Finite Group Databasebeta

← Group #11781937

Character table — Group #11781937

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order12223344446666661212121234666121212121212121212121212246666666612121212121212121212121212888824242424242424248888242424242424242441212884
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
χ51111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-111-1
χ61111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1
χ92222222-22-222222222222-2222-2-2-2-222-22222-20000000000-20000-2-2-2-2000022-2-22222-2-2-2-2000000000000000000
χ102222222-22-222222222222-2222-2-2-2-222-22222-20000000000-20000-2-2-2-20000-2-222-2-2-2-22222000000000000000000
χ11222222-22-22222222-2-2-2-22-222222-2-2-2-22-2-2-2-222-222222222-2-2-2-2-222-2-2-2-2-2-2000000000000000000000000000000
χ12222222-22-22222222-2-2-2-22-222222-2-2-2-22-2-2-2-22-22-2-2-2-2-2-2-2-2-2222222-2-22222000000000000000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2000000000020000-2-2220000000000000000002i−2i2i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2000000000020000-2-222000000000000000000−2i2i−2i−2i2i2i0000000000
χ1522222-1222222-12-1-12222-12-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000022000000-1-1-1-12-1-1000
χ1622222-1222222-12-1-12222-12-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-20000001111-211000
χ1722222-1222222-12-1-12222-12-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111-1-2-211-1-1-1-1111100000000000022000000-1-1-1-1-211000
χ1822222-1222222-12-1-12222-12-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111-1-2-211-1-1-1-11111000000000000-2-200000011112-1-1000
χ1922222-1-22-2222-12-1-1-2-2-2-2-1-2-1-1-122-2-211-11111-12-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-1-22-2222-12-1-1-2-2-2-2-1-2-1-1-122-2-211-11111-12-222-1-1-1-1-1-11-2-211-1-111111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-1-22-2222-12-1-1-2-2-2-2-1-2-1-1-122-2-211-11111-1-22-2-2111111122-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-1-22-2222-12-1-1-2-2-2-2-1-2-1-1-122-2-211-11111-1-22-2-2111111122-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-1-12-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-10000000000
χ242222-122222-1-12-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111100-2-211110000000000
χ252222-122222-1-12-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-12-2-211-2-21111211-2-2-1-1-1-111112222-1-1-1-1-1-1-1-100-2-211110000000000
χ262222-122222-1-12-122-1-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-12-2-211-2-21111211-2-2-1-1-1-11111-2-2-2-2111111110022-1-1-1-10000000000
χ272222-122-22-2-1-12-122-1-1-1-1-1-2-1-1-1111122-2-1-1-1-1-200−i3i300−i3−i3i3i3-2−i3i3001111−i3−i3i3i322-2-2-1-1-1-111110000−i3i3−i3i30000000000
χ282222-122-22-2-1-12-122-1-1-1-1-1-2-1-1-1111122-2-1-1-1-1-200−i3i300−i3−i3i3i3-2−i3i3001111−i3−i3i3i3-2-2221111-1-1-1-10000i3−i3i3−i30000000000
χ292222-122-22-2-1-12-122-1-1-1-1-1-2-1-1-1111122-2-1-1-1-1-200i3−i300i3i3−i3−i3-2i3−i3001111i3i3−i3−i322-2-2-1-1-1-111110000i3−i3i3−i30000000000
χ302222-122-22-2-1-12-122-1-1-1-1-1-2-1-1-1111122-2-1-1-1-1-200i3−i300i3i3−i3−i3-2i3−i3001111i3i3−i3−i3-2-2221111-1-1-1-10000−i3i3−i3i30000000000
χ312222-12-22-22-1-12-1221111-1-2-1-1-1-1-111-2-22111122-2-1-122-1-1-1-1-211-2-2-1-1111111000033−3−333−3−300003−3−330000000000
χ322222-12-22-22-1-12-1221111-1-2-1-1-1-1-111-2-22111122-2-1-122-1-1-1-1-211-2-2-1-11111110000−3−333−3−3330000−333−30000000000
χ332222-12-22-22-1-12-1221111-1-2-1-1-1-1-111-2-2211112-2211-2-21111-2-1-122-1-111-1-1-1-1000033−3−333−3−30000−333−30000000000
χ342222-12-22-22-1-12-1221111-1-2-1-1-1-1-111-2-2211112-2211-2-21111-2-1-122-1-111-1-1-1-10000−3−333−3−33300003−3−330000000000
χ352222-12-2-2-2-2-1-12-1221111-12-1-1-111-1-1-2-2-21111-200−i3i300−i3−i3i3i32i3−i30011-1-1i3i3−i3−i3000033−3−3−3−333002i−2i−i−iii0000000000
χ362222-12-2-2-2-2-1-12-1221111-12-1-1-111-1-1-2-2-21111-200−i3i300−i3−i3i3i32i3−i30011-1-1i3i3−i3−i30000−3−33333−3−300−2i2iii−i−i0000000000
χ372222-12-2-2-2-2-1-12-1221111-12-1-1-111-1-1-2-2-21111-200i3−i300i3i3−i3−i32−i3i30011-1-1−i3−i3i3i3000033−3−3−3−33300−2i2iii−i−i0000000000
χ382222-12-2-2-2-2-1-12-1221111-12-1-1-111-1-1-2-2-21111-200i3−i300i3i3−i3−i32−i3i30011-1-1−i3−i3i3i30000−3−33333−3−3002i−2i−i−iii0000000000
χ392-22-222-2020-2-2-222-2-2-22220-2-2200002-2022-2-2000000000000000000000000002-200002-22-2−i2i2000000−i2i2−i2i2000−i2i20
χ402-22-222-2020-2-2-222-2-2-22220-2-2200002-2022-2-2000000000000000000000000002-200002-22-2i2−i2000000i2−i2i2−i2000i2−i20
χ412-22-222-2020-2-2-222-2-2-22220-2-2200002-2022-2-200000000000000000000000000-220000-22-22−i2i2000000−i2i2−i2i2000i2−i20
χ422-22-222-2020-2-2-222-2-2-22220-2-2200002-2022-2-200000000000000000000000000-220000-22-22i2−i2000000i2−i2i2−i2000−i2i20
χ4344444-24-44-444-24-2-24444-2-4-2-2-2-4-4-4-4-2-22-2-2-2-2200000000002000022220000000000000000000000000000000000
χ4444444-2-4-4-4-444-24-2-2-4-4-4-4-24-2-2-2-4-444222222220000000000-2000022-2-20000000000000000000000000000000000
χ454444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-2-21111-244-2-2-2-21111-2-2-2-2-211111111000000000000000000000000000000
χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-2-21111-2-4-42222-1-1-1-1-222221111-1-1-1-1000000000000000000000000000000
χ474444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-2-221111200−2i32i300i3i3−i3−i32−2i32i300-1-1-1-1i3i3−i3−i3000000000000000000000000000000
χ484444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-41112222-2-2211112002i3−2i300−i3−i3i3i322i3−2i300-1-1-1-1−i3−i3i3i3000000000000000000000000000000
χ494444-2-2-44-44-2-2-2-2-2-222221-4111-2-22222-2-1-1-1-1-24-4-2-2-2-211112222211-1-1-1-1-1-1000000000000000000000000000000
χ504444-2-2-44-44-2-2-2-2-2-222221-4111-2-22222-2-1-1-1-1-2-442222-1-1-1-12-2-2-2-211-1-11111000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-2222-1-1-1-1200−2i32i300i3i3−i3−i3-22i3−2i300-1-111−i3−i3i3i3000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-2222-1-1-1-12002i3−2i300−i3−i3i3i3-2−2i32i300-1-111i3i3−i3−i3000000000000000000000000000000
χ5344-4-44400004-44-4-4-40000404-4-40000000000000000000000000000000000022−220022−2222−220000000000000000000000
χ5444-4-44400004-44-4-4-40000404-4-400000000000000000000000000000000000−222200−2222−22220000000000000000000000
χ5544-4-4-240000-2242-4-423−2323−23-20-222000000023−2323−2300000000000000000000000022−22002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000
χ5644-4-4-240000-2242-4-423−2323−23-20-222000000023−2323−23000000000000000000000000−222200−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000
χ5744-4-4-240000-2242-4-4−2323−2323-20-2220000000−2323−232300000000000000000000000022−22002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000
χ5844-4-4-240000-2242-4-4−2323−2323-20-2220000000−2323−2323000000000000000000000000−222200−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000
χ594-44-44440-40-4-4-444-444-4-440-4-440000-440-4-444000000000000000000000000000000000000000000000000000000
χ604-44-44-240-40-4-424-2244-4-4-2022-200002-2022-2-2000000000000000000000000000000000000000000006−6−66000000
χ614-44-44-240-40-4-424-2244-4-4-2022-200002-2022-2-200000000000000000000000000000000000000000000−666−6000000
χ624-44-44-2-4040-4-424-22-4-444-2022-20000-220-2-222000000000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ634-44-44-2-4040-4-424-22-4-444-2022-20000-220-2-2220000000000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ644-44-4-2440-4022-4-24-4-2-222-2022-20000-44022-2-20000000000000000000000000000000023−23−2323000000000000000000
χ654-44-4-2440-4022-4-24-4-2-222-2022-20000-44022-2-200000000000000000000000000000000−232323−23000000000000000000
χ664-44-4-24-404022-4-24-422-2-2-2022-200004-40-2-222000000000000000000000000004-40000-22-22000000000000000000
χ674-44-4-24-404022-4-24-422-2-2-2022-200004-40-2-22200000000000000000000000000-4400002-22-2000000000000000000
χ684-4-4444040-4-44-4-4-44000040-44-44-40000-4000040000000000000004-4000000000000000000000000000000000000
χ694-4-44440-404-44-4-4-44000040-44-4-44000040000-4000000000000000-44000000000000000000000000000000000000
χ704-4-444-2040-4-442-42-20000-202-224-4000020000-20000−2i32i3−2i32i3−2i32i300000-22000000000000000000000000000000000000
χ714-4-444-2040-4-442-42-20000-202-224-4000020000-200002i3−2i32i3−2i32i3−2i300000-22000000000000000000000000000000000000
χ724-4-444-20-404-442-42-20000-202-22-440000-200002000000000000023−232-20023−2323−23000000000000000000000000000000
χ734-4-444-20-404-442-42-20000-202-22-440000-2000020000000000000−23232-200−2323−2323000000000000000000000000000000
χ744-4-44-24040-42-2-42-4423−23−2323-202-22-2223−2300-4−232323−234000000000000000-2223−230000000000000000000000000000000000
χ754-4-44-24040-42-2-42-44−232323−23-202-22-22−232300-423−23−23234000000000000000-22−23230000000000000000000000000000000000
χ764-4-44-240-4042-2-42-4423−23−2323-202-222-2−2323004−232323−23-40000000000000002-2−23230000000000000000000000000000000000
χ774-4-44-240-4042-2-42-44−232323−23-202-222-223−2300423−23−2323-40000000000000002-223−230000000000000000000000000000000000
χ784-4-44-2-2040-42-2222-223−23−232310-11-1-2223−230023−3−33-20000−2i32i3i3−i3i3−i3000001-1−333i−3i−3i3i000000000000000000000000000000
χ794-4-44-2-2040-42-2222-223−23−232310-11-1-2223−230023−3−33-200002i3−2i3−i3i3−i3i3000001-1−33−3i3i3i−3i000000000000000000000000000000
χ804-4-44-2-2040-42-2222-2−232323−2310-11-1-22−2323002−333−3-20000−2i32i3i3−i3i3−i3000001-13−3−3i3i3i−3i000000000000000000000000000000
χ814-4-44-2-2040-42-2222-2−232323−2310-11-1-22−2323002−333−3-200002i3−2i3−i3i3−i3i3000001-13−33i−3i−3i3i000000000000000000000000000000
χ824-4-44-2-20-4042-2222-223−23−232310-11-12-2−232300-23−3−3320000003-3-3300023−23-113−3−33−33000000000000000000000000000000
χ834-4-44-2-20-4042-2222-223−23−232310-11-12-2−232300-23−3−332000000-333-3000−2323-113−33−33−3000000000000000000000000000000
χ844-4-44-2-20-4042-2222-2−232323−2310-11-12-223−2300-2−333−320000003-3-33000−2323-11−333−33−3000000000000000000000000000000
χ854-4-44-2-20-4042-2222-2−232323−2310-11-12-223−2300-2−333−32000000-333-300023−23-11−33−33−33000000000000000000000000000000
χ8688-8-88-400008-8-4-8440000-40-44400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-44-444443−4343−43202-2-20000000−2323−2323000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-44-4444−4343−4343202-2-2000000023−2323−23000000000000000000000000000000000000000000000000000000
χ898-88-8-4-480-80444-4-44-4-44420-2-2200004-40-2-222000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-8080444-4-4444-4-420-2-220000-44022-2-2000000000000000000000000000000000000000000000000000000

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