Finite Group Databasebeta

← Group #11781897

Character table — Group #11781897

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222244444444444444444888888888888888888888881212121212121212121212122424242424242424242424244848487272144
order1222334444666666121212123466612121212121212121212121244121212121212121212121212121212121212121212888824242424242424248888242424242424242441212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1
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
χ51111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-111-1
χ61111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1
χ92222222-2-22222222-2-2-2-22-2222-2-2222-2-2-2-2-2-222-222-2-2-2-2-22222-2-22222-2-2-2-2000000000000000000000000000000
χ102222222-2-22222222-2-2-2-22-2222-2-2222-2-2-2-2-2-22-22-2-22222-2-2-222-2-2-2-2-2-22222000000000000000000000000000000
χ11222222-222-222222222222-222222-2-2-2-2-22222-200000000-200-2-2-2-20000000022-2-22222-2-2-2-2000000000000000000
χ12222222-222-222222222222-222222-2-2-2-2-22222-200000000-200-2-2-2-200000000-2-222-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-222-2-2-2-2-200000000200-2-222000000000000000000002i−2i002i2i−2i−2i0000000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-222-2-2-2-2-200000000200-2-22200000000000000000000−2i2i00−2i−2i2i2i0000000000
χ1522222-122222-122-1-12222-12-1-1-1-1-122-122-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-12-1-1000
χ1622222-122222-122-1-12222-12-1-1-1-1-122-122-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111-211000
χ1722222-122222-122-1-12222-12-1-1-1-1-122-122-1-1-1-1-1-2-2-2-2-2-211-111-1-1-1-11111111100000000000000220000-1-1-1-1-211000
χ1822222-122222-122-1-12222-12-1-1-1-1-122-122-1-1-1-1-1-2-2-2-2-2-211-111-1-1-1-11111111100000000000000-2-2000011112-1-1000
χ1922222-12-2-222-122-1-1-2-2-2-2-1-2-1-1-11122-1-2-21111-12-222-2-2111-1-1-1-111-1-1-1-1111100000000000000000000−i3−i3i3i30−i3i3000
χ2022222-12-2-222-122-1-1-2-2-2-2-1-2-1-1-11122-1-2-21111-12-222-2-2111-1-1-1-111-1-1-1-1111100000000000000000000i3i3−i3−i30i3−i3000
χ2122222-12-2-222-122-1-1-2-2-2-2-1-2-1-1-11122-1-2-21111-1-22-2-222-1-1111-1-1111111-1-1-1-100000000000000000000−i3−i3i3i30i3−i3000
χ2222222-12-2-222-122-1-1-2-2-2-2-1-2-1-1-11122-1-2-21111-1-22-2-222-1-1111-1-1111111-1-1-1-100000000000000000000i3i3−i3−i30−i3i3000
χ232222-122222-12-1-122-1-1-1-1-12-1-1-122-1-12-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-10000000000
χ242222-122222-12-1-122-1-1-1-1-12-1-1-122-1-12-1-1-1-1-1-1222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-20011110000000000
χ252222-122222-12-1-122-1-1-1-1-12-1-1-122-1-12-1-1-1-1-1-12-2-21111-2-22-2-2-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-20011110000000000
χ262222-122222-12-1-122-1-1-1-1-12-1-1-122-1-12-1-1-1-1-1-12-2-21111-2-22-2-2-1-1-1-111111111-2-2-2-2111111112200-1-1-1-10000000000
χ272222-122-2-22-12-1-1221111-1-2-1-1-1-2-2-1-1211111122-2-1-111-2-2-222-1-111-1-1-1-11111000033−3−333−3−300003−33−30000000000
χ282222-122-2-22-12-1-1221111-1-2-1-1-1-2-2-1-1211111122-2-1-111-2-2-222-1-111-1-1-1-111110000−3−333−3−3330000−33−330000000000
χ292222-122-2-22-12-1-1221111-1-2-1-1-1-2-2-1-121111112-2211-1-122-2-2-2-1-1111111-1-1-1-1000033−3−333−3−30000−33−330000000000
χ302222-122-2-22-12-1-1221111-1-2-1-1-1-2-2-1-121111112-2211-1-122-2-2-2-1-1111111-1-1-1-10000−3−333−3−33300003−33−30000000000
χ312222-12-222-2-12-1-122-1-1-1-1-1-2-1-1-12211-211-1-1-1-1-200−i3i3−i3i300-2001111−i3−i3i3i3−i3−i3i3i322-2-2-1-1-1-111110000−i3i3i3−i30000000000
χ322222-12-222-2-12-1-122-1-1-1-1-1-2-1-1-12211-211-1-1-1-1-200−i3i3−i3i300-2001111−i3−i3i3i3−i3−i3i3i3-2-2221111-1-1-1-10000i3−i3−i3i30000000000
χ332222-12-222-2-12-1-122-1-1-1-1-1-2-1-1-12211-211-1-1-1-1-200i3−i3i3−i300-2001111i3i3−i3−i3i3i3−i3−i322-2-2-1-1-1-111110000i3−i3−i3i30000000000
χ342222-12-222-2-12-1-122-1-1-1-1-1-2-1-1-12211-211-1-1-1-1-200i3−i3i3−i300-2001111i3i3−i3−i3i3i3−i3−i3-2-2221111-1-1-1-10000−i3i3i3−i30000000000
χ352222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-2-1-11111-200−i3i3i3−i30020011-1-1−i3−i3i3i3i3i3−i3−i3000033−3−3−3−3332i−2i00−i−iii0000000000
χ362222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-2-1-11111-200−i3i3i3−i30020011-1-1−i3−i3i3i3i3i3−i3−i30000−3−33333−3−3−2i2i00ii−i−i0000000000
χ372222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-2-1-11111-200i3−i3−i3i30020011-1-1i3i3−i3−i3−i3−i3i3i3000033−3−3−3−333−2i2i00ii−i−i0000000000
χ382222-12-2-2-2-2-12-1-1221111-12-1-1-1-2-211-2-1-11111-200i3−i3−i3i30020011-1-1i3i3−i3−i3−i3−i3i3i30000−3−33333−3−32i−2i00−i−iii0000000000
χ3922-2-22202-2022-2-2-2-222-2-2202-2-22-20000022-2-20000000000000000000000002-2002-22-20000002−200002−22−20002−20
χ4022-2-22202-2022-2-2-2-222-2-2202-2-22-20000022-2-20000000000000000000000002-2002-22-2000000−220000−22−22000−220
χ4122-2-22202-2022-2-2-2-222-2-2202-2-22-20000022-2-2000000000000000000000000-2200-22-220000002−200002−22−2000−220
χ4222-2-22202-2022-2-2-2-222-2-2202-2-22-20000022-2-2000000000000000000000000-2200-22-22000000−220000−22−220002−20
χ4344444-2-444-44-244-2-24444-2-4-2-2-2-2-2-4-42-4-4-2-2-2-2200000000200222200000000000000000000000000000000000000
χ4444444-2-4-4-4-44-244-2-2-4-4-4-4-24-2-2-222-4-42442222200000000-20022-2-200000000000000000000000000000000000000
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
χ464444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-2-2-21111-2-4-4222222-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000
χ474444-2-24-4-44-2-2-2-2-2-222221-411122-2-2-222-1-1-1-1-24-4-2-222222-2-211-1-11111-1-1-1-1000000000000000000000000000000
χ484444-2-24-4-44-2-2-2-2-2-222221-411122-2-2-222-1-1-1-1-2-4422-2-2-2-222211-1-1-1-1-1-11111000000000000000000000000000000
χ494444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-4111-2-2222221111200−2i32i3−2i32i300200-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000
χ504444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-4111-2-22222211112002i3−2i32i3−2i300200-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-2-2-1-1-1-1200−2i32i32i3−2i300-200-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-2-2-1-1-1-12002i3−2i3−2i32i300-200-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000
χ5344-4-4440-44044-4-4-4-4-4-444404-4-4-4400000-4-444000000000000000000000000000000000000000000000000000000
χ5444-4-44-204-404-2-4-42244-4-4-20-222-2200000-2-2220000000000000000000000000000000000000022−220000−22−22000000
χ5544-4-44-204-404-2-4-42244-4-4-20-222-2200000-2-22200000000000000000000000000000000000000−222200002−22−2000000
χ5644-4-44-20-4404-2-4-422-4-444-20-2222-20000022-2-200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ5744-4-44-20-4404-2-4-422-4-444-20-2222-20000022-2-200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ5844-4-4-2404-40-2422-4-4-2-222-20-2224-400000-2-2220000000000000000000000004-400-22-220000000000000000000000
χ5944-4-4-2404-40-2422-4-4-2-222-20-2224-400000-2-222000000000000000000000000-44002-22-20000000000000000000000
χ6044-4-4-240-440-2422-4-422-2-2-20-222-440000022-2-2000000000000000000000000000023−23−23230000000000000000000000
χ6144-4-4-240-440-2422-4-422-2-2-20-222-440000022-2-20000000000000000000000000000−232323−230000000000000000000000
χ624-44-4440000-4-44-4-44000040-44-40000000000000000000000000000000000000−2i22i20000−2i22i2−2i22i2000000000000000000
χ634-44-4440000-4-44-4-44000040-44-400000000000000000000000000000000000002i2−2i200002i2−2i22i2−2i2000000000000000000
χ644-44-4-2400002-4-22-4423−2323−23-202-22000000023−2323−2300000000000000000000000000−2i22i200002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000
χ654-44-4-2400002-4-22-4423−2323−23-202-22000000023−2323−23000000000000000000000000002i2−2i20000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000
χ664-44-4-2400002-4-22-44−2323−2323-202-220000000−2323−232300000000000000000000000000−2i22i200002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000
χ674-44-4-2400002-4-22-44−2323−2323-202-220000000−2323−2323000000000000000000000000002i2−2i20000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000
χ684-4-4444400-4-4-4-444-4000040-4-44004-44000000-4000000000004-40000000000000000000000000000000000000000
χ694-4-4444-4004-4-4-444-4000040-4-4400-44-4000000400000000000-440000000000000000000000000000000000000000
χ704-4-444-2400-4-42-44-220000-2022-2004-4-20000002000000−2i32i3000-22000000−2i32i3−2i32i3000000000000000000000000000000
χ714-4-444-2400-4-42-44-220000-2022-2004-4-200000020000002i3−2i3000-220000002i3−2i32i3−2i3000000000000000000000000000000
χ724-4-444-2-4004-42-44-220000-2022-200-442000000-200000000023−232-20023−2323−230000000000000000000000000000000000
χ734-4-444-2-4004-42-44-220000-2022-200-442000000-2000000000−23232-200−2323−23230000000000000000000000000000000000
χ744-4-44-24400-42-42-24-423−23−2323-2022-200-22423−2323−23−2323-400000000000-2223−2300000000000000000000000000000000000000
χ754-4-44-24400-42-42-24-4−232323−23-2022-200-224−2323−232323−23-400000000000-22−232300000000000000000000000000000000000000
χ764-4-44-24-40042-42-24-423−23−2323-2022-2002-2-4−232323−23−23234000000000002-2−232300000000000000000000000000000000000000
χ774-4-44-24-40042-42-24-4−232323−23-2022-2002-2-423−23−232323−234000000000002-223−2300000000000000000000000000000000000000
χ784-4-44-2-2400-4222-2-2223−23−232310-1-1100-22-223−23−333−32000000−2i32i30001-1−333i−3i−3i3ii3−i3i3−i3000000000000000000000000000000
χ794-4-44-2-2400-4222-2-2223−23−232310-1-1100-22-223−23−333−320000002i3−2i30001-1−33−3i3i3i−3i−i3i3−i3i3000000000000000000000000000000
χ804-4-44-2-2400-4222-2-22−232323−2310-1-1100-22-2−23233−3−332000000−2i32i30001-13−3−3i3i3i−3ii3−i3i3−i3000000000000000000000000000000
χ814-4-44-2-2400-4222-2-22−232323−2310-1-1100-22-2−23233−3−3320000002i3−2i30001-13−33i−3i−3i3i−i3i3−i3i3000000000000000000000000000000
χ824-4-44-2-2-4004222-2-2223−23−232310-1-11002-22−2323−333−3-200000000023−23-113−3−33−333-3-33000000000000000000000000000000
χ834-4-44-2-2-4004222-2-2223−23−232310-1-11002-22−2323−333−3-2000000000−2323-113−33−33−3-333-3000000000000000000000000000000
χ844-4-44-2-2-4004222-2-22−232323−2310-1-11002-2223−233−3−33-200000000023−23-11−33−33−33-333-3000000000000000000000000000000
χ854-4-44-2-2-4004222-2-22−232323−2310-1-11002-2223−233−3−33-2000000000−2323-11−333−33−33-3-33000000000000000000000000000000
χ8688-8-8-4-408-80-4-44444-4-444202-2-2-440000022-2-2000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40-880-4-4444444-4-4202-2-24-400000-2-222000000000000000000000000000000000000000000000000000000
χ888-88-88-40000-848-84-40000-404-4400000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4000044-444-443−4343−4320-22-20000000−2323−2323000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4000044-444-4−4343−434320-22-2000000023−2323−23000000000000000000000000000000000000000000000000000000

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