Finite Group Databasebeta

← Group #10712984

Character table — Group #10712984

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order1222222234444444466666668888888812121212121212124488881212121212121212242424242424242424242424242424244444444412121212121212121212121212121212161616161616161616161616161616162244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ911-11-1-11-111-1ii−i−i1-11-11-1-11-111-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i
χ1011-11-1-11-111-1ii−i−i1-11-11-1-11-111-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii
χ1111-11-1-11-111-1ii−i−i1-11-11-1-11-111-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11−ii
χ1211-11-1-11-111-1ii−i−i1-11-11-1-11-111-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii1-1i−i
χ1311-11-1-11-111-1−i−iii1-11-11-1-11-111-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii
χ1411-11-1-11-111-1−i−iii1-11-11-1-11-111-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11i−i
χ1511-11-1-11-111-1−i−iii1-11-11-1-11-111-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11i−i
χ1611-11-1-11-111-1−i−iii1-11-11-1-11-111-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i1-1−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ19222222222-2-22222-2-222222220000000022222222-2-20000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222-2-22222-2-222222220000000022222222-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-2220000-2-22222-2-2000000000000000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-2220000-2-22222-2-20000000000000000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-12222222211111111-2-2-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ2922222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3122-22-2-22-222-22i2i−2i−2i2-22-22-2-22-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i2i−2i−2i−2i2i2i2-22i2i−2i−2i2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000
χ3222-22-2-22-222-2−2i−2i2i2i2-22-22-2-22-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i−2i2i2i2i−2i−2i2-2−2i−2i2i2i2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000
χ3322-22-2-22-22-222i2i−2i−2i-222-22-2-22-2000000002i2i2i2i−2i−2i−2i−2i−2i2i0000-22−2i−2i2i2i-22000000000000000000000000000000000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i20000
χ3422-22-2-22-22-222i2i−2i−2i-222-22-2-22-2000000002i2i2i2i−2i−2i−2i−2i−2i2i0000-22−2i−2i2i2i-220000000000000000000000000000000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000
χ3522-22-2-22-22-22−2i−2i2i2i-222-22-2-22-200000000−2i−2i−2i−2i2i2i2i2i2i−2i0000-222i2i−2i−2i-22000000000000000000000000000000000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i20000
χ3622-22-2-22-22-22−2i−2i2i2i-222-22-2-22-200000000−2i−2i−2i−2i2i2i2i2i2i−2i0000-222i2i−2i−2i-220000000000000000000000000000000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000
χ3722-22-2-22-2-12-22i2i−2i−2i2-2-11-111-1122-2-222-2-2−i−i−i−iiiii2i−2i2i2i−2i−2i-11−i−iii-11-1-1-1-11111−i−i−i−iiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii00000000000000000000
χ3822-22-2-22-2-12-22i2i−2i−2i2-2-11-111-1122-2-222-2-2−i−i−i−iiiii2i−2i2i2i−2i−2i-11−i−iii-11-1-1-1-11111−i−i−i−iiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i00000000000000000000
χ3922-22-2-22-2-12-22i2i−2i−2i2-2-11-111-11-2-222-2-222−i−i−i−iiiii2i−2i−2i−2i2i2i-11−i−iii-111111-1-1-1-1iiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−33300000000000000000000
χ4022-22-2-22-2-12-22i2i−2i−2i2-2-11-111-11-2-222-2-222−i−i−i−iiiii2i−2i−2i−2i2i2i-11−i−iii-111111-1-1-1-1iiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−300000000000000000000
χ4122-22-2-22-2-12-2−2i−2i2i2i2-2-11-111-1122-2-222-2-2iiii−i−i−i−i−2i2i−2i−2i2i2i-11ii−i−i-11-1-1-1-11111iiii−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i00000000000000000000
χ4222-22-2-22-2-12-2−2i−2i2i2i2-2-11-111-1122-2-222-2-2iiii−i−i−i−i−2i2i−2i−2i2i2i-11ii−i−i-11-1-1-1-11111iiii−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii00000000000000000000
χ4322-22-2-22-2-12-2−2i−2i2i2i2-2-11-111-11-2-222-2-222iiii−i−i−i−i−2i2i2i2i−2i−2i-11ii−i−i-111111-1-1-1-1−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−300000000000000000000
χ4422-22-2-22-2-12-2−2i−2i2i2i2-2-11-111-11-2-222-2-222iiii−i−i−i−i−2i2i2i2i−2i−2i-11ii−i−i-111111-1-1-1-1−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−33300000000000000000000
χ452-222-2-2-222-2200002-2-222-2-2-222222-2-2-2-200000000000000-2200002-222-2-222-2-2000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ462-222-2-2-222-2200002-2-222-2-2-222222-2-2-2-200000000000000-2200002-222-2-222-2-200000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ472-222-2-2-222-2200002-2-222-2-2-22-2-2-2-2222200000000000000-2200002-2-2-222-2-2220000000000002-22-2000000002-22-22-22-200000000000000000000
χ482-222-2-2-222-2200002-2-222-2-2-22-2-2-2-2222200000000000000-2200002-2-2-222-2-222000000000000-22-2200000000-22-22-22-2200000000000000000000
χ492-222-2-2-22-1-2200002-21-1-1111-12222-2-2-2-233−3−333−3−30000001-13−33−3-11-1-111-1-11133−3−333−3−32i−2i2i−2i0000−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i300000000000000000000
χ502-222-2-2-22-1-2200002-21-1-1111-12222-2-2-2-233−3−333−3−30000001-13−33−3-11-1-111-1-11133−3−333−3−3−2i2i−2i2i0000i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i300000000000000000000
χ512-222-2-2-22-1-2200002-21-1-1111-12222-2-2-2-2−3−333−3−3330000001-1−33−33-11-1-111-1-111−3−333−3−3332i−2i2i−2i0000−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i300000000000000000000
χ522-222-2-2-22-1-2200002-21-1-1111-12222-2-2-2-2−3−333−3−3330000001-1−33−33-11-1-111-1-111−3−333−3−333−2i2i−2i2i0000i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i300000000000000000000
χ532-222-2-2-22-1-2200002-21-1-1111-1-2-2-2-2222233−3−333−3−30000001-13−33−3-1111-1-111-1-1−3−333−3−33300002-22-23−3−333−3−33-11-11-11-1100000000000000000000
χ542-222-2-2-22-1-2200002-21-1-1111-1-2-2-2-2222233−3−333−3−30000001-13−33−3-1111-1-111-1-1−3−333−3−3330000-22-22−333−3−333−31-11-11-11-100000000000000000000
χ552-222-2-2-22-1-2200002-21-1-1111-1-2-2-2-22222−3−333−3−3330000001-1−33−33-1111-1-111-1-133−3−333−3−300002-22-2−333−3−333−3-11-11-11-1100000000000000000000
χ562-222-2-2-22-1-2200002-21-1-1111-1-2-2-2-22222−3−333−3−3330000001-1−33−33-1111-1-111-1-133−3−333−3−30000-22-223−3−333−3−331-11-11-11-100000000000000000000
χ572-22-22-22-22002i−2i2i−2i00-22-22-22-22−22−22−22−22i−2i2i−2i2i−2i2i−2i00−i2i2−i2i2000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000−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+ζ470000
χ582-22-22-22-22002i−2i2i−2i00-22-22-22-22−22−22−22−22i−2i2i−2i2i−2i2i−2i00−i2i2−i2i2000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000000000000000000000ζ25−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−ζ470000
χ592-22-22-22-22002i−2i2i−2i00-22-22-22-2−22−22−22−222i−2i2i−2i2i−2i2i−2i00i2−i2i2−i200000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000ζ11−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+ζ430000
χ602-22-22-22-22002i−2i2i−2i00-22-22-22-2−22−22−22−222i−2i2i−2i2i−2i2i−2i00i2−i2i2−i200000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000000000000000000000−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−ζ430000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.