Finite Group Databasebeta

← Group #10714442

Character table — Group #10714442

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444666888812121212668812121616161616161616242424242424242448484848484848484848484848484848888824242424242424242488161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222222-2-2-2-2222222-2-22200000000-2-2-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ1022222222222222-2-2-2-2222222-2-22200000000-2-2-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ112222222-2-2-2-22220000-2-2-2-22200-2-22222−2−2−2−20000000022222222−2−2−2−2−2−2−2−2000000000000002i−2i−i2−i2i2i20000
χ122222222-2-2-2-22220000-2-2-2-22200-2-22222−2−2−2−20000000022222222−2−2−2−2−2−2−2−200000000000000−2i2ii2i2−i2−i20000
χ132222222-2-2-2-22220000-2-2-2-22200-2-2−2−2−2−2222200000000−2−2−2−2−2−2−2−222222222000000000000002i−2ii2i2−i2−i20000
χ142222222-2-2-2-22220000-2-2-2-22200-2-2−2−2−2−2222200000000−2−2−2−2−2−2−2−22222222200000000000000−2i2i−i2−i2i2i20000
χ15222222-12222-1-1-12222-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ192222-2-222-22-222200002222-2-200-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−20000000000002-2002−22−20000
χ202222-2-222-22-222200002222-2-200-2-222−2−222−2−2000000002222−2−2−2−22222−2−2−2−2000000000000-2200−22−220000
χ212222-2-222-22-222200002222-2-200-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−222220000000000002-200−22−220000
χ222222-2-222-22-222200002222-2-200-2-2−2−222−2−22200000000−2−2−2−22222−2−2−2−22222000000000000-22002−22−20000
χ232222-2-22-22-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ242222-2-22-22-222222222-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ252222-2-22-22-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-22222-2-2000000000000000000000000000000002i−2i−2i2i0000
χ262222-2-22-22-22222-2-2-2-2-2-2-2-2-2-2222200000000-2-22222-2-200000000000000000000000000000000−2i2i2i−2i0000
χ272222-2-2-1-22-22-1-1-12222111111-2-2-1-122-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-1000033−3−333−3−3000000000000
χ282222-2-2-1-22-22-1-1-12222111111-2-2-1-122-2-2-2-222-1-11111-1-1-1-1-1-111111111-1-1-1-10000−3−333−3−333000000000000
χ292222-2-2-1-22-22-1-1-12222111111-2-2-1-1-2-22222-2-2-1-11111-1-11111-1-1-1-1-1-1-1-11111000033−3−3−3−333000000000000
χ302222-2-2-1-22-22-1-1-12222111111-2-2-1-1-2-22222-2-2-1-11111-1-11111-1-1-1-1-1-1-1-111110000−3−33333−3−3000000000000
χ312-2-222-222-2-22-2-2222-2-222-2-22-22-2-2200000000-2-222-2-22200000000000000002i−2i002i−2i2i−2i0000000000000000
χ322-2-222-222-2-22-2-2222-2-222-2-22-22-2-2200000000-2-222-2-2220000000000000000−2i2i00−2i2i−2i2i0000000000000000
χ332-2-222-222-2-22-2-22-2-22222-2-22-2-22-220000000022-2-222-2-20000000000000000000000000000000000002i−2i00
χ342-2-222-222-2-22-2-22-2-22222-2-22-2-22-220000000022-2-222-2-2000000000000000000000000000000000000−2i2i00
χ352-2-222-2-12-2-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32i−2i00−ii−ii3−33−3000000000000
χ362-2-222-2-12-2-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−2i2i00i−ii−i−33−33000000000000
χ372-2-222-2-12-2-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32i−2i00−ii−ii−33−33000000000000
χ382-2-222-2-12-2-2211-122-2-2-1-111-112-21-10000000011-1-111-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−2i2i00i−ii−i3−33−3000000000000
χ392-2-22-222-2-222-2-2222-2-2-2-222-22-22-2200000000-2-2-2-222220000000000000000002-200002-2-22000000000000
χ402-2-22-222-2-222-2-2222-2-2-2-222-22-22-2200000000-2-2-2-22222000000000000000000-220000-222-2000000000000
χ412-2-22-222-2-222-2-22-2-222-2-222-222-2-22000000002222-2-2-2-2000000000000000000000000000000000000002-2
χ422-2-22-222-2-222-2-22-2-222-2-222-222-2-22000000002222-2-2-2-200000000000000000000000000000000000000-22
χ432-2-22-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3002-2−i3i3i3−i3-111-1000000000000
χ442-2-22-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300-22i3−i3−i3i31-1-11000000000000
χ452-2-22-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3002-2i3−i3−i3i3-111-1000000000000
χ462-2-22-22-1-2-22211-122-2-211-1-11-1-221-1000000001111-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300-22−i3i3i3−i31-1-11000000000000
χ47444444-24444-2-2-2-4-4-4-4-2-2-2-2-2-2-4-4-2-200000000222222220000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-200002222-2-2002222222222−22−22−22−2200000000−2−2−2−2−2−2−2−222222222000000000000000000000000
χ49444444-2-4-4-4-4-2-2-200002222-2-20022−22−22−22−22222222220000000022222222−2−2−2−2−2−2−2−2000000000000000000000000
χ504444-4-4-24-44-4-2-2-20000-2-2-2-22200222222−22−222222−22−2200000000−2−2−2−22222−2−2−2−22222000000000000000000000000
χ514444-4-4-24-44-4-2-2-20000-2-2-2-2220022−22−222222−22−222222000000002222−2−2−2−22222−2−2−2−2000000000000000000000000
χ524444-4-4-2-44-44-2-2-2-4-4-4-422222244-2-20000000022-2-2-2-2220000000000000000000000000000000000000000
χ5344-4-400400004-4-422−2222−220000000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470022−22000022−2200002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ470000000000000000000000000000
χ5444-4-400400004-4-422−2222−22000000000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470022−22000022−220000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ470000000000000000000000000000
χ5544-4-400400004-4-4−2222−2222000000000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300−22220000−22220000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000000000000000000000000000
χ5644-4-400400004-4-4−2222−22220000000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300−22220000−222200002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000000000000000000000000000
χ5744-4-400-20000-22222−2222−2223−2323−23000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700−226−66−6−22−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−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−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47000000000000000000000000
χ5844-4-400-20000-22222−2222−2223−2323−2300000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700−226−66−6−22ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−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−ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47000000000000000000000000
χ5944-4-400-20000-22222−2222−22−2323−2323000000002ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700−22−66−66−22ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43−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+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47000000000000000000000000
χ6044-4-400-20000-22222−2222−22−2323−232300000000−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700−22−66−66−22−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43ζ11−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−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47000000000000000000000000
χ6144-4-400-20000-222−2222−222223−2323−2300000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43002−2−66−662−2ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43000000000000000000000000
χ6244-4-400-20000-222−2222−222223−2323−23000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43002−2−66−662−2−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−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+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43000000000000000000000000
χ6344-4-400-20000-222−2222−2222−2323−232300000000−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43002−26−66−62−2−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ25−ζ31+ζ41−ζ47−ζ25+ζ31−ζ41+ζ47ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13−ζ29+ζ43−ζ11+ζ13+ζ29−ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43000000000000000000000000
χ6444-4-400-20000-222−2222−2222−2323−2323000000002ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ43002−26−66−62−2ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47ζ25+ζ31−ζ41−ζ47−ζ25−ζ31+ζ41+ζ47−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−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43−ζ11+ζ13−ζ29+ζ43ζ11−ζ13+ζ29−ζ43000000000000000000000000
χ654-44-40040000-44-422−22−222200000000002ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ430000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47−2222000022−222ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47000000000000000000000000
χ664-44-40040000-44-422−22−22220000000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4300002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2222000022−22−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000002ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ47−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ47000000000000000000000000
χ674-44-40040000-44-4−222222−220000000000−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ470000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ4322−220000−2222−2ζ25−2ζ31−2ζ41−2ζ472ζ25+2ζ31+2ζ41+2ζ472ζ25+2ζ31+2ζ41+2ζ47−2ζ25−2ζ31−2ζ41−2ζ4700000000−2ζ11−2ζ13−2ζ29−2ζ432ζ11+2ζ13+2ζ29+2ζ432ζ11+2ζ13+2ζ29+2ζ43−2ζ11−2ζ13−2ζ29−2ζ43000000000000000000000000
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χ844-4-44-44-2-4-44422-2-4-44422-2-22-24-42-200000000-2-2-2-222220000000000000000000000000000000000000000

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