Finite Group Databasebeta

← Group #11781811

Character table — Group #11781811

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
χ92222222-22-222222222222-2222-2-2-2-2-2222222-200-200000000-2-2-2-20000000022-2-22222-2-2-2-2000000000000000000
χ102222222-22-222222222222-2222-2-2-2-2-2222222-200-200000000-2-2-2-200000000-2-222-2-2-2-22222000000000000000000
χ11222222-22-22222222-2-2-2-22-2222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-2222222-2-2-2-2-2-2-2-22-22-2-2-2-2-2222222-2-2-2-2-2-22222000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-222-2-2-2-2-2-2-200200000000-2-22200000000000000000000002i−2i2i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-222-2-2-2-2-2-2-200200000000-2-2220000000000000000000000−2i2i−2i−2i2i2i0000000000
χ1522222-12222222-1-1-12222-12-1-1-122-122-1-1-1-1-1-1-122-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022000000-1-1-1-12-1-1000
χ1622222-12222222-1-1-12222-12-1-1-122-122-1-1-1-1-1-1-122-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-20000001111-211000
χ1722222-12222222-1-1-12222-12-1-1-122-122-1-1-1-1-1-1-1-2-2-1-2-211-2-211-1-1-1-11111111100000000000022000000-1-1-1-1-211000
χ1822222-12222222-1-1-12222-12-1-1-122-122-1-1-1-1-1-1-1-2-2-1-2-211-2-211-1-1-1-111111111000000000000-2-200000011112-1-1000
χ1922222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-122-1-2-2111111-12-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-122-1-2-2111111-12-2122-1-1-2-211-1-111-1-1-1-1111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-122-1-2-2111111-1-221-2-21122-1-1-1-1111111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-1-22-22222-1-1-1-2-2-2-2-1-2-1-1-122-1-2-2111111-1-221-2-21122-1-1-1-1111111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-10000000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100-2-211110000000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12-2-2211-2-211-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-100-2-211110000000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-12-1-122-1-1-1-12-2-2211-2-211-2-2-1-1-1-111111111-2-2-2-2111111110022-1-1-1-10000000000
χ272222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-111-21122-1-1-1-1-200-2−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i322-2-2-1-1-1-111110000−i3i3−i3i30000000000
χ282222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-111-21122-1-1-1-1-200-2−i3i300−i3i3001111−i3−i3i3i3−i3−i3i3i3-2-2221111-1-1-1-10000i3−i3i3−i30000000000
χ292222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-111-21122-1-1-1-1-200-2i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i322-2-2-1-1-1-111110000i3−i3i3−i30000000000
χ302222-122-22-2-1-1-1222-1-1-1-1-1-2-1-1-111-21122-1-1-1-1-200-2i3−i300i3−i3001111i3i3−i3−i3i3i3−i3−i3-2-2221111-1-1-1-10000−i3i3−i3i30000000000
χ312222-12-22-22-1-1-12221111-1-2-1-1-1-1-1211-2-2111122-2-2-1-12211-2-2-1-111-1-1-1-11111000033−3−333−3−300003−3−330000000000
χ322222-12-22-22-1-1-12221111-1-2-1-1-1-1-1211-2-2111122-2-2-1-12211-2-2-1-111-1-1-1-111110000−3−333−3−3330000−333−30000000000
χ332222-12-22-22-1-1-12221111-1-2-1-1-1-1-1211-2-211112-22-211-2-2-1-122-1-1111111-1-1-1-1000033−3−333−3−30000−333−30000000000
χ342222-12-22-22-1-1-12221111-1-2-1-1-1-1-1211-2-211112-22-211-2-2-1-122-1-1111111-1-1-1-10000−3−333−3−33300003−3−330000000000
χ352222-12-2-2-2-2-1-1-12221111-12-1-1-111-2-1-1-2-21111-2002−i3i300i3−i30011-1-1−i3−i3i3i3i3i3−i3−i3000033−3−3−3−333002i−2i−i−iii0000000000
χ362222-12-2-2-2-2-1-1-12221111-12-1-1-111-2-1-1-2-21111-2002−i3i300i3−i30011-1-1−i3−i3i3i3i3i3−i3−i30000−3−33333−3−300−2i2iii−i−i0000000000
χ372222-12-2-2-2-2-1-1-12221111-12-1-1-111-2-1-1-2-21111-2002i3−i300−i3i30011-1-1i3i3−i3−i3−i3−i3i3i3000033−3−3−3−33300−2i2iii−i−i0000000000
χ382222-12-2-2-2-2-1-1-12221111-12-1-1-111-2-1-1-2-21111-2002i3−i300−i3i30011-1-1i3i3−i3−i3−i3−i3i3i30000−3−33333−3−3002i−2i−i−iii0000000000
χ392-2-222220-202-2-2-2-2222-2-2202-2-2000002-222-2-20000000000000000000000002-2002-22-20000−i2i2000000−i2i2−i2i2000−i2i20
χ402-2-222220-202-2-2-2-2222-2-2202-2-2000002-222-2-20000000000000000000000002-2002-22-20000i2−i2000000i2−i2i2−i2000i2−i20
χ412-2-222220-202-2-2-2-2222-2-2202-2-2000002-222-2-2000000000000000000000000-2200-22-220000−i2i2000000−i2i2−i2i2000i2−i20
χ422-2-222220-202-2-2-2-2222-2-2202-2-2000002-222-2-2000000000000000000000000-2200-22-220000i2−i2000000i2−i2i2−i2000−i2i20
χ4344444-24-44-4444-2-2-24444-2-4-2-2-2-4-42-4-4-2-2-2-2-2-2200200000000222200000000000000000000000000000000000000
χ4444444-2-4-4-4-4444-2-2-2-4-4-4-4-24-2-2-2-4-4244222222200-20000000022-2-200000000000000000000000000000000000000
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
χ474444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-411122222-2-211112002−2i32i300−2i32i300-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000
χ484444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-411122222-2-2111120022i3−2i3002i3−2i300-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000
χ494444-2-2-44-44-2-2-2-2-2-222221-4111-2-2-22222-1-1-1-1-24-42-2-2-2-2222211-1-11111-1-1-1-1000000000000000000000000000000
χ504444-2-2-44-44-2-2-2-2-2-222221-4111-2-2-22222-1-1-1-1-2-4422222-2-2-2-211-1-1-1-1-1-11111000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-2222214111222-2-222-1-1-1-1200-2−2i32i3002i3−2i300-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-2222214111222-2-222-1-1-1-1200-22i3−2i300−2i32i300-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000
χ5344-4-4440000-44-44-4-4000040-44-4000000000000000000000000000000000000022−22000022−2222−22000000000000000000
χ5444-4-4440000-44-44-4-4000040-44-40000000000000000000000000000000000000−22220000−2222−2222000000000000000000
χ5544-4-4-2400002-224-4-423−2323−23-202-22000000023−2323−230000000000000000000000000022−2200002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000
χ5644-4-4-2400002-224-4-423−2323−23-202-22000000023−2323−2300000000000000000000000000−22220000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000
χ5744-4-4-2400002-224-4-4−2323−2323-202-220000000−2323−23230000000000000000000000000022−2200002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000
χ5844-4-4-2400002-224-4-4−2323−2323-202-220000000−2323−232300000000000000000000000000−22220000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000
χ594-44-444040-4-4-44-44-4000040-4-444-4-4000000004000000000004-40000000000000000000000000000000000000000
χ604-44-4440-404-4-44-44-4000040-4-44-44400000000-400000000000-440000000000000000000000000000000000000000
χ614-44-44-2040-4-4-442-220000-2022-24-4200000000-20000023−230000-220023−2323−230000000000000000000000000000000000
χ624-44-44-2040-4-4-442-220000-2022-24-4200000000-200000−23230000-2200−2323−23230000000000000000000000000000000000
χ634-44-44-20-404-4-442-220000-2022-2-44-2000000002000000000−2i32i32-2000000−2i32i3−2i32i3000000000000000000000000000000
χ644-44-44-20-404-4-442-220000-2022-2-44-20000000020000000002i3−2i32-20000002i3−2i32i3−2i3000000000000000000000000000000
χ654-44-4-24040-422-2-44-423−23−2323-2022-2-22-423−230023−23−2323400000000000-2223−2300000000000000000000000000000000000000
χ664-44-4-24040-422-2-44-4−232323−23-2022-2-22-4−232300−232323−23400000000000-22−232300000000000000000000000000000000000000
χ674-44-4-240-40422-2-44-423−23−2323-2022-22-24−23230023−23−2323-4000000000002-2−232300000000000000000000000000000000000000
χ684-44-4-240-40422-2-44-4−232323−23-2022-22-2423−2300−232323−23-4000000000002-223−2300000000000000000000000000000000000000
χ694-44-4-2-2040-422-22-2223−23−232310-1-11-22223−2300−333−3-20000023−2300001-1−33−33−333-3-33000000000000000000000000000000
χ704-44-4-2-2040-422-22-2223−23−232310-1-11-22223−2300−333−3-200000−232300001-1−333−33−3-333-3000000000000000000000000000000
χ714-44-4-2-2040-422-22-22−232323−2310-1-11-222−2323003−3−33-20000023−2300001-13−3−33−33-333-3000000000000000000000000000000
χ724-44-4-2-2040-422-22-22−232323−2310-1-11-222−2323003−3−33-200000−232300001-13−33−33−33-3-33000000000000000000000000000000
χ734-44-4-2-20-40422-22-2223−23−232310-1-112-2-2−232300−333−32000000000−2i32i3-113−33i−3i−3i3ii3−i3i3−i3000000000000000000000000000000
χ744-44-4-2-20-40422-22-2223−23−232310-1-112-2-2−232300−333−320000000002i3−2i3-113−3−3i3i3i−3i−i3i3−i3i3000000000000000000000000000000
χ754-44-4-2-20-40422-22-22−232323−2310-1-112-2-223−23003−3−332000000000−2i32i3-11−33−3i3i3i−3ii3−i3i3−i3000000000000000000000000000000
χ764-44-4-2-20-40422-22-22−232323−2310-1-112-2-223−23003−3−3320000000002i3−2i3-11−333i−3i−3i3i−i3i3−i3i3000000000000000000000000000000
χ774-4-4444-40404-4-4-4-44-4-444404-4-400000-44-4-444000000000000000000000000000000000000000000000000000000
χ784-4-444-240-404-4-422-244-4-4-20-22200000-22-2-222000000000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ794-4-444-240-404-4-422-244-4-4-20-22200000-22-2-2220000000000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ804-4-444-2-40404-4-422-2-4-444-20-222000002-222-2-2000000000000000000000000000000000000000000006−6−66000000
χ814-4-444-2-40404-4-422-2-4-444-20-222000002-222-2-200000000000000000000000000000000000000000000−666−6000000
χ824-4-44-2440-40-222-4-44-2-222-20-222000004-4-2-2220000000000000000000000004-400-22-220000000000000000000000
χ834-4-44-2440-40-222-4-44-2-222-20-222000004-4-2-222000000000000000000000000-44002-22-20000000000000000000000
χ844-4-44-24-4040-222-4-4422-2-2-20-22200000-4422-2-2000000000000000000000000000023−23−23230000000000000000000000
χ854-4-44-24-4040-222-4-4422-2-2-20-22200000-4422-2-20000000000000000000000000000−232323−230000000000000000000000
χ8688-8-88-40000-88-8-4440000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-400004-44-44443−4343−4320-22-20000000−2323−2323000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-400004-44-444−4343−434320-22-2000000023−2323−23000000000000000000000000000000000000000000000000000000
χ898-8-88-4-480-80-44444-4-4-444202-2-200000-4422-2-2000000000000000000000000000000000000000000000000000000
χ908-8-88-4-4-8080-44444-444-4-4202-2-2000004-4-2-222000000000000000000000000000000000000000000000000000000

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