Finite Group Databasebeta

← Group #10709981

Character table — Group #10709981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444121212121212121212121212121212123232323232329696
order12223444444666888888888888888812121212121224242424242424242424242424242424242424242424242416161616161616161616161616161616441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111-1
χ922222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222-2-2-2-22222222-2-2-2-200000000-2-222-2-22222-2-2-2-20000000000000000000000002222-2-2-2-200000000
χ122222222-2-2-2-22222222-2-2-2-200000000-2-222-2-22222-2-2-2-2000000000000000000000000-2-2-2-2222200000000
χ132222222-2-2-2-2222-2-2-2-2222200000000-2-222-2-2-2-2-2-2222200000000000000002222-2-2-2-20000000000000000
χ142222222-2-2-2-2222-2-2-2-2222200000000-2-222-2-2-2-2-2-222220000000000000000-2-2-2-222220000000000000000
χ1522222-2-222-2-222200000000000022-2-222-2-2-2-200000000000000002222-2-2-2-222−2−222−2−222−2−222−2−200000000
χ1622222-2-222-2-222200000000000022-2-222-2-2-2-200000000000000002222-2-2-2-2−2−222−2−222−2−222−2−22200000000
χ1722222-2-222-2-2222000000000000-2-22222-2-2-2-20000000000000000-2-2-2-2222222−2−222−2−2−2−222−2−22200000000
χ1822222-2-222-2-2222000000000000-2-22222-2-2-2-20000000000000000-2-2-2-22222−2−222−2−22222−2−222−2−200000000
χ1922222-2-2-2-2222220000000022-2-20000-2-2-2-222000000002222-2-2-2-20000000022−2−2−2−22222−2−2−2−22200000000
χ2022222-2-2-2-2222220000000022-2-20000-2-2-2-222000000002222-2-2-2-200000000−2−22222−2−2−2−22222−2−200000000
χ2122222-2-2-2-22222200000000-2-2220000-2-2-2-22200000000-2-2-2-222220000000022−2−2−2−222−2−22222−2−200000000
χ2222222-2-2-2-22222200000000-2-2220000-2-2-2-22200000000-2-2-2-2222200000000−2−22222−2−222−2−2−2−22200000000
χ232222-1222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-100
χ242222-1222222-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2111100
χ252222-1222222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000002-2-1-11100
χ262222-1222222-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2211-1-100
χ272222-1222222-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000−i3i3−i3i300
χ282222-1222222-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000i3−i3i3−i300
χ292222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000−i3i3i3−i300
χ302222-1222222-1-1-1-2-2-2-2-2-2-2-2-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000i3−i3−i3i300
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χ382-2-22200002-2-22-2−2−222−2−22200−2i2i−i2i2−i2i200002-2−2−222−2−2220000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000
χ392-2-2220000-22-22-222−2−2−2−2222i−2i00−i2i2i2−i20000-2222−2−2−2−2222i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000
χ402-2-2220000-22-22-222−2−2−2−2222i−2i00−i2i2i2−i20000-2222−2−2−2−2222i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000
χ412-2-2220000-22-22-222−2−2−2−222−2i2i00i2−i2−i2i20000-2222−2−2−2−222−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000
χ422-2-2220000-22-22-222−2−2−2−222−2i2i00i2−i2−i2i20000-2222−2−2−2−222−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000
χ432-2-2220000-22-22-2−2−22222−2−22i−2i00i2−i2−i2i20000-22−2−22222−2−22i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000
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χ452-2-2220000-22-22-2−2−22222−2−2−2i2i00−i2i2i2−i20000-22−2−22222−2−2−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4300000000
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χ764-44-4-200-4400-222−222222−2222−22−2222000000002-200002−2−22−222−2−i6i6i6−i6i6−i6−i6i6−2i32i32i3−2i30000000000000000000000000000
χ774-4-44-200004-42-222222−22−222222−22−22004i−4i−2i22i2−2i22i20000-22−2−222−2−2220000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ784-4-44-200004-42-222222−22−222222−22−2200−4i4i2i2−2i22i2−2i20000-22−2−222−2−22200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ794-4-44-200004-42-22−22−222222−22−222222004i−4i2i2−2i22i2−2i20000-2222−2−222−2−20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ804-4-44-200004-42-22−22−222222−22−22222200−4i4i−2i22i2−2i22i20000-2222−2−222−2−200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ814-4-44-20000-442-222222−22−22−22−2222224i−4i00−2i22i22i2−2i200002-2−2−22222−2−2−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ824-4-44-20000-442-222222−22−22−22−222222−4i4i002i2−2i2−2i22i200002-2−2−22222−2−22i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ834-4-44-20000-442-22−22−2222222222−22−224i−4i002i2−2i2−2i22i200002-222−2−2−2−222−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ844-4-44-20000-442-22−22−2222222222−22−22−4i4i00−2i22i22i2−2i200002-222−2−2−2−2222i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000000000000000

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