1722222-12-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1000000000000
χ1822222-12-1-1-122-1-1-1-1-122-1-1-1-122-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2111111000000000000
χ1922222-12-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111222222-1-1-1-1-2-21111-1-1000000000000
χ2022222-12-1-1-122-1-1-1-1-122-1-1-1-1-2-2-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-2111122-1-1-1-111000000000000
χ212222-22-2222222222-222222200-22222222222220000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-22222000000-2-2000000000000
χ222222-22-2222222222-222222200-22222222222220000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-222-2-2-2-200000022000000000000
χ232222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32222-2-2-1-1-1-100−i3i3−i3i311000000000000
χ242222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1−i3i3−i3i3-2-21111-2-211110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-2-222111100i3−i3i3−i3-1-1000000000000
χ252222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32222-2-2-1-1-1-100i3−i3i3−i311000000000000
χ262222-2-1-2-1-1-122-1-1-1-1122-1-1-1-10012222-1-1-1-1-1-1-1-1i3−i3i3−i3-2-21111-2-211110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-2-222111100−i3i3−i3i3-1-1000000000000
χ2722-2-222-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-20000000000000000000000002i2i−2i−2i−2i2i2i2i−2i−2i000000−2i2i000000000000
χ2822-2-222-22-2-2222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2000000000000000000000000−2i−2i2i2i2i−2i−2i−2i2i2i0000002i−2i000000000000
χ2922-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−3−3322-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−333332i2i−2i−2i−2i2i−i−iii00−i3i3i3−i3i−i000000000000
χ3022-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-2111111113−3−3322-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−33333−2i−2i2i2i2i−2iii−i−i00i3−i3−i3i3−ii000000000000
χ3122-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−333−322-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−32i2i−2i−2i−2i2i−i−iii00i3−i3−i3i3i−i000000000000
χ3222-2-22-1-2-11122-1-1-1-1-122-1-1-1-1001-2-2-2-211111111−333−322-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−3−2i−2i2i2i2i−2iii−i−i00−i3i3i3−i3−ii000000000000
χ3322-2-2-2-12-11122-1-1-1-1122-1-1-1-12i−2i-1-2-2-2-211111111−i−iii-2-2111122-1-1-1-12i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii2i2i−2i−2i2i−2i−i−iii2-2-1-111−ii000000000000
χ3422-2-2-2-12-11122-1-1-1-1122-1-1-1-12i−2i-1-2-2-2-211111111−i−iii-2-2111122-1-1-1-12i2i2i2i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiii−2i−2i2i2i−2i2iii−i−i-2211-1-1i−i000000000000
χ3522-2-2-2-12-11122-1-1-1-1122-1-1-1-1−2i2i-1-2-2-2-211111111ii−i−i-2-2111122-1-1-1-1−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i2i2i−2i−2i2i−2i−i−iii-2211-1-1−ii000000000000
χ3622-2-2-2-12-11122-1-1-1-1122-1-1-1-1−2i2i-1-2-2-2-211111111ii−i−i-2-2111122-1-1-1-1−2i−2i−2i−2iiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−2i−2i2i2i−2i2iii−i−i2-2-1-111i−i000000000000
χ372-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000−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
χ382-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ26002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ2600000000ζ13+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
χ392-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000−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
χ402-22i−2i020-22i−2i2222220-2-2-2-2-2-20002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ2600000000ζ13−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
χ412-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000ζ11+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
χ422-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600−2ζ10−2ζ262ζ10+2ζ262ζ14+2ζ46−2ζ14−2ζ4600000000−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
χ432-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000ζ11−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
χ442-2−2i2i020-2−2i2i2222220-2-2-2-2-2-2000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ46002ζ10+2ζ26−2ζ10−2ζ26−2ζ14−2ζ462ζ14+2ζ4600000000−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
χ4544444444441-211-2-241-211-2-24441-21-211-2-211-2-244441-211-2-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000000000000000
χ4644444444441-211-2-241-211-2-2-4-441-21-211-2-211-2-2-4-4-4-41-211-2-21-211-2-2-1-122-1-122-1-122-1-122-1-122-1-122000000000000000000000000000000
χ474444444444-21-2-2114-21-2-211444-21-21-2-211-2-2114444-21-2-211-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000000000000
χ484444444444-21-2-2114-21-2-211-4-44-21-21-2-211-2-211-4-4-4-4-21-2-211-21-2-21122-1-122-1-122-1-122-1-122-1-122-1-1000000000000000000000000000000
χ4944444-24-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i321144-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i3211-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i3211000000000000000000000000000000
χ5044444-24-2-2-21-2−1−3i32−1+3i3211-21-2−1−3i32−1+3i3211-4-4-21-21-2−1−3i32−1+3i3211−1−3i32−1+3i321122221-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-1000000000000000000000000000000
χ5144444-24-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i321144-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i3211-2-2-2-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i3211000000000000000000000000000000
χ5244444-24-2-2-21-2−1+3i32−1−3i3211-21-2−1+3i32−1−3i3211-4-4-21-21-2−1+3i32−1−3i3211−1+3i32−1−3i321122221-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-1000000000000000000000000000000
χ5344444-24-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i3244-2-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i32000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.