Finite Group Databasebeta

← Group #11781970

Character table — Group #11781970

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order1222334444666666121212123466612121212121212121212121244121212121212121212121212121212121212121212888824242424242424248888242424242424242441212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-111-1
χ61111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1
χ92222222-22-222222222222-222222-2-2-2-2-22222-200-200000000-2-2-2-20000000022-2-22222-2-2-2-2000000000000000000
χ102222222-22-222222222222-222222-2-2-2-2-22222-200-200000000-2-2-2-200000000-2-222-2-2-2-22222000000000000000000
χ11222222-22-22222222-2-2-2-22-2222-2-222-2-22-2-2-2-222-2-22222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-2-222-2-22-2-2-2-22-22-2-2-2-2-2222222-2-2-2-2-2-22222000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-2-222-2-2-2-2-2-200200000000-2-22200000000000000000000002i−2i2i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-2-222-2-2-2-2-2-200200000000-2-2220000000000000000000000−2i2i−2i−2i2i2i0000000000
χ1522222-122222-122-1-12222-12-1-1-1-1-12222-1-1-1-1-1-122-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022000000-1-1-1-12-1-1000
χ1622222-122222-122-1-12222-12-1-1-1-1-12222-1-1-1-1-1-122-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-20000001111-211000
χ1722222-122222-122-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-2-2-1-2-211-2-211-1-1-1-11111111100000000000022000000-1-1-1-1-211000
χ1822222-122222-122-1-12222-12-1-1-1-1-12222-1-1-1-1-1-1-2-2-1-2-211-2-211-1-1-1-111111111000000000000-2-200000011112-1-1000
χ1922222-1-22-222-122-1-1-2-2-2-2-1-2-1-1-11122-2-2-11111-12-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-1-22-222-122-1-1-2-2-2-2-1-2-1-1-11122-2-2-11111-12-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-1-22-222-122-1-1-2-2-2-2-1-2-1-1-11122-2-2-11111-1-221-2-21122-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-1-22-222-122-1-1-2-2-2-2-1-2-1-1-11122-2-2-11111-1-221-2-21122-1-1-1-1111111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-12-1-122-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-10000000000
χ242222-122222-12-1-122-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100-2-211110000000000
χ252222-122222-12-1-122-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-2211-2-211-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-100-2-211110000000000
χ262222-122222-12-1-122-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-2211-2-211-2-2-1-1-1-111111111-2-2-2-2111111110022-1-1-1-10000000000
χ272222-122-22-2-12-1-122-1-1-1-1-1-2-1-1-1221111-2-1-1-1-1-200-2−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i322-2-2-1-1-1-111110000−i3i3−i3i30000000000
χ282222-122-22-2-12-1-122-1-1-1-1-1-2-1-1-1221111-2-1-1-1-1-200-2−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i3-2-2221111-1-1-1-10000i3−i3i3−i30000000000
χ292222-122-22-2-12-1-122-1-1-1-1-1-2-1-1-1221111-2-1-1-1-1-200-2i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i322-2-2-1-1-1-111110000i3−i3i3−i30000000000
χ302222-122-22-2-12-1-122-1-1-1-1-1-2-1-1-1221111-2-1-1-1-1-200-2i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i3-2-2221111-1-1-1-10000−i3i3−i3i30000000000
χ312222-12-22-22-12-1-1221111-1-2-1-1-1-2-2-1-1112111122-2-2-1-12211-2-2-1-111-1-1-1-11111000033−3−333−3−300003−3−330000000000
χ322222-12-22-22-12-1-1221111-1-2-1-1-1-2-2-1-1112111122-2-2-1-12211-2-2-1-111-1-1-1-111110000−3−333−3−3330000−333−30000000000
χ332222-12-22-22-12-1-1221111-1-2-1-1-1-2-2-1-111211112-22-211-2-2-1-122-1-1111111-1-1-1-1000033−3−333−3−30000−333−30000000000
χ342222-12-22-22-12-1-1221111-1-2-1-1-1-2-2-1-111211112-22-211-2-2-1-122-1-1111111-1-1-1-10000−3−333−3−33300003−3−330000000000
χ352222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-1-1-21111-2002−i3i300i3−i30011-1-1−i3−i3i3i3i3i3−i3−i3000033−3−3−3−333002i−2i−i−iii0000000000
χ362222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-1-1-21111-2002−i3i300i3−i30011-1-1−i3−i3i3i3i3i3−i3−i30000−3−33333−3−300−2i2iii−i−i0000000000
χ372222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-1-1-21111-2002i3−i300−i3i30011-1-1i3i3−i3−i3−i3−i3i3i3000033−3−3−3−33300−2i2iii−i−i0000000000
χ382222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-1-1-21111-2002i3−i300−i3i30011-1-1i3i3−i3−i3−i3−i3i3i30000−3−33333−3−3002i−2i−i−iii0000000000
χ3922-2-22220-2022-2-2-2-222-2-2202-2-22-20000022-2-20000000000000000000000002-2002-22-200002−20000002−22−20002−20
χ4022-2-22220-2022-2-2-2-222-2-2202-2-22-20000022-2-20000000000000000000000002-2002-22-20000−22000000−22−22000−220
χ4122-2-22220-2022-2-2-2-222-2-2202-2-22-20000022-2-2000000000000000000000000-2200-22-2200002−20000002−22−2000−220
χ4222-2-22220-2022-2-2-2-222-2-2202-2-22-20000022-2-2000000000000000000000000-2200-22-220000−22000000−22−220002−20
χ4344444-24-44-44-244-2-24444-2-4-2-2-2-2-2-4-4-4-42-2-2-2-2200200000000222200000000000000000000000000000000000000
χ4444444-2-4-4-4-44-244-2-2-4-4-4-4-24-2-2-222-4-44422222200-20000000022-2-200000000000000000000000000000000000000
χ454444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-2-21111-244-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000
χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-2-21111-2-4-4-2222222221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ474444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2-22222211112002−2i32i300−2i32i300-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000
χ484444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2-222222111120022i3−2i3002i3−2i300-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000
χ494444-2-2-44-44-2-2-2-2-2-222221-411122-2-222-2-1-1-1-1-24-42-2-2-2-2222211-1-11111-1-1-1-1000000000000000000000000000000
χ504444-2-2-44-44-2-2-2-2-2-222221-411122-2-222-2-1-1-1-1-2-4422222-2-2-2-211-1-1-1-1-1-11111000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-22222141112222-2-22-1-1-1-1200-2−2i32i3002i3−2i300-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-22222141112222-2-22-1-1-1-1200-22i3−2i300−2i32i300-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000
χ5344-4-444-404044-4-4-4-4-4-444404-4-4-4400000-4-444000000000000000000000000000000000000000000000000000000
χ5444-4-44-240-404-2-4-42244-4-4-20-222-2200000-2-22200000000000000000000000000000000000022−22000000−22−22000000
χ5544-4-44-240-404-2-4-42244-4-4-20-222-2200000-2-222000000000000000000000000000000000000−22220000002−22−2000000
χ5644-4-44-2-40404-2-4-422-4-444-20-2222-20000022-2-200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ5744-4-44-2-40404-2-4-422-4-444-20-2222-20000022-2-200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ5844-4-4-2440-40-2422-4-4-2-222-20-2224-400000-2-2220000000000000000000000004-400-22-220000000000000000000000
χ5944-4-4-2440-40-2422-4-4-2-222-20-2224-400000-2-222000000000000000000000000-44002-22-20000000000000000000000
χ6044-4-4-24-4040-2422-4-422-2-2-20-222-440000022-2-2000000000000000000000000000023−23−23230000000000000000000000
χ6144-4-4-24-4040-2422-4-422-2-2-20-222-440000022-2-20000000000000000000000000000−232323−230000000000000000000000
χ624-44-4440000-4-44-44-4000040-44-4000000000000000000000000000000000000022−22000022−2222−22000000000000000000
χ634-44-4440000-4-44-44-4000040-44-40000000000000000000000000000000000000−22220000−2222−2222000000000000000000
χ644-44-4-2400002-4-224-423−2323−23-202-22000000023−2323−230000000000000000000000000022−2200002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000
χ654-44-4-2400002-4-224-423−2323−23-202-22000000023−2323−2300000000000000000000000000−22220000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000
χ664-44-4-2400002-4-224-4−2323−2323-202-220000000−2323−23230000000000000000000000000022−2200002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000
χ674-44-4-2400002-4-224-4−2323−2323-202-220000000−2323−232300000000000000000000000000−22220000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000
χ684-4-4444040-4-4-4-44-44000040-4-44004-400-400004000000000004-40000000000000000000000000000000000000000
χ694-4-44440-404-4-4-44-44000040-4-4400-440040000-400000000000-440000000000000000000000000000000000000000
χ704-4-444-2040-4-42-442-20000-2022-2004-40020000-2000000000−2i32i3-22000000−2i32i3−2i32i3000000000000000000000000000000
χ714-4-444-2040-4-42-442-20000-2022-2004-40020000-20000000002i3−2i3-220000002i3−2i32i3−2i3000000000000000000000000000000
χ724-4-444-20-404-42-442-20000-2022-200-4400-2000020000023−2300002-20023−2323−230000000000000000000000000000000000
χ734-4-444-20-404-42-442-20000-2022-200-4400-20000200000−232300002-200−2323−23230000000000000000000000000000000000
χ744-4-44-24040-42-42-2-4423−23−2323-2022-200-2223−23-423−23−2323400000000000-2223−2300000000000000000000000000000000000000
χ754-4-44-24040-42-42-2-44−232323−23-2022-200-22−2323-4−232323−23400000000000-22−232300000000000000000000000000000000000000
χ764-4-44-240-4042-42-2-4423−23−2323-2022-2002-2−2323423−23−2323-4000000000002-2−232300000000000000000000000000000000000000
χ774-4-44-240-4042-42-2-44−232323−23-2022-2002-223−234−232323−23-4000000000002-223−2300000000000000000000000000000000000000
χ784-4-44-2-2040-4222-22-223−23−232310-1-1100-2223−232−333−3-2000000000−2i32i31-1−333i−3i−3i3ii3−i3i3−i3000000000000000000000000000000
χ794-4-44-2-2040-4222-22-223−23−232310-1-1100-2223−232−333−3-20000000002i3−2i31-1−33−3i3i3i−3i−i3i3−i3i3000000000000000000000000000000
χ804-4-44-2-2040-4222-22-2−232323−2310-1-1100-22−232323−3−33-2000000000−2i32i31-13−3−3i3i3i−3ii3−i3i3−i3000000000000000000000000000000
χ814-4-44-2-2040-4222-22-2−232323−2310-1-1100-22−232323−3−33-20000000002i3−2i31-13−33i−3i−3i3i−i3i3−i3i3000000000000000000000000000000
χ824-4-44-2-20-404222-22-223−23−232310-1-11002-2−2323-2−333−320000023−230000-113−3−33−333-3-33000000000000000000000000000000
χ834-4-44-2-20-404222-22-223−23−232310-1-11002-2−2323-2−333−3200000−23230000-113−33−33−3-333-3000000000000000000000000000000
χ844-4-44-2-20-404222-22-2−232323−2310-1-11002-223−23-23−3−3320000023−230000-11−33−33−33-333-3000000000000000000000000000000
χ854-4-44-2-20-404222-22-2−232323−2310-1-11002-223−23-23−3−33200000−23230000-11−333−33−33-3-33000000000000000000000000000000
χ8688-8-8-4-480-80-4-44444-4-444202-2-2-440000022-2-2000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-4-8080-4-4444444-4-4202-2-24-400000-2-222000000000000000000000000000000000000000000000000000000
χ888-88-88-40000-848-8-440000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4000044-44-4443−4343−4320-22-20000000−2323−2323000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4000044-44-44−4343−434320-22-2000000023−2323−23000000000000000000000000000000000000000000000000000000

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