Finite Group Databasebeta

← Group #10709366

Character table — Group #10709366

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444444444444444444444444444424242424242424242424242424242424323232323232
order122234444666888888884888888881212121212122424242424242424242424242424242424242424242424242244888816161616161616164412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111-1-1-1-111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ611111111111111-1-1-1-111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ711111111111111-1-1-1-111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ811111111111111-1-1-1-111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1
χ9222222222222-2-22222-2-22-2-222-2-2-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000
χ10222222222222-2-2-2-2-2-2-2-22-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000
χ11222222-2-2222200222200-200-2-2000022-2-2-2-2000000002222-2-2-2-2000000000000000022−2−222−2−2000000
χ12222222-2-2222200222200-200-2-2000022-2-2-2-2000000002222-2-2-2-20000000000000000−2−222−2−222000000
χ13222222-2-2222200-2-2-2-200-20022000022-2-2-2-200000000-2-2-2-22222000000000000000022−2−2−2−222000000
χ14222222-2-2222200-2-2-2-200-20022000022-2-2-2-200000000-2-2-2-222220000000000000000−2−22222−2−2000000
χ1522222-222-222222000022-2-2-2000000-2-2-2-2222222-2-2-2-2000000000000000022-2-2000000000000000000
χ1622222-222-222222000022-2-2-2000000-2-2-2-2222222-2-2-2-20000000000000000-2-222000000000000000000
χ1722222-222-2222-2-20000-2-2-222000000-2-2-2-222-2-2-2-22222000000000000000000002i2i−2i−2i00000000000000
χ1822222-222-2222-2-20000-2-2-222000000-2-2-2-222-2-2-2-2222200000000000000000000−2i−2i2i2i00000000000000
χ192222-12222-1-1-122222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1
χ202222-12222-1-1-122222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111
χ212222-12222-1-1-122-2-2-2-222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000002-2-1-111
χ222222-12222-1-1-122-2-2-2-222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2211-1-1
χ232222-12222-1-1-1-2-22222-2-22-2-222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000−i3i3−i3i3
χ242222-12222-1-1-1-2-22222-2-22-2-222-2-2-2-2-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000000000i3−i3i3−i3
χ252222-12222-1-1-1-2-2-2-2-2-2-2-22-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000−i3i3i3−i3
χ262222-12222-1-1-1-2-2-2-2-2-2-2-22-2-2-2-22222-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000000000i3−i3−i3i3
χ272-22-22-20022-2-22−222-2-22−202−20022−2−22-2000022−2−222−2−222-2-200002222−2−2−2−200000000−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−ζ43000000
χ282-22-22-20022-2-22−222-2-22−202−20022−2−22-2000022−2−222−2−222-2-200002222−2−2−2−200000000ζ25+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+ζ43000000
χ292-22-22-20022-2-22−2-2-2222−202−200−2−2222-2000022−2−222−2−2-2-2220000−2−2−2−2222200000000−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+ζ43000000
χ302-22-22-20022-2-22−2-2-2222−202−200−2−2222-2000022−2−222−2−2-2-2220000−2−2−2−2222200000000ζ25+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−ζ43000000
χ312-22-22-20022-2-2−2222-2-2−220−2200−2−2222-20000−2−222−2−22222-2-20000−2−2−2−2222200000000ζ11+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−ζ47000000
χ322-22-22-20022-2-2−2222-2-2−220−2200−2−2222-20000−2−222−2−22222-2-20000−2−2−2−2222200000000−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+ζ47000000
χ332-22-22-20022-2-2−22-2-222−220−220022−2−22-20000−2−222−2−222-2-22200002222−2−2−2−200000000ζ11+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+ζ47000000
χ342-22-22-20022-2-2−22-2-222−220−220022−2−22-20000−2−222−2−222-2-22200002222−2−2−2−200000000−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−ζ47000000
χ352-2-22202-20-2-22222−22−2-2-20002−22−22−200002-22-22-200002−22−222−2−222−2−222−2−2002i−2i−i2i2−i2i200000000000000
χ362-2-22202-20-2-22222−22−2-2-20002−22−22−200002-22-22-200002−22−222−2−222−2−222−2−200−2i2ii2−i2i2−i200000000000000
χ372-2-22202-20-2-2222−22−22-2-2000−22−22−2200002-22-22-20000−22−22−2−222−2−222−2−222002i−2ii2−i2i2−i200000000000000
χ382-2-22202-20-2-2222−22−22-2-2000−22−22−2200002-22-22-20000−22−22−2−222−2−222−2−22200−2i2i−i2i2−i2i200000000000000
χ392-2-22202-20-2-22-2-22−22−2220002−2−22−2200002-2-22-2200002−22−222−2−2−2−222−2−2222-2002−2−2200000000000000
χ402-2-22202-20-2-22-2-22−22−2220002−2−22−2200002-2-22-2200002−22−222−2−2−2−222−2−222-2200−222−200000000000000
χ412-2-22202-20-2-22-2-2−22−2222000−222−22−200002-2-22-220000−22−22−2−22222−2−222−2−22-200−222−200000000000000
χ422-2-22202-20-2-22-2-2−22−2222000−222−22−200002-2-22-220000−22−22−2−22222−2−222−2−2-22002−2−2200000000000000
χ4344444-4-4-4-444400000000400000000-4-444-4-40000000000000000000000000000000000000000000000
χ444444-24-4-44-2-2-200444400-400-4-40000-2-2222200000000-2-2-2-22222000000000000000000000000000000
χ454444-24-4-44-2-2-200-4-4-4-400-400440000-2-22222000000002222-2-2-2-2000000000000000000000000000000
χ464444-2-444-4-2-2-244000044-4-4-40000002222-2-2-2-2-2-2222200000000000000000000000000000000000000
χ474444-2-444-4-2-2-2-4-40000-4-4-4440000002222-2-22222-2-2-2-200000000000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-20000000040000000022-2-2220000000000000000−2i32i3−2i32i3−2i32i3−2i32i30000000000000000000000
χ494444-2-4-4-4-4-2-2-20000000040000000022-2-22200000000000000002i3−2i32i3−2i32i3−2i32i3−2i30000000000000000000000
χ5044-4-440000-44-422−2222−22−2222−2222000002-2-2200000022−22−2222000022−22−2222000022-2-2-2-2220000000000000000000000
χ5144-4-440000-44-422−22−222222−22−222200000-222-200000022−22−22220000−222222−220000-2-22222-2-20000000000000000000000
χ5244-4-440000-44-4−222222−22−222222−2200000-222-2000000−222222−22000022−22−22220000-2-22222-2-20000000000000000000000
χ5344-4-440000-44-4−2222−222222−2222−22000002-2-22000000−222222−220000−222222−22000022-2-2-2-2220000000000000000000000
χ5444-4-4-200002-2222−2222−22−2222−2222000002-2-2200−2i32i300−222−2i6−i6i6−i6−222−2i6−i6i6−i6−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000000000000000000
χ5544-4-4-200002-2222−2222−22−2222−2222000002-2-22002i3−2i300−222−2−i6i6−i6i6−222−2−i6i6−i6i6−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000000000000000000
χ5644-4-4-200002-2222−22−222222−22−222200000-222-200−2i32i300−222−2i6−i6i6−i62−2−22−i6i6−i6i61+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i30000000000000000000000
χ5744-4-4-200002-2222−22−222222−22−222200000-222-2002i3−2i300−222−2−i6i6−i6i62−2−22i6−i6i6−i61−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i30000000000000000000000
χ5844-4-4-200002-22−222222−22−222222−2200000-222-200−2i32i3002−2−22−i6i6−i6i6−222−2i6−i6i6−i61+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i30000000000000000000000
χ5944-4-4-200002-22−222222−22−222222−2200000-222-2002i3−2i3002−2−22i6−i6i6−i6−222−2−i6i6−i6i61−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i30000000000000000000000
χ6044-4-4-200002-22−2222−222222−2222−22000002-2-2200−2i32i3002−2−22−i6i6−i6i62−2−22−i6i6−i6i6−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000000000000000000
χ6144-4-4-200002-22−2222−222222−2222−22000002-2-22002i3−2i3002−2−22i6−i6i6−i62−2−22i6−i6i6−i6−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000000000000000000
χ624-44-44400-44-4-422−22000022−220−2222000000-4400002222−22−22−22−22222200000000000000000000000000000000000000
χ634-44-44400-44-4-4−22220000−2222022−22000000-440000−22−2222222222−22−2200000000000000000000000000000000000000
χ644-44-4-2400-4-22222−22000022−220−22220000002-20000−2−22222−2−20000−2i32i32i3−2i3i6−i6i6−i6−i6i6−i6i60000000000000000000000
χ654-44-4-2400-4-22222−22000022−220−22220000002-20000−2−22222−2−200002i3−2i3−2i32i3−i6i6−i6i6i6−i6i6−i60000000000000000000000
χ664-44-4-2400-4-222−22220000−2222022−220000002-2000022−2−2−2−2220000−2i32i32i3−2i3−i6i6−i6i6i6−i6i6−i60000000000000000000000
χ674-44-4-2400-4-222−22220000−2222022−220000002-2000022−2−2−2−22200002i3−2i3−2i32i3i6−i6i6−i6−i6i6−i6i60000000000000000000000
χ684-44-4-2-4004-22222−2244-4-422−22022−22002222−22−22-220000−2−222−2−222-2-2220000−2−2−2−222220000000000000000000000
χ694-44-4-2-4004-22222−22-4-44422−22022−2200−22−222222-220000−2−222−2−22222-2-200002222−2−2−2−20000000000000000000000
χ704-44-4-2-4004-222−222244-4-4−22220−222200−22−222222-22000022−2−222−2−2-2-22200002222−2−2−2−20000000000000000000000
χ714-44-4-2-4004-222−2222-4-444−22220−2222002222−22−22-22000022−2−222−2−222-2-20000−2−2−2−222220000000000000000000000
χ724-4-4440-440-4-440022−2222−2200000−222200000000-440000000022−2222−22−22−222222000000000000000000000000000000
χ734-4-4440-440-4-4400−2222−22220000022−2200000000-4400000000−2222−22222222−22−22000000000000000000000000000000
χ744-4-44-204-4022-24422−2222−22-4-400022−2222−2222−220000-22-22-220000−22−22−2−222−2−222−2−2220000000000000000000000
χ754-4-44-204-4022-244−2222−2222-4-4000−2222−2222−22220000-22-22-2200002−22−222−2−222−2−222−2−20000000000000000000000
χ764-4-44-204-4022-2-4-422−2222−224400022−22−2222−22220000-222-22-20000−22−22−2−22222−2−222−2−20000000000000000000000
χ774-4-44-204-4022-2-4-4−2222−222244000−222222−2222−220000-222-22-200002−22−222−2−2−2−222−2−2220000000000000000000000
χ784-4-44-20-44022-20022−2222−2200000−2222000000002-20000−2i32i32i3−2i3−22−2222−2−2i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ794-4-44-20-44022-20022−2222−2200000−2222000000002-200002i3−2i3−2i32i3−22−2222−2−2−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ804-4-44-20-44022-200−2222−22220000022−22000000002-20000−2i32i32i3−2i32−22−2−2−222−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ814-4-44-20-44022-200−2222−22220000022−22000000002-200002i3−2i3−2i32i32−22−2−2−222i6−i6−i6i6i6−i6−i6i60000000000000000000000

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