Finite Group Databasebeta

← Group #10858376

Character table — Group #10858376

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666222244121212121212121244444666688881212121212122424242424242424444444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ5111111111111111111111111-1-111-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-11111-1-111-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-11-1-1-1-111-1-1111
χ7111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-111-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111111-1-11111-1-1-1
χ911111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1
χ1111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ1211111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-111-1-111-1-111-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-11-1-111-1-111-1-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-11-1-111-1-1-1-1-11111-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-111-1
χ17222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-200000000000022-2-2-2-200000200000000000
χ18222222222-2-2-2-22222222000022-2-22222-2-2-2000000000000-2-2000000000000-2-2222200000-200000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-220000000000002200000000000022-2-22200000-200000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2200000000000022000000000000-2-222-2-200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-222-1-1-1-1-2-222111111-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-1-11111-1-1-2-2-2-2-2-1-1-1-122-2-21111111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2221111-2-2-2-2-1-11111111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-12-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-22222111122-2-211-1-1-1-11111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-1-222-2-21111-2-22211-1-1-1-1-1-1-1-11111000000211-1-1000000000000
χ29222-2-2-22-222-22-222-22-2-2-222-2-200220000-2-20000022-2-20000000000000000000000000000002-200002-2000
χ30222-2-2-22-222-22-222-22-2-2-222-2-200220000-2-20000022-2-2000000000000000000000000000000-220000-22000
χ31222-2-2-22-222-22-222-22-2-2-2-2-22200220000-2-200000-2-2220000000000000000000000000000002-20000-22000
χ32222-2-2-22-222-22-222-22-2-2-2-2-22200220000-2-200000-2-222000000000000000000000000000000-2200002-2000
χ332-2-222-22-222-2-22-2-2-22-2220000002-200002-202-200000000000022-2-2000000002i−2i2i−2i0000000000002i−2i00000
χ342-2-222-22-222-2-22-2-2-22-2220000002-200002-202-200000000000022-2-200000000−2i2i−2i2i000000000000−2i2i00000
χ352-2-222-22-222-2-22-2-2-22-2220000002-200002-20-22000000000000-2-222000000002i−2i2i−2i000000000000−2i2i00000
χ362-2-222-22-222-2-22-2-2-22-2220000002-200002-20-22000000000000-2-22200000000−2i2i−2i2i0000000000002i−2i00000
χ372-2-222-22-22-222-2-2-2-22-2222-22-200-220000-22000002-22-20000000000000000002i−2i−2i2i00000000002i−2i0000000
χ382-2-222-22-22-222-2-2-2-22-2222-22-200-220000-22000002-22-2000000000000000000−2i2i2i−2i0000000000−2i2i0000000
χ392-2-222-22-22-222-2-2-2-22-222-22-2200-220000-2200000-22-220000000000000000002i−2i−2i2i0000000000−2i2i0000000
χ402-2-222-22-22-222-2-2-2-22-222-22-2200-220000-2200000-22-22000000000000000000−2i2i2i−2i00000000002i−2i0000000
χ412-2-2-2-22222-2-222-2-2222-2-22-2-2200-2200002-20002-22-2-22002-200000022-2-2000000000002-200000000000000
χ422-2-2-2-22222-2-222-2-2222-2-22-2-2200-2200002-2000-222-2-2200-22000000-2-22200000000000-2200000000000000
χ432-2-2-2-22222-2-222-2-2222-2-2-222-200-2200002-20002-2-222-200-22000000-2-222000000000002-200000000000000
χ442-2-2-2-22222-2-222-2-2222-2-2-222-200-2200002-2000-22-222-2002-200000022-2-200000000000-2200000000000000
χ452-2-2-2-2222-1-2-22211-1-1-1112-2-22001-133−3−3-110002-2-111-1002-23−33−33−3-1-11133−3−30000000-113−3000000000000
χ462-2-2-2-2222-1-2-22211-1-1-1112-2-22001-133−3−3-11000-22-111-100-223−33−33−311-1-1−3−33300000001-1−33000000000000
χ472-2-2-2-2222-1-2-22211-1-1-1112-2-22001-1−3−333-110002-2-111-1002-2−33−33−33-1-111−3−3330000000-11−33000000000000
χ482-2-2-2-2222-1-2-22211-1-1-1112-2-22001-1−3−333-11000-22-111-100-22−33−33−3311-1-133−3−300000001-13−3000000000000
χ492-2-2-2-2222-1-2-22211-1-1-111-222-2001-133−3−3-110002-21-1-1100-223−3−33−3311-1-1−3−3330000000-113−3000000000000
χ502-2-2-2-2222-1-2-22211-1-1-111-222-2001-133−3−3-11000-221-1-11002-23−3−33−33-1-11133−3−300000001-1−33000000000000
χ512-2-2-2-2222-1-2-22211-1-1-111-222-2001-1−3−333-110002-21-1-1100-22−333−33−311-1-133−3−30000000-11−33000000000000
χ522-2-2-2-2222-1-2-22211-1-1-111-222-2001-1−3−333-11000-221-1-11002-2−333−33−3-1-111−3−33300000001-13−3000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-200004422-2-2-2-222-40000000000002200000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4222222224000000000000-2-200000000000000000000000000000000000
χ55444-4-4-44-44-44-4444-44-4-4-4000000-4-400004400000000000000000000000000000000000000000000000000
χ56444-4-4-44-4-24-44-4-2-22-222244-4-400-2-200002200000-2-22200000000000000000000000000000000000000000
χ57444-4-4-44-4-24-44-4-2-22-2222-4-44400-2-20000220000022-2-200000000000000000000000000000000000000000
χ58444-4-4-44-4-2-44-44-2-22-2222000000220000-2-200000000000000023−23−23230000000000000000000000000000000
χ59444-4-4-44-4-2-44-44-2-22-2222000000220000-2-2000000000000000−232323−230000000000000000000000000000000
χ6044-44-44-4-4400004-44-4-44-40000000000000000000000022−2200000000000022−2222−2200000000000000000000000
χ6144-44-44-4-4400004-44-4-44-400000000000000000000000−2222000000000000−2222−222200000000000000000000000
χ6244-44-44-4-4-20000-22-222-220000000023−2323−230000000000022−22000000006−66−6−22−2200000000000000000000000
χ6344-44-44-4-4-20000-22-222-220000000023−2323−2300000000000−222200000000−66−662−22−200000000000000000000000
χ6444-44-44-4-4-20000-22-222-2200000000−2323−23230000000000022−2200000000−66−66−22−2200000000000000000000000
χ6544-44-44-4-4-20000-22-222-2200000000−2323−232300000000000−2222000000006−66−62−22−200000000000000000000000
χ6644-4-44-4-44400004-4-4-44-440000000000000000000000000000000000000000000004-400000000000000000
χ6744-4-44-4-44400004-4-4-44-44000000000000000000000000000000000000000000000-4400000000000000000
χ684-444-4-4-4440000-44-4-444-4000000000000000000000000000000000000000000000000000000000000022−220
χ694-444-4-4-4440000-44-4-444-40000000000000000000000000000000000000000000000000000000000000−22220
χ704-44-444-4-440000-444-4-4-4400004-4004-4-440000000000000000000000000000000000000000000000000000
χ714-44-444-4-440000-444-4-4-440000-4400-444-40000000000000000000000000000000000000000000000000000
χ724-44-444-4-4-200002-2-2222-200004-400-222-20000000000000000000006−6−66−666−600000000000000000000000
χ734-44-444-4-4-200002-2-2222-200004-400-222-2000000000000000000000−666−66−6−6600000000000000000000000
χ744-44-444-4-4-200002-2-2222-20000-44002-2-220000000000000000000006−6−666−6−6600000000000000000000000
χ754-44-444-4-4-200002-2-2222-20000-44002-2-22000000000000000000000−666−6−666−600000000000000000000000
χ764-4-444-44-4-24-4-44222-22-2-2000000-220000-2204-4000000000000-2-2220000000000000000000000000000000
χ774-4-444-44-4-24-4-44222-22-2-2000000-220000-220-4400000000000022-2-20000000000000000000000000000000
χ784-4-444-44-4-2-444-4222-22-2-24-44-4002-200002-200000-22-2200000000000000000000000000000000000000000
χ794-4-444-44-4-2-444-4222-22-2-2-44-44002-200002-2000002-22-200000000000000000000000000000000000000000
χ804-4-4-4-4444444-4-4-4-4444-4-40000004-40000-4400000000000000000000000000000000000000000000000000
χ814-4-4-4-4444-244-4-422-2-2-222000000-222323−23−232-20000000000000−232300000000000000000000000000000000000
χ824-4-4-4-4444-244-4-422-2-2-222000000-22−23−2323232-2000000000000023−2300000000000000000000000000000000000
χ8388-8-88-8-88-40000-4444-44-40000000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).