Finite Group Databasebeta

← Group #10858713

Character table — Group #10858713

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222222444444444444444488888888888888888888888888121212121616161616242424242424242424244848
order12222234444666121212124444668888121224242424444488881212121212121212242424242424242424242244812122424444444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-1111-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1111111-1-1-1-1111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-111-11111-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1111-1-11-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111111-1-1
χ9111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-11-1-1-1-11-1-111-11
χ10111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-111-1-11-1
χ11111111111111111111-1-1-1-11111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-11-1
χ12111111111111111111-1-1-1-11111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11111-1-1-111-11
χ13111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111-1-1111111111-1-111-111-1-1-1-1-1111-1
χ14111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-111111-1-1-11
χ15111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-111-1-1-111-1-1-111-1-1-11
χ16111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1111-1-1111-1
χ17222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-122-2-2-1-1-1-1-1-1-2-2-2-2222-2-1-1-1-11111-1-1-1-1-1-111110000-21111000000000000
χ19222222-12222-1-1-1-1-1-1-12222-1-1-2-222-1-1111122-2-2-2-2-22-1-1-1-11111111111-1-1-1-10000-2-1-111000000000000
χ20222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-11111-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111110000211-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-10000-21111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1-1-122-2-2-2-22-2111111111111-1-1111100002-1-1-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-222-1-11111-2-2-2-222-2211111111-1-1-1-111-1-1-1-10000211-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-11111222222-2-21111-1-1-1-1-1-1-1-11111110000-2-1-111000000000000
χ252222-2-222-2-22222-2-2-2-222-2-2-2-200222200002-200000-222-2-2000000000022-2-2000002-200000000000000
χ262222-2-222-2-22222-2-2-2-222-2-2-2-200-2-2220000-2200000222-2-20000000000-2-22200000-2200000000000000
χ272222-2-222-2-22222-2-2-2-2-2-222-2-20022220000-2200000-2-2-222000000000022-2-200000-2200000000000000
χ282222-2-222-2-22222-2-2-2-2-2-222-2-200-2-22200002-2000002-2-2220000000000-2-222000002-200000000000000
χ292222-2-22-222-222222220000-2-22200-2-22222000000-20000000000000-2-2000022-2-20000020000-2000000
χ302222-2-22-222-222222220000-2-22200-2-22222000000-20000000000000-2-20000-2-22200000-200002000000
χ312222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-20000002000000000000022000022-2-200000-200002000000
χ322222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-200000020000000000000220000-2-2220000020000-2000000
χ332222-2-2-12-2-22-1-1-1111122-2-2110022-1-133−3−32-200000-2-1-11133−3−333−3−33−3-1-11100000-113−3000000000000
χ342222-2-2-12-2-22-1-1-1111122-2-2110022-1-1−3−3332-200000-2-1-111−3−333−3−333−33-1-11100000-11−33000000000000
χ352222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-133−3−3-22000002-1-111−3−33333−3−33−311-1-1000001-1−33000000000000
χ362222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-1−3−333-22000002-1-11133−3−3−3−333−3311-1-1000001-13−3000000000000
χ372222-2-2-12-2-22-1-1-11111-2-222110022-1-133−3−3-2200000-211-1-133−3−3−3−3333−3-1-111000001-1−33000000000000
χ382222-2-2-12-2-22-1-1-11111-2-222110022-1-1−3−333-2200000-211-1-1−3−33333−3−3−33-1-111000001-13−3000000000000
χ392222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-133−3−32-200000211-1-1−3−333−3−3333−311-1-100000-113−3000000000000
χ402222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-1−3−3332-200000211-1-133−3−333−3−3−3311-1-100000-11−33000000000000
χ412-22-22-2222-2-22-2-222-2-200002-200002-2000000002-200000000002-22-20000002-22-20000002-2000000000
χ422-22-22-2222-2-22-2-222-2-200002-200002-2000000002-200000000002-22-2000000-22-22000000-22000000000
χ432-22-22-2222-2-22-2-222-2-200002-200002-200000000-220000000000-22-220000002-22-2000000-22000000000
χ442-22-22-2222-2-22-2-222-2-200002-200002-200000000-220000000000-22-22000000-22-220000002-2000000000
χ452-22-22-22-2-2222-2-2-2-2222i−2i2i−2i2-20000-220000000000002i−2i2i−2i000000000000000000000000000002i−2i2-200
χ462-22-22-22-2-2222-2-2-2-2222i−2i2i−2i2-20000-220000000000002i−2i2i−2i00000000000000000000000000000−2i2i-2200
χ472-22-22-22-2-2222-2-2-2-222−2i2i−2i2i2-20000-22000000000000−2i2i−2i2i000000000000000000000000000002i−2i-2200
χ482-22-22-22-2-2222-2-2-2-222−2i2i−2i2i2-20000-22000000000000−2i2i−2i2i00000000000000000000000000000−2i2i2-200
χ492-22-2-222-22-222-2-222-2-22i−2i−2i2i-220000-220000000000002i−2i−2i2i000000000000002-2-22000000002i−2i0000000
χ502-22-2-222-22-222-2-222-2-22i−2i−2i2i-220000-220000000000002i−2i−2i2i00000000000000-222-200000000−2i2i0000000
χ512-22-2-222-22-222-2-222-2-2−2i2i2i−2i-220000-22000000000000−2i2i2i−2i000000000000002-2-2200000000−2i2i0000000
χ522-22-2-222-22-222-2-222-2-2−2i2i2i−2i-220000-22000000000000−2i2i2i−2i00000000000000-222-2000000002i−2i0000000
χ534444444-4-4-4-4444-4-4-4-40000440000-4-4000000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-222220000-2-20000222323−23−2300000000000000000000−23230000000000000000000000000
χ55444444-2-4-4-4-4-2-2-222220000-2-2000022−23−2323230000000000000000000023−230000000000000000000000000
χ564444-4-4-2-444-4-2-2-2-2-2-2-2000022440022-2-2-2-2000000-40000000000000220000000000000000000000000
χ574444-4-4-2-444-4-2-2-2-2-2-2-2000022-4-40022222200000040000000000000-2-20000000000000000000000000
χ5844-4-40040000-44-4000000000022−2222−220022−2222−22002-2000000002-22-200000022−2200000000000000000000000
χ5944-4-40040000-44-4000000000022−22−22220022−2222−2200-2200000000-22-22000000−222200000000000000000000000
χ6044-4-40040000-44-40000000000−222222−2200−2222−222200-2200000000-22-2200000022−2200000000000000000000000
χ6144-4-40040000-44-40000000000−2222−222200−2222−2222002-2000000002-22-2000000−222200000000000000000000000
χ6244-4-400-200002-2223−2323−2300000022−2222−22002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23002-200000000−1+31−3−1−31+3000000−226−6000000000000000000000
χ6344-4-400-200002-2223−2323−2300000022−22−2222002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300-22000000001−3−1+31+3−1−30000002−2−66000000000000000000000
χ6444-4-400-200002-2223−2323−23000000−222222−2200−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300-22000000001−3−1+31+3−1−3000000−226−6000000000000000000000
χ6544-4-400-200002-2223−2323−23000000−2222−222200−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23002-200000000−1+31−3−1−31+30000002−2−66000000000000000000000
χ6644-4-400-200002-22−2323−232300000022−2222−22002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7002-200000000−1−31+3−1+31−3000000−22−66000000000000000000000
χ6744-4-400-200002-22−2323−232300000022−22−2222002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700-22000000001+3−1−31−3−1+30000002−26−6000000000000000000000
χ6844-4-400-200002-22−2323−2323000000−222222−2200−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700-22000000001+3−1−31−3−1+3000000−22−66000000000000000000000
χ6944-4-400-200002-22−2323−2323000000−2222−222200−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7002-200000000−1−31+3−1+31−30000002−26−6000000000000000000000
χ704-44-44-4-244-4-4-222-2-2220000-220000-22000000004-40000000000-22-22000000000000000000000000000
χ714-44-44-4-244-4-4-222-2-2220000-220000-2200000000-4400000000002-22-2000000000000000000000000000
χ724-44-44-4-2-4-444-22222-2-24i−4i4i−4i-2200002-2000000000000−2i2i−2i2i00000000000000000000000000000000000
χ734-44-44-4-2-4-444-22222-2-2−4i4i−4i4i-2200002-20000000000002i−2i2i−2i00000000000000000000000000000000000
χ744-44-4-4444-44-44-4-4-4-4440000-4400004-4000000000000000000000000000000000000000000000000000
χ754-44-4-44-24-44-4-22222-2-200002-20000-220000000000000000000023−23−2323000000000000000000000000000
χ764-44-4-44-24-44-4-22222-2-200002-20000-2200000000000000000000−232323−23000000000000000000000000000
χ774-44-4-44-2-44-44-222-2-2224i−4i−4i4i2-200002-2000000000000−2i2i2i−2i00000000000000000000000000000000000
χ784-44-4-44-2-44-44-222-2-222−4i4i4i−4i2-200002-20000000000002i−2i−2i2i00000000000000000000000000000000000
χ798-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000

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