Finite Group Databasebeta

← Group #13135954

Character table — Group #13135954

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size111111111111222222222222222222666666666666666688888812121212121212121212121212121212121212121212121218181818181818181818181818181818181818181818181824242424242424242424242424242424727272727272
order122233666666448888121212122424242424242424333366666666666622666612121212121212122424242424242424242424242424242416161616161616164848484848484848484848484848484866666666666666664412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51-11-111-1-111-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1i−iii−i−i
χ61-11-111-1-111-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−ii−i−iii
χ71-11-111-1-111-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−ii−i−iii
χ81-11-111-1-111-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111i−iii−i−i
χ92222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000022-1-1-1-1-1-122-1-1-1-1-1-1000000
χ102222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000-2-2111111-2-2111111000000
χ11222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000-1-122-1-1-1-1-1-122-1-1-1-1000000
χ12222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000000011-2-2111111-2-21111000000
χ13222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000-1-1-1-122-1-1-1-1-1-122-1-1000000
χ14222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-10000000000000000000000001111-2-2111111-2-211000000
χ15222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000-1-1-1-1-1-122-1-1-1-1-1-122000000
χ16222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000111111-2-2111111-2-2000000
χ1722222222222222-2-2-2-22222-2-2-2-2-2-2-2-2222222222222222200000022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ1822222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100000000000000000000000000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000
χ1922222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100000000000000000000000000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000
χ2022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1000000-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000000−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000
χ2122222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1000000-12-1-1-12-1-111-2-2111111-2-21111000000000000000000000000i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000
χ2222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1000000-1-12-1-1-12-11111-2-2111111-2-211000000000000000000000000−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000
χ2322222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1000000-1-12-1-1-12-11111-2-2111111-2-211000000000000000000000000i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000
χ2422222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000000000−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000
χ2522222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12000000-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000000000i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000
χ26222222222222-2-20000-2-2-2-2000000002222222222222222000000-2-2-2-2-2-2-2-2000000000000000022−2−222−2−22222−2−2−2−22222−2−2−2−20000000000000000000000
χ27222222222222-2-20000-2-2-2-2000000002222222222222222000000-2-2-2-2-2-2-2-20000000000000000−2−222−2−222−2−2−2−22222−2−2−2−222220000000000000000000000
χ2822-2-22222-2-2-2-2002−22−2000022−2−222−2−222222-22-22-22-2-2-2-2-2000000000000002−22−22−22−22−22−22−22−2−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−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ430000000000000000000000
χ2922-2-22222-2-2-2-2002−22−2000022−2−222−2−222222-22-22-22-2-2-2-2-2000000000000002−22−22−22−22−22−22−22−2ζ25+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+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ430000000000000000000000
χ3022-2-22222-2-2-2-200−22−220000−2−222−2−22222222-22-22-22-2-2-2-2-200000000000000−22−22−22−22−22−22−22−22ζ11+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−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ470000000000000000000000
χ3122-2-22222-2-2-2-200−22−220000−2−222−2−22222222-22-22-22-2-2-2-2-200000000000000−22−22−22−22−22−22−22−22−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+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ470000000000000000000000
χ322-22-222-2-222-2-22-2000022-2-2000000002222-2-2-2-2-2-2-2-222220000002222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000000000
χ332-22-222-2-222-2-22-2000022-2-2000000002222-2-2-2-2-2-2-2-222220000002222-2-2-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000
χ342-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-22-1-1-1-2-21111112-1-1-12-222-2-2-21112-1-1-122-1-1-1-1-1-1-2-211111100000000000000000000000022-1-1-1-1-1-1-2-2111111000000
χ352-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-22-1-1-1-2-21111112-1-1-1-22-2-222-21112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000000-2-211111122-1-1-1-1-1-1000000
χ362-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-12-1-111-2-21111-12-1-12-222-2-21-211-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000-1-122-1-1-1-111-2-21111000000
χ372-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-12-1-111-2-21111-12-1-1-22-2-2221-211-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000000011-2-21111-1-122-1-1-1-1000000
χ382-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-1-12-11111-2-211-1-12-12-222-2-211-21-1-12-1-1-1-1-122-1-11111-2-211000000000000000000000000-1-1-1-122-1-11111-2-211000000
χ392-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-1-12-11111-2-211-1-12-1-22-2-22211-21-1-12-1-1-1-1-122-1-11111-2-2110000000000000000000000001111-2-211-1-1-1-122-1-1000000
χ402-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-1-1-12111111-2-2-1-1-122-222-2-2111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000000000000000-1-1-1-1-1-122111111-2-2000000
χ412-22-222-2-222-2-2-2222-2-2-2-2222222-2-2-2-2-1-1-12111111-2-2-1-1-12-22-2-222111-2-1-1-12-1-1-1-1-1-122111111-2-2000000000000000000000000111111-2-2-1-1-1-1-1-122000000
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χ432-22-222-2-222-2-2-22-2-222-2-222-2-2-2-222222-1-1-1-2-21111112-1-1-1000000-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000
χ442-22-222-2-222-2-2-22-2-222-2-222-2-2-2-222222-1-1-1-2-21111112-1-1-1000000-21112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000000000i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000
χ452-22-222-2-222-2-2-22-2-222-2-222-2-2-2-22222-12-1-111-2-21111-12-1-10000001-211-12-1-111-2-21111-1-122-1-1-1-1000000000000000000000000−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000
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χ472-22-222-2-222-2-2-22-2-222-2-222-2-2-2-22222-1-12-11111-2-211-1-12-100000011-21-1-12-11111-2-211-1-1-1-122-1-1000000000000000000000000−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000
χ482-22-222-2-222-2-2-22-2-222-2-222-2-2-2-22222-1-12-11111-2-211-1-12-100000011-21-1-12-11111-2-211-1-1-1-122-1-1000000000000000000000000i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.