Finite Group Databasebeta

← Group #10877344

Character table — Group #10877344

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order1222222234444666666612121212121212122244444444668888888812121212121212121212242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111111111111111111111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111111111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ121111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ131111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ141111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ151111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-222200000000-2-222-2-222-2-200000000000000000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2222-22200000000-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-22-2-2-2000000002222-2-2-2-22200000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-22-2-20000000022-2-22222-2-200000000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-1-1-2-2-2-22222-1-11111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-21122-2-222-2-211-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-211-2-222-2-22211-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2221122-2-2-2-222111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211-2-22222-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-22-1-10000000011-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-22-1-10000000011-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-2-1-1000000001111-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-2-1-1000000001111-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-22-21100000000-1-1-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-22-21100000000-1-1-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-221100000000-1-111-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-221100000000-1-111-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ3722-22-22-2-2222-2-222-2-22-2-22222-2-2-2-22-2002-200002-2000000002-20000000000000000000000002-2002-20000000000
χ3822-22-22-2-2222-2-222-2-22-2-22222-2-2-2-22-2002-200002-2000000002-2000000000000000000000000-2200-220000000000
χ3922-22-22-2-2222-2-222-2-22-2-22222-2-2-2-2-2200-220000-2200000000-220000000000000000000000002-200-220000000000
χ4022-22-22-2-2222-2-222-2-22-2-22222-2-2-2-2-2200-220000-2200000000-22000000000000000000000000-22002-20000000000
χ4122-22-22-2-22-2-22222-2-22-2-2-2-2-2-222222-200-2200002-200000000-220000000000000000000000000000002i−2i2i−2i000000
χ4222-22-22-2-22-2-22222-2-22-2-2-2-2-2-222222-200-2200002-200000000-22000000000000000000000000000000−2i2i−2i2i000000
χ4322-22-22-2-22-2-22222-2-22-2-2-2-2-2-22222-22002-20000-22000000002-20000000000000000000000000000002i−2i−2i2i000000
χ4422-22-22-2-22-2-22222-2-22-2-2-2-2-2-22222-22002-20000-22000000002-2000000000000000000000000000000−2i2i2i−2i000000
χ452-22-2-222-222-22-2-2-2-2-222222-2-222-2-2002-2002-2000000000000002-22-200000000000000000000002i−2i000000002i−2i00
χ462-22-2-222-222-22-2-2-2-2-222222-2-222-2-2002-2002-2000000000000002-22-20000000000000000000000−2i2i00000000−2i2i00
χ472-22-2-222-222-22-2-2-2-2-222222-2-222-2-200-2200-2200000000000000-22-2200000000000000000000002i−2i00000000−2i2i00
χ482-22-2-222-222-22-2-2-2-2-222222-2-222-2-200-2200-2200000000000000-22-220000000000000000000000−2i2i000000002i−2i00
χ492-22-2-222-22-22-22-2-2-2-2222-2-222-2-222002-200-22000000000000002-2-220000000000000000000000000000002i−2i002i−2i
χ502-22-2-222-22-22-22-2-2-2-2222-2-222-2-222002-200-22000000000000002-2-22000000000000000000000000000000−2i2i00−2i2i
χ512-22-2-222-22-22-22-2-2-2-2222-2-222-2-22200-22002-200000000000000-222-20000000000000000000000000000002i−2i00−2i2i
χ522-22-2-222-22-22-22-2-2-2-2222-2-222-2-22200-22002-200000000000000-222-2000000000000000000000000000000−2i2i002i−2i
χ53444-4-4-4-44400004-44-4-44-4000000000000000000000000−2i22i200000000000000000000−2i22i2−2i22i200000000000000000000
χ54444-4-4-4-44400004-44-4-44-40000000000000000000000002i2−2i2000000000000000000002i2−2i22i2−2i200000000000000000000
χ55444-4-4-4-44-20000-22-222-2223−2323−2323−2323−230000000000000000−2i22i2000000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000
χ56444-4-4-4-44-20000-22-222-2223−2323−2323−2323−2300000000000000002i2−2i200000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000
χ57444-4-4-4-44-20000-22-222-22−2323−2323−2323−23230000000000000000−2i22i2000000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000
χ58444-4-4-4-44-20000-22-222-22−2323−2323−2323−232300000000000000002i2−2i200000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000
χ5944-44-44-4-4-244-4-4-2-222-222-2-2-2-222224-4004-40000-2200000000-220000000000000000000000000000000000000000
χ6044-44-44-4-4-244-4-4-2-222-222-2-2-2-22222-4400-4400002-2000000002-20000000000000000000000000000000000000000
χ6144-44-44-4-4-2-4-444-2-222-2222222-2-2-2-24-400-440000-22000000002-20000000000000000000000000000000000000000
χ6244-44-44-4-4-2-4-444-2-222-2222222-2-2-2-2-44004-400002-200000000-220000000000000000000000000000000000000000
χ6344-4-44-44-4400004-4-44-4-440000000000000000000000000022−22000000000000000000000022−2222−220000000000000000
χ6444-4-44-44-4400004-4-44-4-4400000000000000000000000000−22220000000000000000000000−2222−22220000000000000000
χ6544-4-44-44-4-20000-222-222-223−2323−23−2323−232300000000000000000022−2200000000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000
χ6644-4-44-44-4-20000-222-222-223−2323−23−2323−2323000000000000000000−22220000000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000
χ6744-4-44-44-4-20000-222-222-2−2323−232323−2323−2300000000000000000022−2200000000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000
χ6844-4-44-44-4-20000-222-222-2−2323−232323−2323−23000000000000000000−22220000000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000
χ694-4444-4-4-440000-44-44-44-40000000000000000000022−22000000000000000022−2222−220000000000000000000000000000
χ704-4444-4-4-440000-44-44-44-400000000000000000000−22220000000000000000−2222−22220000000000000000000000000000
χ714-4444-4-4-4-200002-22-22-2223−23−232323−23−232300000000000022−2200000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000
χ724-4444-4-4-4-200002-22-22-2223−23−232323−23−2323000000000000−22220000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000
χ734-4444-4-4-4-200002-22-22-22−232323−23−232323−2300000000000022−2200000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000
χ744-4444-4-4-4-200002-22-22-22−232323−23−232323−23000000000000−22220000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000
χ754-44-4-444-4-24-44-42222-2-2-2-2-222-2-222004-4004-400000000000000-22-22000000000000000000000000000000000000
χ764-44-4-444-4-24-44-42222-2-2-2-2-222-2-22200-4400-44000000000000002-22-2000000000000000000000000000000000000
χ774-44-4-444-4-2-44-442222-2-2-222-2-222-2-2004-400-4400000000000000-222-2000000000000000000000000000000000000
χ784-44-4-444-4-2-44-442222-2-2-222-2-222-2-200-44004-4000000000000002-2-22000000000000000000000000000000000000
χ794-4-44-4-44440000-444-4-4-44000000000000000000000022−2200000000000000000022−2222−22000000000000000000000000
χ804-4-44-4-44440000-444-4-4-440000000000000000000000−2222000000000000000000−2222−2222000000000000000000000000
χ814-4-44-4-444-200002-2-2222-223−23−2323−232323−230000000000000022−220000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ824-4-44-4-444-200002-2-2222-223−23−2323−232323−2300000000000000−2222000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ834-4-44-4-444-200002-2-2222-2−232323−2323−23−23230000000000000022−220000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ844-4-44-4-444-200002-2-2222-2−232323−2323−23−232300000000000000−2222000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ854-4-4-444-4444-4-44-4-4444-4-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000
χ864-4-4-444-444-444-4-4-4444-4-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000
χ874-4-4-444-44-24-4-4422-2-2-222-2-22222-2-20000000000000000000000000023−2323−2300000000000000000000000000000000
χ884-4-4-444-44-24-4-4422-2-2-222-2-22222-2-200000000000000000000000000−2323−232300000000000000000000000000000000
χ894-4-4-444-44-2-444-422-2-2-22222-2-2-2-2220000000000000000000000000023−23−232300000000000000000000000000000000
χ904-4-4-444-44-2-444-422-2-2-22222-2-2-2-22200000000000000000000000000−232323−2300000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.