Finite Group Databasebeta

← Group #10843150

Character table — Group #10843150

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222222444444444444444488888888888888888888888888121212121616161616242424242424242424244848
order1222223444466612121212444466888812122424242424448888121212121212121224242424242424242424224468122424222244448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-1111-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111-1-1111111-1-1-1-1111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-111-111-111-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-111-1-11-1-11-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-111-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1111-1-1
χ9111111111111111111-1-1-1-1111111111111-1-1111-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1111-11
χ10111111111111111111-1-1-1-1111111111111-1-1111-1-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-111-1-1-11-1
χ11111111111111111111-1-1-1-11111-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-11-1-11-1
χ12111111111111111111-1-1-1-11111-1-111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-111-11
χ13111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111111-11-11111-1-1-1-1-1-1111-1
χ14111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-111-1-1111111-1-1-11
χ15111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-1-1-11111-1-11111-1-1-1-111111-11-1-11111-1-1-1-1-1-1-11
χ16111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111111-1
χ17222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-12-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-122-2-2-1-1-1-1-1-1-2-2-2-2222-2-1-1-1-11111-1-1-1-1-1-1111100001-2111000000000000
χ19222222-12222-1-1-1-1-1-1-12222-1-1-2-222-1-1111122-2-2-2-2-22-1-1-1-11111111111-1-1-1-10000-1-2-111000000000000
χ20222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-11111-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111110000121-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-2-2222-2-221111-1-1-1-1-1-11111-1-1-1-100001-2111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1-1-122-2-22-2-2-211111111-1-1111111110000-12-1-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-222-1-11111-2-2-2-2-22221111111111-1-1-1-1-1-1-1-10000121-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-111112222-222-21111-1-1-1-111-1-1-1-111110000-1-2-111000000000000
χ252222-2-222-2-22222-2-2-2-222-2-2-2-20022220000-2200000-222-2-2000000000022-2-20000-20200000000000000
χ262222-2-222-2-22222-2-2-2-222-2-2-2-200-2-22200002-200000222-2-20000000000-2-222000020-200000000000000
χ272222-2-222-2-22222-2-2-2-2-2-222-2-200222200002-200000-2-2-222000000000022-2-2000020-200000000000000
χ282222-2-222-2-22222-2-2-2-2-2-222-2-200-2-2220000-22000002-2-2220000000000-2-2220000-20200000000000000
χ292222-2-22-222-222222220000-2-22200-2-222220000-200000000000-2-20000000022-2-2000000000-20020000
χ302222-2-22-222-222222220000-2-22200-2-222220000-200000000000-2-200000000-2-222000000000200-20000
χ312222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-20000200000000000220000000022-2-2000000000200-20000
χ322222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-200002000000000002200000000-2-222000000000-20020000
χ332222-2-2-12-2-22-1-1-1111122-2-2110022-1-133−3−3-2200000-2-1-11133−3−33−333−3−3-1-111000010-13−3000000000000
χ342222-2-2-12-2-22-1-1-1111122-2-2110022-1-1−3−333-2200000-2-1-111−3−333−33−3−333-1-111000010-1−33000000000000
χ352222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-133−3−32-2000002-1-111−3−3333−333−3−311-1-10000-101−33000000000000
χ362222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-1−3−3332-2000002-1-11133−3−3−33−3−33311-1-10000-1013−3000000000000
χ372222-2-2-12-2-22-1-1-11111-2-222110022-1-133−3−32-200000-211-1-133−3−33−3−3−333-1-1110000-101−33000000000000
χ382222-2-2-12-2-22-1-1-11111-2-222110022-1-1−3−3332-200000-211-1-1−3−333−3333−3−3-1-1110000-1013−3000000000000
χ392222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-133−3−3-2200000211-1-1−3−3333−3−3−33311-1-1000010-13−3000000000000
χ402222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-1−3−333-2200000211-1-133−3−3−3333−3−311-1-1000010-1−33000000000000
χ412-2-222-222-22-2-2-22-2-2222i−2i2i−2i2-200002-20000000000002i−2i2i−2i000000000000002-22-200000000002i−2i00000
χ422-2-222-222-22-2-2-22-2-2222i−2i2i−2i2-200002-20000000000002i−2i2i−2i00000000000000-22-220000000000−2i2i00000
χ432-2-222-222-22-2-2-22-2-222−2i2i−2i2i2-200002-2000000000000−2i2i−2i2i000000000000002-22-20000000000−2i2i00000
χ442-2-222-222-22-2-2-22-2-222−2i2i−2i2i2-200002-2000000000000−2i2i−2i2i00000000000000-22-2200000000002i−2i00000
χ452-2-22-22222-2-2-2-2222-2-22i−2i−2i2i-2200002-20000000000002i−2i−2i2i00000000000000000000000002-200002i−2i00
χ462-2-22-22222-2-2-2-2222-2-22i−2i−2i2i-2200002-20000000000002i−2i−2i2i0000000000000000000000000-220000−2i2i00
χ472-2-22-22222-2-2-2-2222-2-2−2i2i2i−2i-2200002-2000000000000−2i2i2i−2i00000000000000000000000002-20000−2i2i00
χ482-2-22-22222-2-2-2-2222-2-2−2i2i2i−2i-2200002-2000000000000−2i2i2i−2i0000000000000000000000000-2200002i−2i00
χ492-2-22-222-2-222-2-22-2-2220000-220000-220000000002-2000000000002-22-200002-2-22000002-20000000000
χ502-2-22-222-2-222-2-22-2-2220000-220000-220000000002-2000000000002-22-20000-222-200000-220000000000
χ512-2-22-222-2-222-2-22-2-2220000-220000-22000000000-2200000000000-22-2200002-2-2200000-220000000000
χ522-2-22-222-2-222-2-22-2-2220000-220000-22000000000-2200000000000-22-220000-222-2000002-20000000000
χ534444444-4-4-4-4444-4-4-4-40000440000-4-4000000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-222220000-2-20000222323−23−230000000000000000−232300000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-222220000-2-2000022−23−232323000000000000000023−2300000000000000000000000000000
χ564444-4-4-2-444-4-2-2-2-2-2-2-2000022440022-2-2-2-20000-4000000000002200000000000000000000000000000
χ574444-4-4-2-444-4-2-2-2-2-2-2-2000022-4-4002222220000400000000000-2-200000000000000000000000000000
χ5844-4-400400004-4-40000000000−2i22i2−2i22i200−2i22i2−2i22i2002-2000000002-22-2000000−2i22i200000000000000000000000
χ5944-4-400400004-4-40000000000−2i22i22i2−2i200−2i22i2−2i22i200-2200000000-22-220000002i2−2i200000000000000000000000
χ6044-4-400400004-4-400000000002i2−2i2−2i22i2002i2−2i22i2−2i200-2200000000-22-22000000−2i22i200000000000000000000000
χ6144-4-400400004-4-400000000002i2−2i22i2−2i2002i2−2i22i2−2i2002-2000000002-22-20000002i2−2i200000000000000000000000
χ6244-4-400-20000-22223−2323−23000000−2i22i2−2i22i2002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23002-200000000−1−31+3−1+31−3000000i2−i2i6−i6000000000000000000000
χ6344-4-400-20000-22223−2323−23000000−2i22i22i2−2i2002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300-22000000001+3−1−31−3−1+3000000−i2i2−i6i6000000000000000000000
χ6444-4-400-20000-22223−2323−230000002i2−2i2−2i22i200−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300-22000000001+3−1−31−3−1+3000000i2−i2i6−i6000000000000000000000
χ6544-4-400-20000-22223−2323−230000002i2−2i22i2−2i200−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23002-200000000−1−31+3−1+31−3000000−i2i2−i6i6000000000000000000000
χ6644-4-400-20000-222−2323−2323000000−2i22i2−2i22i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7002-200000000−1+31−3−1−31+3000000i2−i2−i6i6000000000000000000000
χ6744-4-400-20000-222−2323−2323000000−2i22i22i2−2i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700-22000000001−3−1+31+3−1−3000000−i2i2i6−i6000000000000000000000
χ6844-4-400-20000-222−2323−23230000002i2−2i2−2i22i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700-22000000001−3−1+31+3−1−3000000i2−i2−i6i6000000000000000000000
χ6944-4-400-20000-222−2323−23230000002i2−2i22i2−2i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7002-200000000−1+31−3−1−31+3000000−i2i2i6−i6000000000000000000000
χ704-4-444-44-44-44-4-4444-4-400004-40000-44000000000000000000000000000000000000000000000000000
χ714-4-444-4-24-44-422-222-2-24i−4i4i−4i-220000-22000000000000−2i2i−2i2i00000000000000000000000000000000000
χ724-4-444-4-24-44-422-222-2-2−4i4i−4i4i-220000-220000000000002i−2i2i−2i00000000000000000000000000000000000
χ734-4-444-4-2-44-4422-2-2-2220000-2200002-2000000000000000000000023−23−23230000000000000000000000000
χ744-4-444-4-2-44-4422-2-2-2220000-2200002-20000000000000000000000−232323−230000000000000000000000000
χ754-4-44-44-244-4-422-2-2-2224i−4i−4i4i2-20000-22000000000000−2i2i2i−2i00000000000000000000000000000000000
χ764-4-44-44-244-4-422-2-2-222−4i4i4i−4i2-20000-220000000000002i−2i−2i2i00000000000000000000000000000000000
χ774-4-44-44-2-4-44422-222-2-200002-200002-20000000004-400000000000-22-220000000000000000000000000
χ784-4-44-44-2-4-44422-222-2-200002-200002-2000000000-44000000000002-22-20000000000000000000000000
χ798-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4443−43−4343000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44−434343−43000000000000000000000000000000000000000000000000000000000000000

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