Finite Group Databasebeta

← Group #10835916

Character table — Group #10835916

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888812121212121212122424242448484848
order1222222234444666666644444444121212121212121212121212244444444466121212121212121212121212121212121212121212128888888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-111-1-1111111111111-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-111-1-1111111111111-111-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111-1-111-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-111-1-1111111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-11-1
χ1011111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ1111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ1211111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ17222222222-2-2-2-222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2000000200-2-22200000000-2-222000000000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2222222-2-2-2-2-2-2-2-22000000-20022-2-20000000022-2-2000000000000000000000000
χ19222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-222222000000-200222200000000-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2000000200-2-2-2-2000000002222000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-22-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-222-2-222-2-2-21111-1-1-1-1-1-1-1-11111111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2-2221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-22222-2-2-2-2-211-1-1-1-1-1-11111-1-111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-2-2-2-2-222-22211-1-11111-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-11111222-2-2-2-2222-1-111-1-1-1-1111111-1-11111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-1-1-111112-2-222222-2-2-1-1111111-1-1-1-111-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-200000020011-1-1−i3−i3i3i3−i3−i3i3i311-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-200000020011-1-1i3i3−i3−i3i3i3−i3−i311-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1111111112000000-200-1-111−i3−i3i3i3−i3−i3i3i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1111111112000000-200-1-111i3i3−i3−i3i3i3−i3−i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-12000000-200-1-1-1-1−i3−i3i3i3i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i30000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211111111-1-1-1-12000000-200-1-1-1-1i3i3−i3−i3−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-20000002001111−i3−i3i3i3i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-20000002001111i3i3−i3−i3−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ37222-2-2-2-2222-22-22-22-2-22-2002i−2i002i−2i000022-2-20000000002i−2i02-2002i−2i00002i−2i2i−2i2i−2i0000002-22-20000000000000000
χ38222-2-2-2-2222-22-22-22-2-22-2002i−2i002i−2i000022-2-2000000000−2i2i0-22002i−2i0000−2i2i−2i2i2i−2i000000-22-220000000000000000
χ39222-2-2-2-2222-22-22-22-2-22-200−2i2i00−2i2i000022-2-20000000002i−2i0-2200−2i2i00002i−2i2i−2i−2i2i000000-22-220000000000000000
χ40222-2-2-2-2222-22-22-22-2-22-200−2i2i00−2i2i000022-2-2000000000−2i2i02-200−2i2i0000−2i2i−2i2i−2i2i0000002-22-20000000000000000
χ41222-2-2-2-222-22-222-22-2-22-2002i−2i00−2i2i0000-2-222000002-22i−2i00000002i−2i2-22-20000−2i2i002i−2i2i−2i00000000000000000000
χ42222-2-2-2-222-22-222-22-2-22-2002i−2i00−2i2i0000-2-22200000-22−2i2i00000002i−2i-22-220000−2i2i00−2i2i−2i2i00000000000000000000
χ43222-2-2-2-222-22-222-22-2-22-200−2i2i002i−2i0000-2-222000002-2−2i2i0000000−2i2i2-22-200002i−2i00−2i2i−2i2i00000000000000000000
χ44222-2-2-2-222-22-222-22-2-22-200−2i2i002i−2i0000-2-22200000-222i−2i0000000−2i2i-22-2200002i−2i002i−2i2i−2i00000000000000000000
χ45222-2-2-2-22-12-22-2-11-111-11002i−2i002i−2i33−3−3-1-11133−3−3000002i−2i02-2−i3i3−ii−i3i3i3−i3−ii−ii−ii−i3i33−3−33-11-110000000000000000
χ46222-2-2-2-22-12-22-2-11-111-11002i−2i002i−2i33−3−3-1-11133−3−300000−2i2i0-22−i3i3−iii3−i3−i3i3i−ii−i−ii−i3i3−333−31-11-10000000000000000
χ47222-2-2-2-22-12-22-2-11-111-11002i−2i002i−2i−3−333-1-111−3−333000002i−2i02-2i3−i3−iii3−i3−i3i3−ii−ii−iii3−i3−333−3-11-110000000000000000
χ48222-2-2-2-22-12-22-2-11-111-11002i−2i002i−2i−3−333-1-111−3−33300000−2i2i0-22i3−i3−ii−i3i3i3−i3i−ii−i−iii3−i33−3−331-11-10000000000000000
χ49222-2-2-2-22-12-22-2-11-111-1100−2i2i00−2i2i33−3−3-1-11133−3−3000002i−2i0-22i3−i3i−i−i3i3i3−i3−ii−iii−ii3−i3−333−31-11-10000000000000000
χ50222-2-2-2-22-12-22-2-11-111-1100−2i2i00−2i2i33−3−3-1-11133−3−300000−2i2i02-2i3−i3i−ii3−i3−i3i3i−ii−ii−ii3−i33−3−33-11-110000000000000000
χ51222-2-2-2-22-12-22-2-11-111-1100−2i2i00−2i2i−3−333-1-111−3−333000002i−2i0-22−i3i3i−ii3−i3−i3i3−ii−iii−i−i3i33−3−331-11-10000000000000000
χ52222-2-2-2-22-12-22-2-11-111-1100−2i2i00−2i2i−3−333-1-111−3−33300000−2i2i02-2−i3i3i−i−i3i3i3−i3i−ii−ii−i−i3i3−333−3-11-110000000000000000
χ53222-2-2-2-22-1-22-22-11-111-11002i−2i00−2i2i33−3−311-1-1−3−33302-22i−2i00000i3−i3−ii-11-113−3−33i−i−i3i3−ii−ii−i3i3i3−i30000000000000000
χ54222-2-2-2-22-1-22-22-11-111-11002i−2i00−2i2i33−3−311-1-1−3−3330-22−2i2i00000i3−i3−ii1-11-1−333−3i−i−i3i3i−ii−ii3−i3−i3i30000000000000000
χ55222-2-2-2-22-1-22-22-11-111-11002i−2i00−2i2i−3−33311-1-133−3−302-22i−2i00000−i3i3−ii-11-11−333−3i−ii3−i3−ii−iii3−i3−i3i30000000000000000
χ56222-2-2-2-22-1-22-22-11-111-11002i−2i00−2i2i−3−33311-1-133−3−30-22−2i2i00000−i3i3−ii1-11-13−3−33i−ii3−i3i−ii−i−i3i3i3−i30000000000000000
χ57222-2-2-2-22-1-22-22-11-111-1100−2i2i002i−2i33−3−311-1-1−3−33302-2−2i2i00000−i3i3i−i-11-113−3−33−iii3−i3i−ii−ii3−i3−i3i30000000000000000
χ58222-2-2-2-22-1-22-22-11-111-1100−2i2i002i−2i33−3−311-1-1−3−3330-222i−2i00000−i3i3i−i1-11-1−333−3−iii3−i3−ii−ii−i3i3i3−i30000000000000000
χ59222-2-2-2-22-1-22-22-11-111-1100−2i2i002i−2i−3−33311-1-133−3−302-2−2i2i00000i3−i3i−i-11-11−333−3−ii−i3i3i−ii−i−i3i3i3−i30000000000000000
χ60222-2-2-2-22-1-22-22-11-111-1100−2i2i002i−2i−3−33311-1-133−3−30-222i−2i00000i3−i3i−i1-11-13−3−33−ii−i3i3−ii−iii3−i3−i3i30000000000000000
χ612-2-222-2-22222-2-2-2-2-22-2222-2002-2002-22-22-22-22-22-2000000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ622-2-222-2-22222-2-2-2-2-22-2222-2002-2002-22-22-22-22-22-200000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ632-2-222-2-22222-2-2-2-2-22-222-2200-2200-22-222-22-2-22-22000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ642-2-222-2-22222-2-2-2-2-22-222-2200-2200-22-222-22-2-22-2200000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ652-2-222-2-222-2-222-2-2-22-2222-200-22002-22-2-22-22-22-22000000000000000000000000000000000022-2-200002-2000000
χ662-2-222-2-222-2-222-2-2-22-2222-200-22002-22-2-22-22-22-220000000000000000000000000000000000-2-2220000-22000000
χ672-2-222-2-222-2-222-2-2-22-222-22002-200-22-22-22-222-22-2000000000000000000000000000000000022-2-20000-22000000
χ682-2-222-2-222-2-222-2-2-22-222-22002-200-22-22-22-222-22-20000000000000000000000000000000000-2-22200002-2000000
χ6944-44-4-44-4400004-4-444-4-400000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ7044-44-4-44-4400004-4-444-4-4000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ7144-4-444-4-44000044-4-4-4-44000000000000000000000000000000000000000000000000000000000022−2222−2200000000
χ7244-4-444-4-44000044-4-4-4-440000000000000000000000000000000000000000000000000000000000−2222−222200000000
χ734-444-44-4-440000-4444-4-4-400000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ744-444-44-4-440000-4444-4-4-4000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ754-44-44-44-440000-4-44-44-440000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ764-44-44-44-440000-4-44-44-4400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ774-4-444-4-44-244-4-4222-22-2-24-4004-400-22-22-22-22-22-2200000000000000000000000000000000000000000000000000
χ784-4-444-4-44-244-4-4222-22-2-2-4400-44002-22-2-22-222-22-200000000000000000000000000000000000000000000000000
χ794-4-444-4-44-2-4-444222-22-2-24-400-4400-22-222-22-22-22-200000000000000000000000000000000000000000000000000
χ804-4-444-4-44-2-4-444222-22-2-2-44004-4002-22-22-22-2-22-2200000000000000000000000000000000000000000000000000
χ814-4-4-4-444444-4-44-44-4-444-40000000000004-4-44000000000000000000000000000000000000000000000000000000
χ824-4-4-4-44444-444-4-44-4-444-4000000000000-444-4000000000000000000000000000000000000000000000000000000
χ834-4-4-4-4444-24-4-442-222-2-220000000023−23−2323-222-223−23−232300000000000000000000000000000000000000000000000000
χ844-4-4-4-4444-24-4-442-222-2-2200000000−232323−23-222-2−232323−2300000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-2-444-42-222-2-220000000023−23−23232-2-22−232323−2300000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-2-444-42-222-2-2200000000−232323−232-2-2223−23−232300000000000000000000000000000000000000000000000000
χ8788-88-8-88-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-888-8-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-888-88-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).