Finite Group Databasebeta

← Group #10901271

Character table — Group #10901271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222222244448888888888888888888888888888888888888888242424242424242448484848
order1222222234444666666612121212121212124444244466888888881212121212121212121224242424242424242424242424242424224444442444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ611111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ91111111111111111111111111111-1-1-1-11-11-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111111111111111-1-1-1-11-11-11111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111111111111111111111111111-1-1-1-11-11-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ121111111111111111111111111111-1-1-1-11-11-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ131111111111111111111111111111-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-11-1
χ141111111111111111111111111111-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-11
χ151111111111111111111111111111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-11-11
χ161111111111111111111111111111-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-11-1
χ17222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22-2-22220000000022-2-2-2-222-2-20000000000000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-222-2-2-20000000022-2-222-2-2220000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000-2-222-2-2-2-2220000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000-2-2222222-2-20000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2112222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-111111111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211-2-2-2-22222-1-1-1-111111111111111-1-1-1-1-1-1-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-122-2-222-2-21111-1-11111-1-1-1-11111-1-1-1-11111000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-1-2-222-2-2221111-1-111111111-1-1-1-11111-1-1-1-1000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-221122-2-2-2-222111111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2211-2-22222-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-22-2-22-1-100000000-1-11111-1-11133−3−333−3−333−3−333−3−3000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-22-2-22-1-100000000-1-11111-1-111−3−333−3−333−3−333−3−333000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-222-21100000000-1-111-1-111-1-133−3−333−3−3−3−333−3−333000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-222-21100000000-1-111-1-111-1-1−3−333−3−33333−3−333−3−3000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-1-10000000011-1-11111-1-133−3−3−3−33333−3−3−3−333000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-1-10000000011-1-11111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222110000000011-1-1-1-1-1-11133−3−3−3−333−3−33333−3−3000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222110000000011-1-1-1-1-1-111−3−33333−3−333−3−3−3−333000000000000
χ372-2-2-22-22222-22-2-2-2-2-222222-2-222-2-22-22-2000000000000002-22-200000000000000000000002-22-200000000
χ382-2-2-22-22222-22-2-2-2-2-222222-2-222-2-22-22-2000000000000002-22-20000000000000000000000-22-2200000000
χ392-2-2-22-22222-22-2-2-2-2-222222-2-222-2-2-22-2200000000000000-22-2200000000000000000000002-2-2200000000
χ402-2-2-22-22222-22-2-2-2-2-222222-2-222-2-2-22-2200000000000000-22-220000000000000000000000-222-200000000
χ412-2-2-22-2222-22-22-2-2-2-2222-2-222-2-2222-2-22000000000000002-2-22000000000000000000000000002-22-20000
χ422-2-2-22-2222-22-22-2-2-2-2222-2-222-2-2222-2-22000000000000002-2-2200000000000000000000000000-22-220000
χ432-2-2-22-2222-22-22-2-2-2-2222-2-222-2-222-222-200000000000000-222-2000000000000000000000000002-2-220000
χ442-2-2-22-2222-22-22-2-2-2-2222-2-222-2-222-222-200000000000000-222-200000000000000000000000000-222-20000
χ45444-44-4-4-44000044-4-44-4-400000000000000000022−22000000000000000022−2222−22000000000000000000000000
χ46444-44-4-4-44000044-4-44-4-4000000000000000000−22220000000000000000−2222−2222000000000000000000000000
χ47444-44-4-4-4-20000-2-222-22223−2323−2323−2323−23000000000022−2200000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000
χ48444-44-4-4-4-20000-2-222-22223−2323−2323−2323−230000000000−22220000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000
χ49444-44-4-4-4-20000-2-222-222−2323−2323−2323−2323000000000022−2200000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000
χ50444-44-4-4-4-20000-2-222-222−2323−2323−2323−23230000000000−22220000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000
χ5144-44-4-44-4400004-44-4-44-4000000000000000000000000−2i22i20000000000000000000000−2i22i2−2i22i2000000000000
χ5244-44-4-44-4400004-44-4-44-40000000000000000000000002i2−2i200000000000000000000002i2−2i22i2−2i2000000000000
χ5344-44-4-44-4-20000-22-222-2223−23−2323−232323−230000000000000000−2i22i200000000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000
χ5444-44-4-44-4-20000-22-222-2223−23−2323−232323−2300000000000000002i2−2i20000000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000
χ5544-44-4-44-4-20000-22-222-22−232323−2323−23−23230000000000000000−2i22i200000000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000
χ5644-44-4-44-4-20000-22-222-22−232323−2323−23−232300000000000000002i2−2i20000000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000
χ5744-4-4-44-4444-4-444-4-44-4-4444-4-4-4-44400000000000000000000000000000000000000000000000000000000
χ5844-4-4-44-444-444-44-4-44-4-44-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ5944-4-4-44-44-24-4-44-222-222-2-2-22222-2-200000000000000000000000023−2323−230000000000000000000000000000
χ6044-4-4-44-44-24-4-44-222-222-2-2-22222-2-2000000000000000000000000−2323−23230000000000000000000000000000
χ6144-4-4-44-44-2-444-4-222-222-222-2-2-2-22200000000000000000000000023−23−23230000000000000000000000000000
χ6244-4-4-44-44-2-444-4-222-222-222-2-2-2-222000000000000000000000000−232323−230000000000000000000000000000
χ634-444-4-4-44444-4-4-444-4-4-444444-4-4-4-400000000000000000000000000000000000000000000000000000000
χ644-444-4-4-444-4-444-444-4-4-44-4-4-4-4444400000000000000000000000000000000000000000000000000000000
χ654-444-4-4-44-244-4-42-2-2222-2-2-2-2-2222200000000−2i32i3000000000000−2i32i300000000000000000000000000000000
χ664-444-4-4-44-244-4-42-2-2222-2-2-2-2-22222000000002i3−2i30000000000002i3−2i300000000000000000000000000000000
χ674-444-4-4-44-2-4-4442-2-2222-22222-2-2-2-200000000−2i32i30000000000002i3−2i300000000000000000000000000000000
χ684-444-4-4-44-2-4-4442-2-2222-22222-2-2-2-2000000002i3−2i3000000000000−2i32i300000000000000000000000000000000
χ694-44-4-444-440000-44-44-44-4000000000000000000000022−220000000000000000000022−2222−220000000000000000
χ704-44-4-444-440000-44-44-44-40000000000000000000000−222200000000000000000000−2222−22220000000000000000
χ714-44-4-444-4-200002-22-22-2223−2323−23−2323−23230000000000000022−22000000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000
χ724-44-4-444-4-200002-22-22-2223−2323−23−2323−232300000000000000−222200000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000
χ734-44-4-444-4-200002-22-22-22−2323−232323−2323−230000000000000022−22000000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000
χ744-44-4-444-4-200002-22-22-22−2323−232323−2323−2300000000000000−222200000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000
χ754-4-4444-4-440000-4-4444-4-400000000000000000000−2i22i2000000000000000000−2i22i2−2i22i200000000000000000000
χ764-4-4444-4-440000-4-4444-4-4000000000000000000002i2−2i20000000000000000002i2−2i22i2−2i200000000000000000000
χ774-4-4444-4-4-2000022-2-2-22223−23−232323−23−2323000000000000−2i22i20000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000
χ784-4-4444-4-4-2000022-2-2-22223−23−232323−23−23230000000000002i2−2i2000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000
χ794-4-4444-4-4-2000022-2-2-222−232323−23−232323−23000000000000−2i22i20000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000
χ804-4-4444-4-4-2000022-2-2-222−232323−23−232323−230000000000002i2−2i2000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000
χ814-4-4-44-444-24-44-42222-2-2-2-2-222-2-2224-44-400000000000000-22-220000000000000000000000000000000000
χ824-4-4-44-444-24-44-42222-2-2-2-2-222-2-222-44-44000000000000002-22-20000000000000000000000000000000000
χ834-4-4-44-444-2-44-442222-2-2-222-2-222-2-24-4-4400000000000000-222-20000000000000000000000000000000000
χ844-4-4-44-444-2-44-442222-2-2-222-2-222-2-2-444-4000000000000002-2-220000000000000000000000000000000000

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