Finite Group Databasebeta

← Group #10713293

Character table — Group #10713293

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order122244442234444446668888888812121212121212121212121244668888121212121212242424242424242424242424242424248888888824242424242424242424242424242424161616161616161616161616161616168888
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
χ511111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-1111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1i−ii−i
χ101111-1-1-1-1-1-1111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ii−ii
χ111111-1-1-1-1-1-1111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ii−ii
χ121111-1-1-1-1-1-1111-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111i−ii−i
χ131111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111i−i−ii
χ141111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−iii−i
χ151111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−iii−i
χ161111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1i−i−ii
χ1722222222222222222222-2-2-2-2-2-2-2-22222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ192222222222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ202222222222-1222222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ212222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ222222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ232222222222-1-2-2-2-222-1-1-12222222211111111-1-1-1-1-2-2-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ242222222222-1-2-2-2-222-1-1-12222222211111111-1-1-1-1-2-2-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ252222222222-1-2-2-2-222-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-2-2-1-122221111-1-111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ262222222222-1-2-2-2-222-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-2-2-1-122221111-1-111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-2-222222-2-222200000000222222222222-2-2-2-20000-2-2-2-2-2-2000000000000000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ2822222222-2-222222-2-222200000000222222222222-2-2-2-20000-2-2-2-2-2-20000000000000000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2922222222-2-22-2-2-2-2-2-222200000000-2-2-2-2-2-2-2-2222222-2-200002222-2-2000000000000000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ3022222222-2-22-2-2-2-2-2-222200000000-2-2-2-2-2-2-2-2222222-2-200002222-2-20000000000000000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ312222-2-2-2-222222-2-2-2-2222000000002222-2-2-2-2-2-2-2-2-22220000-2-222-2-2000000000000000000000000000000000000000022−2−2−2−22222−2−2−2−2220000
χ322222-2-2-2-222222-2-2-2-2222000000002222-2-2-2-2-2-2-2-2-22220000-2-222-2-20000000000000000000000000000000000000000−2−22222−2−2−2−22222−2−20000
χ332222-2-2-2-2222-2-222-2-222200000000-2-2-2-22222-2-2-2-22-222000022-2-2-2-2000000000000000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ342222-2-2-2-2222-2-222-2-222200000000-2-2-2-22222-2-2-2-22-222000022-2-2-2-20000000000000000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ352222-2-2-2-2-2-2222-2-222222-2-22222-2-22222-2-2-2-2-2-2-2-22-2-2-2-2-22222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-22222222-2-22222-2-2-2-2-2-22222-2-2-2-2-22-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-122-2-222-1-1-122-2-2-2-222-1-1-1-1111111112-21122-2-2-1-111-1-1-1-1-1-11111-1-1-1-111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
χ382222-2-2-2-2-2-2-122-2-222-1-1-122-2-2-2-222-1-1-1-1111111112-21122-2-2-1-111-1-1-1-1-1-11111-1-1-1-11111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000
χ392222-2-2-2-2-2-2-122-2-222-1-1-1-2-22222-2-2-1-1-1-1111111112-211-2-222-1-111-1-11111-1-1-1-11111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ402222-2-2-2-2-2-2-122-2-222-1-1-1-2-22222-2-2-1-1-1-1111111112-211-2-222-1-111-1-11111-1-1-1-11111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ412222-2-2-2-2-2-2-1-2-22222-1-1-122-2-2-2-2221111-1-1-1-11111-2211-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ422222-2-2-2-2-2-2-1-2-22222-1-1-122-2-2-2-2221111-1-1-1-11111-2211-2-22211-1-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ432222-2-2-2-2-2-2-1-2-22222-1-1-1-2-22222-2-21111-1-1-1-11111-221122-2-211-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−300000000000000000000
χ442222-2-2-2-2-2-2-1-2-22222-1-1-1-2-22222-2-21111-1-1-1-11111-221122-2-211-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−33300000000000000000000
χ4522-2-222-2-22-2200002-22-2-22222-2-2-2-20000000022-2-2002-2000000002-222-2-222-2-2000000002-22-200002-22-22-22-20000000000000000000000000000
χ4622-2-222-2-22-2200002-22-2-22222-2-2-2-20000000022-2-2002-2000000002-222-2-222-2-200000000-22-220000-22-22-22-220000000000000000000000000000
χ4722-2-222-2-22-2200002-22-2-2-2-2-2-222220000000022-2-2002-2000000002-2-2-222-2-2220000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ4822-2-222-2-22-2200002-22-2-2-2-2-2-222220000000022-2-2002-2000000002-2-2-222-2-222000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ4922-2-222-2-22-2-100002-2-1112222-2-2-2-233−3−333−3−3-1-11100-1100003−33−3-11-1-111-1-11133−3−333−3−32-22-20000-11-11-11-113−3−333−3−3300000000000000000000
χ5022-2-222-2-22-2-100002-2-1112222-2-2-2-233−3−333−3−3-1-11100-1100003−33−3-11-1-111-1-11133−3−333−3−3-22-2200001-11-11-11-1−333−3−333−300000000000000000000
χ5122-2-222-2-22-2-100002-2-1112222-2-2-2-2−3−333−3−333-1-11100-110000−33−33-11-1-111-1-111−3−333−3−3332-22-20000-11-11-11-11−333−3−333−300000000000000000000
χ5222-2-222-2-22-2-100002-2-1112222-2-2-2-2−3−333−3−333-1-11100-110000−33−33-11-1-111-1-111−3−333−3−333-22-2200001-11-11-11-13−3−333−3−3300000000000000000000
χ5322-2-222-2-22-2-100002-2-111-2-2-2-2222233−3−333−3−3-1-11100-1100003−33−3-1111-1-111-1-1−3−333−3−33300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii00000000000000000000
χ5422-2-222-2-22-2-100002-2-111-2-2-2-2222233−3−333−3−3-1-11100-1100003−33−3-1111-1-111-1-1−3−333−3−3330000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i00000000000000000000
χ5522-2-222-2-22-2-100002-2-111-2-2-2-22222−3−333−3−333-1-11100-110000−33−33-1111-1-111-1-133−3−333−3−300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii00000000000000000000
χ5622-2-222-2-22-2-100002-2-111-2-2-2-22222−3−333−3−333-1-11100-110000−33−33-1111-1-111-1-133−3−333−3−30000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i00000000000000000000
χ5722-2-2-2-222-22200002-22-2-222-2-222-2-200000000-2-22200-22000000002-222-2-2-2-222000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ5822-2-2-2-222-22200002-22-2-222-2-222-2-200000000-2-22200-22000000002-222-2-2-2-22200000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ5922-2-2-2-222-22200002-22-2-2-2-222-2-22200000000-2-22200-22000000002-2-2-22222-2-20000000000002-2-22000000002-22-2-22-2200000000000000000000
χ6022-2-2-2-222-22200002-22-2-2-2-222-2-22200000000-2-22200-22000000002-2-2-22222-2-2000000000000-222-200000000-22-222-22-200000000000000000000
χ6122-2-2-2-222-22-100002-2-11122-2-222-2-233−3−3−3−33311-1-1001-100003−3−33-11-1-11111-1-133−3−3−3−3332i−2i−2i2i0000−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i300000000000000000000
χ6222-2-2-2-222-22-100002-2-11122-2-222-2-233−3−3−3−33311-1-1001-100003−3−33-11-1-11111-1-133−3−3−3−333−2i2i2i−2i0000i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i300000000000000000000
χ6322-2-2-2-222-22-100002-2-11122-2-222-2-2−3−33333−3−311-1-1001-10000−333−3-11-1-11111-1-1−3−33333−3−32i−2i−2i2i0000−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i300000000000000000000
χ6422-2-2-2-222-22-100002-2-11122-2-222-2-2−3−33333−3−311-1-1001-10000−333−3-11-1-11111-1-1−3−33333−3−3−2i2i2i−2i0000i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i300000000000000000000
χ6522-2-2-2-222-22-100002-2-111-2-222-2-22233−3−3−3−33311-1-1001-100003−3−33-1111-1-1-1-111−3−33333−3−300002-2-22−333−33−3−33-11-111-11-100000000000000000000
χ6622-2-2-2-222-22-100002-2-111-2-222-2-22233−3−3−3−33311-1-1001-100003−3−33-1111-1-1-1-111−3−33333−3−30000-222-23−3−33−333−31-11-1-11-1100000000000000000000
χ6722-2-2-2-222-22-100002-2-111-2-222-2-222−3−33333−3−311-1-1001-10000−333−3-1111-1-1-1-11133−3−3−3−33300002-2-223−3−33−333−3-11-111-11-100000000000000000000
χ6822-2-2-2-222-22-100002-2-111-2-222-2-222−3−33333−3−311-1-1001-10000−333−3-1111-1-1-1-11133−3−3−3−3330000-222-2−333−33−3−331-11-1-11-1100000000000000000000
χ692-22-22i−2i2i−2i0022-22i−2i00-22-22−2−i2i2−i2i22−22-22-22i−2i2i−2i2i−2i2i−2i00002−2−i2i20000002−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000000000000000−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−ζ47−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−ζ470000
χ702-22-22i−2i2i−2i0022-22i−2i00-22-22−2−i2i2−i2i22−22-22-22i−2i2i−2i2i−2i2i−2i00002−2−i2i20000002−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000000000000000ζ25+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+ζ47ζ25+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+ζ470000
χ712-22-22i−2i2i−2i0022-22i−2i00-22-2−22i2−i2i2−i2−222-22-22i−2i2i−2i2i−2i2i−2i0000−22i2−i2000000−22−22i2−i2i2−i2−22−22i2−i2i2−i2000000000000000000000000ζ11+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+ζ43ζ11+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+ζ430000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.