Finite Group Databasebeta

← Group #10831709

Character table — Group #10831709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888812121212242424242424242424244848
order122222223444466666661212121212121212444444444488888888121212121212121212121212242424242424242424242424242424242222224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ91111111111111111111111111111-1-1-1-111-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11-1
χ101111111111111111111111111111-1-1-1-111-1-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ111111111111111111111111111111-1-1-1-111-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-11
χ121111111111111111111111111111-1-1-1-111-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1111-1
χ131111111111111111111111111111-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11
χ141111111111111111111111111111-1-1-1-1-1-111-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1
χ151111111111111111111111111111-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1111-1
χ161111111111111111111111111111-1-1-1-1-1-111-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-11
χ17222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-2-220000000022-2-222-2-222-2-200000000000000000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2-2-2222-20000000022-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222222-2-200000000-2-22222-2-2-2-22200000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22200000000-2-222-2-22222-2-200000000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-22222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-22222-1-1-1-11111111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-22-222-2-222-2-21111-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-22-2-2-222-2-2221111-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2222-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-22-2-22222-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-2200000000-1-111-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-2200000000-1-111-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-200000000-1-11111-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-2-2222-200000000-1-11111-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2222222-2-20000000011-1-1-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2222222-2-20000000011-1-1-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2-2-2220000000011-1-111-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2-2-2220000000011-1-111-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ372222-2-2-2-2222-2-222-2-22-2-22222-2-2-2-200000000002-20000000000000000002-22-200000000000022-2-22-20000000000
χ382222-2-2-2-2222-2-222-2-22-2-22222-2-2-2-200000000002-20000000000000000002-22-2000000000000-2-222-220000000000
χ392222-2-2-2-2222-2-222-2-22-2-22222-2-2-2-20000000000-22000000000000000000-22-2200000000000022-2-2-220000000000
χ402222-2-2-2-2222-2-222-2-22-2-22222-2-2-2-20000000000-22000000000000000000-22-22000000000000-2-2222-20000000000
χ412-2-2222-2-22-22-22-2-2222-2-2-2-222-2-2220000000000002i−2i000000000000000000002i−2i2i−2i000000002-22-2002i−2i00000000
χ422-2-2222-2-22-22-22-2-2222-2-2-2-222-2-2220000000000002i−2i000000000000000000002i−2i2i−2i00000000-22-2200−2i2i00000000
χ432-2-2222-2-22-22-22-2-2222-2-2-2-222-2-222000000000000−2i2i00000000000000000000−2i2i−2i2i000000002-22-200−2i2i00000000
χ442-2-2222-2-22-22-22-2-2222-2-2-2-222-2-222000000000000−2i2i00000000000000000000−2i2i−2i2i00000000-22-22002i−2i00000000
χ452-2-22-2-22222-2-22-2-2-2-222222-2-2-2-2222-22-2000000000000002-22-200000000000000000000000000000000002-22-200
χ462-2-22-2-22222-2-22-2-2-2-222222-2-2-2-2222-22-2000000000000002-22-20000000000000000000000000000000000-22-2200
χ472-2-22-2-22222-2-22-2-2-2-222222-2-2-2-222-22-2200000000000000-22-2200000000000000000000000000000000002-2-2200
χ482-2-22-2-22222-2-22-2-2-2-222222-2-2-2-222-22-2200000000000000-22-220000000000000000000000000000000000-222-200
χ492-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-22-2-22000000000000002-2-220000000000000000000000002-2-2200002-2000000
χ502-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-22-2-22000000000000002-2-22000000000000000000000000-222-20000-22000000
χ512-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-2-222-200000000000000-222-20000000000000000000000002-2-220000-22000000
χ522-2-22-2-2222-222-2-2-2-2-2222-2-22222-2-2-222-200000000000000-222-2000000000000000000000000-222-200002-2000000
χ534444-4-4-4-44-4-44444-4-44-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-244-4-4-2-222-222-2-2-2-2222200000000004-4000000000000000000-22-220000000000000000000000000000
χ554444-4-4-4-4-244-4-4-2-222-222-2-2-2-222220000000000-440000000000000000002-22-20000000000000000000000000000
χ564444-4-4-4-4-2-4-444-2-222-2222222-2-2-2-200000000000000000000000000000023−23−23230000000000000000000000000000
χ574444-4-4-4-4-2-4-444-2-222-2222222-2-2-2-2000000000000000000000000000000−232323−230000000000000000000000000000
χ5844-4-44-44-4400004-44-4-44-4000000000000000000000000−2i22i2000000000000000000000000−2i22i2−2i22i20000000000000000
χ5944-4-44-44-4400004-44-4-44-40000000000000000000000002i2−2i20000000000000000000000002i2−2i22i2−2i20000000000000000
χ6044-4-44-44-4-20000-22-222-2223−2323−2323−2323−230000000000000000−2i22i20000000000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000
χ6144-4-44-44-4-20000-22-222-2223−2323−2323−2323−2300000000000000002i2−2i2000000000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000
χ6244-4-44-44-4-20000-22-222-22−2323−2323−2323−23230000000000000000−2i22i20000000000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000
χ6344-4-44-44-4-20000-22-222-22−2323−2323−2323−232300000000000000002i2−2i2000000000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000
χ6444-4-4-44-44400004-4-44-4-44000000000000004-4000000000000000000004-400000000000000000000000000000000
χ6544-4-4-44-44400004-4-44-4-4400000000000000-4400000000000000000000-4400000000000000000000000000000000
χ6644-4-4-44-44-20000-222-222-223−2323−23−2323−23230000004-400000000000000000023−23-2200000000000000000000000000000000
χ6744-4-4-44-44-20000-222-222-223−2323−23−2323−2323000000-44000000000000000000−23232-200000000000000000000000000000000
χ6844-4-4-44-44-20000-222-222-2−2323−232323−2323−230000004-4000000000000000000−2323-2200000000000000000000000000000000
χ6944-4-4-44-44-20000-222-222-2−2323−232323−2323−23000000-4400000000000000000023−232-200000000000000000000000000000000
χ704-44-44-4-4440000-444-4-4-440000000000004-400000000000000004-400000000000000000000000000000000000000
χ714-44-44-4-4440000-444-4-4-44000000000000-440000000000000000-4400000000000000000000000000000000000000
χ724-44-44-4-44-200002-2-2222-223−23−232323−23−232300004-40000000000000000-2223−23000000000000000000000000000000000000
χ734-44-44-4-44-200002-2-2222-223−23−232323−23−23230000-4400000000000000002-2−2323000000000000000000000000000000000000
χ744-44-44-4-44-200002-2-2222-2−232323−23−232323−2300004-40000000000000000-22−2323000000000000000000000000000000000000
χ754-44-44-4-44-200002-2-2222-2−232323−23−232323−230000-4400000000000000002-223−23000000000000000000000000000000000000
χ764-44-4-444-440000-44-44-44-40000000000000000000000−2i22i20000000000000000000000−2i22i2−2i22i200000000000000000000
χ774-44-4-444-440000-44-44-44-400000000000000000000002i2−2i200000000000000000000002i2−2i22i2−2i200000000000000000000
χ784-44-4-444-4-200002-22-22-2223−23−2323−232323−2300000000000000−2i22i200000000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000
χ794-44-4-444-4-200002-22-22-2223−23−2323−232323−23000000000000002i2−2i20000000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000
χ804-44-4-444-4-200002-22-22-22−232323−2323−23−232300000000000000−2i22i200000000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000
χ814-44-4-444-4-200002-22-22-22−232323−2323−23−2323000000000000002i2−2i20000000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000
χ824-4-4444-4-444-44-4-4-4444-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-4-4-24-44-422-2-2-222-2-222-2-2220000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ844-4-4444-4-4-24-44-422-2-2-222-2-222-2-22200000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ854-4-4444-4-4-2-44-4422-2-2-22222-2-222-2-20000000000004i−4i00000000000000000000−2i2i−2i2i000000000000000000000000
χ864-4-4444-4-4-2-44-4422-2-2-22222-2-222-2-2000000000000−4i4i000000000000000000002i−2i2i−2i000000000000000000000000
χ874-4-44-4-444-24-4-442222-2-2-2-2-22222-2-24-44-400000000000000-22-220000000000000000000000000000000000000000
χ884-4-44-4-444-24-4-442222-2-2-2-2-22222-2-2-44-44000000000000002-22-20000000000000000000000000000000000000000
χ894-4-44-4-444-2-444-42222-2-2-222-2-2-2-2224-4-4400000000000000-222-20000000000000000000000000000000000000000
χ904-4-44-4-444-2-444-42222-2-2-222-2-2-2-222-444-4000000000000002-2-220000000000000000000000000000000000000000

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