Finite Group Databasebeta

← Group #10712981

Character table — Group #10712981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122222223444444446666666888888884488881212121212121212121212122424242424242424242424242424242416161616161616161616161616161616224466661212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ911-11-1-11-111-1ii−i−i1-111-11-1-1-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011-11-1-11-111-1ii−i−i1-111-11-1-1-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−i−iii
χ1111-11-1-11-111-1ii−i−i1-111-11-1-1-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-1-111−i−iii
χ1211-11-1-11-111-1ii−i−i1-111-11-1-1-111-1-111-1-1i−iii−i−i1-1iiii−i−i−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii11-1-1ii−i−i
χ1311-11-1-11-111-1−i−iii1-111-11-1-1-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii
χ1411-11-1-11-111-1−i−iii1-111-11-1-1-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111ii−i−i
χ1511-11-1-11-111-1−i−iii1-111-11-1-1-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-1-111ii−i−i
χ1611-11-1-11-111-1−i−iii1-111-11-1-1-111-1-111-1-1−ii−i−iii1-1−i−i−i−iiiii1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ19222222222-2-22222-2-2222222200000000-2-20000-2-222-2-222-2-2-2-2000000000000000022−2−222−2−222−2−222−2−200000000000000000000
χ20222222222-2-22222-2-2222222200000000-2-20000-2-222-2-222-2-2-2-20000000000000000−2−222−2−222−2−222−2−22200000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222200000000220000-2-2-2-222-2-222-2-2000000000000000022−2−222−2−2−2−222−2−22200000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222200000000220000-2-2-2-222-2-222-2-20000000000000000−2−222−2−22222−2−222−2−200000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ2422222222-122222222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-122222222-2-2-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-1111100000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-122222222-2-2-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-100000000
χ2922222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ3022222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3122-22-2-22-222-22i2i−2i−2i2-222-22-2-2-2-2-222-2-2222i−2i−2i−2i2i2i2-22i2i2i2i−2i−2i−2i−2i2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ3222-22-2-22-222-2−2i−2i2i2i2-222-22-2-2-2-2-222-2-222−2i2i2i2i−2i−2i2-2−2i−2i−2i−2i2i2i2i2i2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ3322-22-2-22-22-222i2i−2i−2i-2222-22-2-2-200000000−2i2i0000-222i2i−2i−2i−2i−2i2i2i-22000000000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000
χ3422-22-2-22-22-222i2i−2i−2i-2222-22-2-2-200000000−2i2i0000-222i2i−2i−2i−2i−2i2i2i-220000000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ3522-22-2-22-22-22−2i−2i2i2i-2222-22-2-2-2000000002i−2i0000-22−2i−2i2i2i2i2i−2i−2i-22000000000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000
χ3622-22-2-22-22-22−2i−2i2i2i-2222-22-2-2-2000000002i−2i0000-22−2i−2i2i2i2i2i−2i−2i-220000000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ3722-22-2-22-2-12-22i2i−2i−2i2-2-1-11-111122-2-222-2-22i−2i2i2i−2i−2i-11−i−i−i−iiiii-11-1-1-1-11111−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii00000000
χ3822-22-2-22-2-12-22i2i−2i−2i2-2-1-11-111122-2-222-2-22i−2i2i2i−2i−2i-11−i−i−i−iiiii-11-1-1-1-11111−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i00000000
χ3922-22-2-22-2-12-22i2i−2i−2i2-2-1-11-1111-2-222-2-2222i−2i−2i−2i2i2i-11−i−i−i−iiiii-111111-1-1-1-1iiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−3300000000
χ4022-22-2-22-2-12-22i2i−2i−2i2-2-1-11-1111-2-222-2-2222i−2i−2i−2i2i2i-11−i−i−i−iiiii-111111-1-1-1-1iiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ4122-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-111122-2-222-2-2−2i2i−2i−2i2i2i-11iiii−i−i−i−i-11-1-1-1-11111iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i00000000
χ4222-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-111122-2-222-2-2−2i2i−2i−2i2i2i-11iiii−i−i−i−i-11-1-1-1-11111iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii00000000
χ4322-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-1111-2-222-2-222−2i2i2i2i−2i−2i-11iiii−i−i−i−i-111111-1-1-1-1−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−300000000
χ4422-22-2-22-2-12-2−2i−2i2i2i2-2-1-11-1111-2-222-2-222−2i2i2i2i−2i−2i-11iiii−i−i−i−i-111111-1-1-1-1−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−3300000000
χ452-222-2-2-222-2200002-2-2-222-2-222222-2-2-2-2000000-22000000002-222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ462-222-2-2-222-2200002-2-2-222-2-222222-2-2-2-2000000-22000000002-222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ472-222-2-2-222-2200002-2-2-222-2-22-2-2-2-22222000000-22000000002-2-2-222-2-22200000000000000000000000000000000000000002-22-2
χ482-222-2-2-222-2200002-2-2-222-2-22-2-2-2-22222000000-22000000002-2-2-222-2-2220000000000000000000000000000000000000000-22-22
χ492-22-22-22-22002i−2i2i−2i002-22-22-2-22−22−22−22−200−i2i2−i2i2002i−2i002i−2i00002−22−22−22−2−i2−i2i2i2−i2−i2i2i2−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−ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000000000000000
χ502-22-22-22-22002i−2i2i−2i002-22-22-2-22−22−22−22−200−i2i2−i2i2002i−2i002i−2i00002−22−22−22−2−i2−i2i2i2−i2−i2i2i2ζ25−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+ζ43−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000000000000000
χ512-22-22-22-22002i−2i2i−2i002-22-22-2-2−22−22−22−2200i2−i2i2−i2002i−2i002i−2i0000−22−22−22−22i2i2−i2−i2i2i2−i2−i2ζ11−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+ζ47−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000000000000000
χ522-22-22-22-22002i−2i2i−2i002-22-22-2-2−22−22−22−2200i2−i2i2−i2002i−2i002i−2i0000−22−22−22−22i2i2−i2−i2i2i2−i2−i2−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−ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4300000000000000000000
χ532-22-22-22-2200−2i2i−2i2i002-22-22-2-22−22−22−22−200i2−i2i2−i200−2i2i00−2i2i00002−22−22−22−2i2i2−i2−i2i2i2−i2−i2−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−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ4700000000000000000000
χ542-22-22-22-2200−2i2i−2i2i002-22-22-2-22−22−22−22−200i2−i2i2−i200−2i2i00−2i2i00002−22−22−22−2i2i2−i2−i2i2i2−i2−i2ζ25−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+ζ43ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ4700000000000000000000
χ552-22-22-22-2200−2i2i−2i2i002-22-22-2-2−22−22−22−2200−i2i2−i2i200−2i2i00−2i2i0000−22−22−22−22−i2−i2i2i2−i2−i2i2i2ζ11−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+ζ47ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ43ζ25+ζ31+ζ41+ζ47−ζ25−ζ31−ζ41−ζ47ζ11+ζ13+ζ29+ζ43−ζ11−ζ13−ζ29−ζ4300000000000000000000
χ562-22-22-22-2200−2i2i−2i2i002-22-22-2-2−22−22−22−2200−i2i2−i2i200−2i2i00−2i2i0000−22−22−22−22−i2−i2i2i2−i2−i2i2i2−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−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ43−ζ25−ζ31−ζ41−ζ47ζ25+ζ31+ζ41+ζ47−ζ11−ζ13−ζ29−ζ43ζ11+ζ13+ζ29+ζ4300000000000000000000
χ572-2-2222-2-22-2-2000022-2-2-2222-222-2-2-2-222000000-2-2000000002222-2-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ582-2-2222-2-22-2-2000022-2-2-2222-222-2-2-2-222000000-2-2000000002222-2-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ592-2-2222-2-22-2-2000022-2-2-2222-2-2-22222-2-2000000-2-20000000022-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i
χ602-2-2222-2-22-2-2000022-2-2-2222-2-2-22222-2-2000000-2-20000000022-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i
χ612-2-2-2-22222002-2-22002-2-2-2-2222−2−222−2−2200−222−2002-200-2200002−22−2−22−22−2−22222−2−2−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ4300000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.