Finite Group Databasebeta

← Group #10713291

Character table — Group #10713291

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order122244442234444446668888888812121212446688881212121212121212121224242424242424242424242424242424161616161616161616161616161616168888242424242424242488888888
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
χ511111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111-1-1-1-111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-11-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-11-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-11-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-11-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1-11-1-1111111111-1-1-1-111-1-1-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-1222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ202222222222-1222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ212222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ222222222222-1222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ232222222222-1-2-2-2-222-1-1-122222222-1-1-1-1-2-2-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-1111100000000
χ242222222222-1-2-2-2-222-1-1-122222222-1-1-1-1-2-2-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-100000000
χ252222222222-1-2-2-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-1-1222211111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ262222222222-1-2-2-2-222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-1-1222211111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ2722222222-2-222222-2-2222000000002222-2-2-2-2000022-2-222-2-2-2-2000000000000000022−2−222−2−222−2−222−2−200000000000000000000
χ2822222222-2-222222-2-2222000000002222-2-2-2-2000022-2-222-2-2-2-20000000000000000−2−222−2−222−2−222−2−22200000000000000000000
χ2922222222-2-22-2-2-2-2-2-222200000000222222-2-20000-2-222-2-222-2-2000000000000000022−2−222−2−2−2−222−2−22200000000000000000000
χ3022222222-2-22-2-2-2-2-2-222200000000222222-2-20000-2-222-2-222-2-20000000000000000−2−222−2−22222−2−222−2−200000000000000000000
χ312222-2-2-2-222222-2-2-2-222200000000-2-2-2-2-2222000022-2-2-2-222-2-2000000000000000022−2−2−2−22222−2−2−2−22200000000000000000000
χ322222-2-2-2-222222-2-2-2-222200000000-2-2-2-2-2222000022-2-2-2-222-2-20000000000000000−2−22222−2−2−2−22222−2−200000000000000000000
χ332222-2-2-2-2222-2-222-2-222200000000-2-2-2-22-2220000-2-22222-2-2-2-2000000000000000022−2−2−2−222−2−22222−2−200000000000000000000
χ342222-2-2-2-2222-2-222-2-222200000000-2-2-2-22-2220000-2-22222-2-2-2-20000000000000000−2−22222−2−222−2−2−2−22200000000000000000000
χ352222-2-2-2-2-2-2222-2-222222-2-22222-2-2-2-2-2-22-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-22222222-2-22222-2-2-2-2-2-2-22-2-222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-122-2-222-1-1-122-2-2-2-22211112-21122-2-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii00000000
χ382222-2-2-2-2-2-2-122-2-222-1-1-122-2-2-2-22211112-21122-2-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i00000000
χ392222-2-2-2-2-2-2-122-2-222-1-1-1-2-22222-2-211112-211-2-222-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−3−333−3−3300000000
χ402222-2-2-2-2-2-2-122-2-222-1-1-1-2-22222-2-211112-211-2-222-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−333−3−333−300000000
χ412222-2-2-2-2-2-2-1-2-22222-1-1-122-2-2-2-2221111-2211-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i00000000
χ422222-2-2-2-2-2-2-1-2-22222-1-1-122-2-2-2-2221111-2211-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii00000000
χ432222-2-2-2-2-2-2-1-2-22222-1-1-1-2-22222-2-21111-221122-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−300000000
χ442222-2-2-2-2-2-2-1-2-22222-1-1-1-2-22222-2-21111-221122-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−3300000000
χ4522-2-222-2-22-2200002-22-2-22222-2-2-2-222-2-2002-20000000000002-222-2-222-2-20000000000000000000000000000000000002-22-20000
χ4622-2-222-2-22-2200002-22-2-22222-2-2-2-222-2-2002-20000000000002-222-2-222-2-2000000000000000000000000000000000000-22-220000
χ4722-2-222-2-22-2200002-22-2-2-2-2-2-2222222-2-2002-20000000000002-2-2-222-2-22200000000000000000000000000000000000000002i−2i2i−2i
χ4822-2-222-2-22-2200002-22-2-2-2-2-2-2222222-2-2002-20000000000002-2-2-222-2-2220000000000000000000000000000000000000000−2i2i−2i2i
χ4922-2-2-2-222-22200002-22-2-222-2-222-2-2-2-22200-220000000000002-222-2-2-2-2220000000000000000000000000000000000002i−2i−2i2i0000
χ5022-2-2-2-222-22200002-22-2-222-2-222-2-2-2-22200-220000000000002-222-2-2-2-222000000000000000000000000000000000000−2i2i2i−2i0000
χ5122-2-2-2-222-22200002-22-2-2-2-222-2-222-2-22200-220000000000002-2-2-22222-2-200000000000000000000000000000000000000002-2-22
χ5222-2-2-2-222-22200002-22-2-2-2-222-2-222-2-22200-220000000000002-2-2-22222-2-20000000000000000000000000000000000000000-222-2
χ532-22-22i−2i2i−2i0022-22i−2i00-22-22−2−i2i2−i2i22−22i−2i2i−2i00002−2−i2i22-2002i−2i00002−22−2−i2i2−i2i222−2−2−i2−i2i2i2−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−ζ4700000000000000000000
χ542-22-22i−2i2i−2i0022-22i−2i00-22-22−2−i2i2−i2i22−22i−2i2i−2i00002−2−i2i22-2002i−2i00002−22−2−i2i2−i2i222−2−2−i2−i2i2i2ζ25+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+ζ4700000000000000000000
χ552-22-22i−2i2i−2i0022-22i−2i00-22-2−22i2−i2i2−i2−222i−2i2i−2i0000−22i2−i22-2002i−2i0000−22−22i2−i2i2−i2−2−222i2i2−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+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+ζ4300000000000000000000
χ562-22-22i−2i2i−2i0022-22i−2i00-22-2−22i2−i2i2−i2−222i−2i2i−2i0000−22i2−i22-2002i−2i0000−22−22i2−i2i2−i2−2−222i2i2−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−ζ43−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−ζ4300000000000000000000
χ572-22-22i−2i2i−2i002-22−2i2i00-22-22−2−i2i2−i2i22−22i−2i2i−2i0000−22i2−i2-2200−2i2i00002−22−2−i2i2−i2i2−2−222i2i2−i2−i2−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−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+ζ4700000000000000000000
χ582-22-22i−2i2i−2i002-22−2i2i00-22-22−2−i2i2−i2i22−22i−2i2i−2i0000−22i2−i2-2200−2i2i00002−22−2−i2i2−i2i2−2−222i2i2−i2−i2ζ25+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−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−ζ4700000000000000000000
χ592-22-22i−2i2i−2i002-22−2i2i00-22-2−22i2−i2i2−i2−222i−2i2i−2i00002−2−i2i2-2200−2i2i0000−22−22i2−i2i2−i222−2−2−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+ζ43−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−ζ4300000000000000000000
χ602-22-22i−2i2i−2i002-22−2i2i00-22-2−22i2−i2i2−i2−222i−2i2i−2i00002−2−i2i2-2200−2i2i0000−22−22i2−i2i2−i222−2−2−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−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+ζ4300000000000000000000
χ612-22-2−2i2i−2i2i0022-2−2i2i00-22-22−2i2−i2i2−i22−2−2i2i−2i2i00002−2i2−i22-200−2i2i00002−22−2i2−i2i2−i222−2−2i2i2−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−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+ζ4700000000000000000000
χ622-22-2−2i2i−2i2i0022-2−2i2i00-22-22−2i2−i2i2−i22−2−2i2i−2i2i00002−2i2−i22-200−2i2i00002−22−2i2−i2i2−i222−2−2i2i2−i2−i2ζ25+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−ζ47ζ25+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−ζ4700000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.