Finite Group Databasebeta

← Group #10945057

Character table — Group #10945057

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212121212121212121248484848
order1222222234444666666612121212121212122244444444446688888888121212121212121212122424242424242424242424242424242444444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ101111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11
χ121111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ131111111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ141111111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ151111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ161111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22200000000-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22200000000-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000000002222-2-2-2-222000000000000000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000022-2-22222-2-2000000000000000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-2-2-2-22222-1-11111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21122-2-222-2-211-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-211-2-222-2-22211-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222-2-21122-2-2-2-222111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-222-2-211-2-22222-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-222-2-2-1-10000000011-1-111-1-11133−3−333−3−333−3−333−3−300000000000000000000
χ3022222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-222-2-2-1-10000000011-1-111-1-111−3−333−3−333−3−333−3−33300000000000000000000
χ3122222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-22222-2-2-2-2-1-1000000001111-1-111-1-133−3−333−3−3−3−333−3−33300000000000000000000
χ3222222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-22222-2-2-2-2-1-1000000001111-1-111-1-1−3−333−3−33333−3−333−3−300000000000000000000
χ3322222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2221100000000-1-1-1-11111-1-133−3−3−3−33333−3−3−3−33300000000000000000000
χ3422222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22222-2-2-2-2221100000000-1-1-1-11111-1-1−3−33333−3−3−3−33333−3−300000000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222221100000000-1-111-1-1-1-11133−3−3−3−333−3−33333−3−300000000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2-2-22222221100000000-1-111-1-1-1-111−3−33333−3−333−3−3−3−33300000000000000000000
χ3722-22-2-2-22222-2-222-2-22-2-22222-2-2-2-200002i−2i002i−2i0000000000000000002i−2i2i−2i00000000000000002i2i−2i−2i0000000022-2-20000
χ3822-22-2-2-22222-2-222-2-22-2-22222-2-2-2-200002i−2i002i−2i0000000000000000002i−2i2i−2i0000000000000000−2i−2i2i2i00000000-2-2220000
χ3922-22-2-2-22222-2-222-2-22-2-22222-2-2-2-20000−2i2i00−2i2i000000000000000000−2i2i−2i2i00000000000000002i2i−2i−2i00000000-2-2220000
χ4022-22-2-2-22222-2-222-2-22-2-22222-2-2-2-20000−2i2i00−2i2i000000000000000000−2i2i−2i2i0000000000000000−2i−2i2i2i0000000022-2-20000
χ4122-22-2-2-222-2-22222-2-22-2-2-2-2-2-2222200002i−2i00−2i2i000000000000000000−2i2i2i−2i000000000000000000002i2i−2i−2i22-2-200000000
χ4222-22-2-2-222-2-22222-2-22-2-2-2-2-2-2222200002i−2i00−2i2i000000000000000000−2i2i2i−2i00000000000000000000−2i−2i2i2i-2-22200000000
χ4322-22-2-2-222-2-22222-2-22-2-2-2-2-2-222220000−2i2i002i−2i0000000000000000002i−2i−2i2i000000000000000000002i2i−2i−2i-2-22200000000
χ4422-22-2-2-222-2-22222-2-22-2-2-2-2-2-222220000−2i2i002i−2i0000000000000000002i−2i−2i2i00000000000000000000−2i−2i2i2i22-2-200000000
χ452-22-22-2-2222-22-2-2-2222-2-222-2-222-2-2002i−2i002i−2i00000000000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i00002-22-20000
χ462-22-22-2-2222-22-2-2-2222-2-222-2-222-2-2002i−2i002i−2i00000000000000002i−2i2i−2i000000000000000000000000−2i2i−2i2i0000-22-220000
χ472-22-22-2-2222-22-2-2-2222-2-222-2-222-2-200−2i2i00−2i2i0000000000000000−2i2i−2i2i0000000000000000000000002i−2i2i−2i0000-22-220000
χ482-22-22-2-2222-22-2-2-2222-2-222-2-222-2-200−2i2i00−2i2i0000000000000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i00002-22-20000
χ492-22-22-2-222-22-22-2-2222-2-2-2-222-2-222002i−2i00−2i2i00000000000000002i−2i−2i2i000000000000000000002i−2i2i−2i00002-22-200000000
χ502-22-22-2-222-22-22-2-2222-2-2-2-222-2-222002i−2i00−2i2i00000000000000002i−2i−2i2i00000000000000000000−2i2i−2i2i0000-22-2200000000
χ512-22-22-2-222-22-22-2-2222-2-2-2-222-2-22200−2i2i002i−2i0000000000000000−2i2i2i−2i000000000000000000002i−2i2i−2i0000-22-2200000000
χ522-22-22-2-222-22-22-2-2222-2-2-2-222-2-22200−2i2i002i−2i0000000000000000−2i2i2i−2i00000000000000000000−2i2i−2i2i00002-22-200000000
χ532-2-2-2-222222-2-22-2-2-2-222222-2-2-2-2222-2000000002-22-2000000002-2000000000000000000000000000000002-2-222-2-220000
χ542-2-2-2-222222-2-22-2-2-2-222222-2-2-2-2222-2000000002-22-2000000002-200000000000000000000000000000000-222-2-222-20000
χ552-2-2-2-222222-2-22-2-2-2-222222-2-2-2-222-2200000000-22-2200000000-22000000000000000000000000000000002-2-22-222-20000
χ562-2-2-2-222222-2-22-2-2-2-222222-2-2-2-222-2200000000-22-2200000000-2200000000000000000000000000000000-222-22-2-220000
χ572-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-22-200000000-222-200000000-220000000000000000000000002-2-22-222-2000000000000
χ582-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-22-200000000-222-200000000-22000000000000000000000000-222-22-2-22000000000000
χ592-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-2-22000000002-2-22000000002-20000000000000000000000002-2-222-2-22000000000000
χ602-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-2-22000000002-2-22000000002-2000000000000000000000000-222-2-222-2000000000000
χ61444-4-4-44-4400004-44-4-44-4000000000000000000000000000022−22000000000000000000000022−2222−2200000000000000000000
χ62444-4-4-44-4400004-44-4-44-40000000000000000000000000000−22220000000000000000000000−2222−222200000000000000000000
χ63444-4-4-44-4-20000-22-222-2223−2323−2323−2323−230000000000000000000022−2200000000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000
χ64444-4-4-44-4-20000-22-222-2223−2323−2323−2323−2300000000000000000000−22220000000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000
χ65444-4-4-44-4-20000-22-222-22−2323−2323−2323−23230000000000000000000022−2200000000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000
χ66444-4-4-44-4-20000-22-222-22−2323−2323−2323−232300000000000000000000−22220000000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000
χ6744-44-4-4-44-244-4-4-2-222-222-2-2-2-2222200004i−4i004i−4i000000000000000000−2i2i−2i2i000000000000000000000000000000000000
χ6844-44-4-4-44-244-4-4-2-222-222-2-2-2-222220000−4i4i00−4i4i0000000000000000002i−2i2i−2i000000000000000000000000000000000000
χ6944-44-4-4-44-2-4-444-2-222-2222222-2-2-2-200004i−4i00−4i4i0000000000000000002i−2i−2i2i000000000000000000000000000000000000
χ7044-44-4-4-44-2-4-444-2-222-2222222-2-2-2-20000−4i4i004i−4i000000000000000000−2i2i2i−2i000000000000000000000000000000000000
χ7144-4-444-4-4400004-4-44-4-44000000000000000000000022−22000000000000000022−2222−2200000000000000000000000000000000
χ7244-4-444-4-4400004-4-44-4-440000000000000000000000−22220000000000000000−2222−222200000000000000000000000000000000
χ7344-4-444-4-4-20000-222-222-223−2323−23−2323−23230000000000000022−2200000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000
χ7444-4-444-4-4-20000-222-222-223−2323−23−2323−232300000000000000−22220000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000
χ7544-4-444-4-4-20000-222-222-2−2323−232323−2323−230000000000000022−2200000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000
χ7644-4-444-4-4-20000-222-222-2−2323−232323−2323−2300000000000000−22220000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000
χ774-444-44-4-440000-444-4-4-4400000000000000000000000022−2200000000000000000022−2222−220000000000000000000000000000
χ784-444-44-4-440000-444-4-4-44000000000000000000000000−2222000000000000000000−2222−22220000000000000000000000000000
χ794-444-44-4-4-200002-2-2222-223−23−232323−23−2323000000000000000022−220000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000
χ804-444-44-4-4-200002-2-2222-223−23−232323−23−23230000000000000000−2222000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000
χ814-444-44-4-4-200002-2-2222-2−232323−23−232323−23000000000000000022−220000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000
χ824-444-44-4-4-200002-2-2222-2−232323−23−232323−230000000000000000−2222000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000
χ834-44-44-4-44-24-44-422-2-2-222-2-222-2-222004i−4i004i−4i0000000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ844-44-44-4-44-24-44-422-2-2-222-2-222-2-22200−4i4i00−4i4i00000000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ854-44-44-4-44-2-44-4422-2-2-22222-2-222-2-2004i−4i00−4i4i0000000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ864-44-44-4-44-2-44-4422-2-2-22222-2-222-2-200−4i4i004i−4i00000000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ874-4-444-44-440000-44-44-44-400000000000000000000000000−2i22i200000000000000000000−2i22i2−2i22i2000000000000000000000000
χ884-4-444-44-440000-44-44-44-4000000000000000000000000002i2−2i2000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ894-4-444-44-4-200002-22-22-2223−23−2323−232323−23000000000000000000−2i22i2000000000000000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000
χ904-4-444-44-4-200002-22-22-2223−23−2323−232323−230000000000000000002i2−2i200000000000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000
χ914-4-444-44-4-200002-22-22-22−232323−2323−23−2323000000000000000000−2i22i2000000000000000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000
χ924-4-444-44-4-200002-22-22-22−232323−2323−23−23230000000000000000002i2−2i200000000000000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000
χ934-4-4-4-4444-24-4-442222-2-2-2-2-22222-2-24-4000000004-4-2200000000-2200000000000000000000000000000000000000000000
χ944-4-4-4-4444-24-4-442222-2-2-2-2-22222-2-2-4400000000-442-2000000002-200000000000000000000000000000000000000000000
χ954-4-4-4-4444-2-444-42222-2-2-222-2-2-2-2224-400000000-44-22000000002-200000000000000000000000000000000000000000000
χ964-4-4-4-4444-2-444-42222-2-2-222-2-2-2-222-44000000004-42-200000000-2200000000000000000000000000000000000000000000

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