Finite Group Databasebeta

← Group #10950855

Character table — Group #10950855

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444466661212121212121212121212121212161616163232323248484848
order122234466688881616161616161616448812121212121216161616242424242424242448484848484848484848484848484848444424888816161616161616164444121212122444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1
χ911111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ1111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-11-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11-111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111-1-111-1-111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-111-1-111-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-11-1-111-1-11-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1-111-1-111-11-1-11
χ172222222222-2-2-2-20000000022-2-22222220000-2-2-2-2-2-2-2-20000000000000000222222-2-2-2-200000000000000000000
χ182222222222-2-2-2-20000000022-2-22222220000-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-200000000-2-222-2-2-2-22200002222-2-2-2-200000000000000002222-2-2-2-22200000000000000000000
χ202222222222-2-2-2-200000000-2-222-2-2-2-22200002222-2-2-2-20000000000000000-2-2-2-22222-2-200000000000000000000
χ2122222-2-222200002222−2−2−2−22-20022-2-2-2-222−2−2000000002222−2−2−2−22222−2−2−2−222-2-2-22000022−2−222−2−2000000000000
χ2222222-2-222200002222−2−2−2−22-20022-2-2-2-222−2−2000000002222−2−2−2−22222−2−2−2−2-2-2222-20000−2−222−2−222000000000000
χ2322222-2-222200002222−2−2−2−2-2200-2-222-2-2−2−222000000002222−2−2−2−2−2−2−2−2222222-2-22-2000022−2−2−2−222000000000000
χ2422222-2-222200002222−2−2−2−2-2200-2-222-2-2−2−222000000002222−2−2−2−2−2−2−2−22222-2-222-220000−2−22222−2−2000000000000
χ2522222-2-22220000−2−2−2−222222-20022-2-2-2-2−2−22200000000−2−2−2−22222−2−2−2−2222222-2-2-220000−2−222−2−222000000000000
χ2622222-2-22220000−2−2−2−222222-20022-2-2-2-2−2−22200000000−2−2−2−22222−2−2−2−22222-2-2222-2000022−2−222−2−2000000000000
χ2722222-2-22220000−2−2−2−22222-2200-2-222-2-222−2−200000000−2−2−2−222222222−2−2−2−222-2-22-20000−2−22222−2−2000000000000
χ2822222-2-22220000−2−2−2−22222-2200-2-222-2-222−2−200000000−2−2−2−222222222−2−2−2−2-2-222-22000022−2−2−2−222000000000000
χ292222-122-1-1-12222222222222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-10000
χ302222-122-1-1-12222222222222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-211110000
χ312222-122-1-1-1222222222222-2-2-2-21111-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000022-2-2-1-1110000
χ322222-122-1-1-1222222222222-2-2-2-21111-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000000-2-22211-1-10000
χ332222-122-1-1-12222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000002-22-2-11-110000
χ342222-122-1-1-12222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000000000-22-221-11-10000
χ352222-122-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-21111-1-122221111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000002-2-22-111-10000
χ362222-122-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-21111-1-122221111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000000000-222-21-1-110000
χ372-22-222-2-22-20000−i2−i2i2i2−i2−i2i2i2002-200002-2−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00002i−2i2−22−22−22−2000000000000
χ382-22-222-2-22-20000−i2−i2i2i2−i2−i2i2i2002-200002-2−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0000−2i2i−22−22−22−22000000000000
χ392-22-222-2-22-20000−i2−i2i2i2−i2−i2i2i200-2200002-2i2−i2i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0000−2i2i2−22−2−22−22000000000000
χ402-22-222-2-22-20000−i2−i2i2i2−i2−i2i2i200-2200002-2i2−i2i2−i2-2-2220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00002i−2i−22−222−22−2000000000000
χ412-22-222-2-22-20000i2i2−i2−i2i2i2−i2−i2002-200002-2i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i2i−2i00002i−2i−22−22−22−22000000000000
χ422-22-222-2-22-20000i2i2−i2−i2i2i2−i2−i2002-200002-2i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i0000−2i2i2−22−22−22−2000000000000
χ432-22-222-2-22-20000i2i2−i2−i2i2i2−i2−i200-2200002-2−i2i2−i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i2i−2i0000−2i2i−22−222−22−2000000000000
χ442-22-222-2-22-20000i2i2−i2−i2i2i2−i2−i200-2200002-2−i2i2−i2i2-2-2220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i00002i−2i2−22−2−22−22000000000000
χ452-22-22-22-22-222-2-20000000000000000-222i−2i−2i2i000022-2-2000000002i2i−2i−2i−2i−2i2i2i2i−2i−2i2i002i−2i000000-222-2000000000000
χ462-22-22-22-22-222-2-20000000000000000-222i−2i−2i2i000022-2-2000000002i2i−2i−2i−2i−2i2i2i−2i2i2i−2i00−2i2i0000002-2-22000000000000
χ472-22-22-22-22-222-2-20000000000000000-22−2i2i2i−2i000022-2-200000000−2i−2i2i2i2i2i−2i−2i2i−2i−2i2i002i−2i0000002-2-22000000000000
χ482-22-22-22-22-222-2-20000000000000000-22−2i2i2i−2i000022-2-200000000−2i−2i2i2i2i2i−2i−2i−2i2i2i−2i00−2i2i000000-222-2000000000000
χ492-22-22-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i00000000-2200000000-2-2222i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i00−2i2i00-222-20000000000000000
χ502-22-22-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i00000000-2200000000-2-2222i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i002i−2i002-2-220000000000000000
χ512-22-22-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i00000000-2200000000-2-222−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i00−2i2i002-2-220000000000000000
χ522-22-22-22-22-2-2-222−2i−2i2i2i2i2i−2i−2i00000000-2200000000-2-222−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i002i−2i00-222-20000000000000000
χ534444-244-2-2-2-4-4-4-40000000044-4-4-2-2-2-2-2-20000222222220000000000000000000000000000000000000000000000
χ544444-244-2-2-2-4-4-4-400000000-4-4442222-2-20000-2-2-2-222220000000000000000000000000000000000000000000000
χ554444-2-4-4-2-2-2000022222222−22−22−22−224-400-2-222222222−22−2200000000−2−2−2−22222−2−2−2−22222000000000000000000000000000000
χ564444-2-4-4-2-2-2000022222222−22−22−22−22-440022-2-222−22−22222200000000−2−2−2−222222222−2−2−2−2000000000000000000000000000000
χ574444-2-4-4-2-2-20000−22−22−22−22222222224-400-2-22222−22−222222000000002222−2−2−2−22222−2−2−2−2000000000000000000000000000000
χ584444-2-4-4-2-2-20000−22−22−22−2222222222-440022-2-2222222−22−22000000002222−2−2−2−2−2−2−2−22222000000000000000000000000000000
χ5944-4-44004-4-422−2222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000022−2222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300000000000000000000000000000000000000
χ6044-4-44004-4-422−2222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000022−2222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ4300000000000000000000000000000000000000
χ6144-4-44004-4-4−2222−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47000000000000000000−2222−22222ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ4700000000000000000000000000000000000000
χ6244-4-44004-4-4−2222−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47000000000000000000−2222−2222−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ4700000000000000000000000000000000000000
χ6344-4-4-200-22222−2222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ430000−2i32i300000000i6−i6i6−i6−22−22ζ25−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+ζ43−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−ζ43000000000000000000000000000000
χ6444-4-4-200-22222−2222−22−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ472ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ4300002i3−2i300000000−i6i6−i6i6−22−22ζ25−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−ζ47ζ25−ζ31−ζ41+ζ47−ζ25+ζ31+ζ41−ζ47ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43ζ11+ζ13−ζ29−ζ43−ζ11−ζ13+ζ29+ζ43000000000000000000000000000000
χ6544-4-4-200-22222−2222−222ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ472ζ25−2ζ31+2ζ41−2ζ47−2ζ25+2ζ31−2ζ41+2ζ47−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ43−2ζ11+2ζ13+2ζ29−2ζ432ζ11−2ζ13−2ζ29+2ζ430000−2i32i300000000i6−i6i6−i6−22−22−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−ζ43ζ25−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+ζ43000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.