Finite Group Databasebeta

← Group #10943910

Character table — Group #10943910

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222222234444666121212122222244444466661212121244446666612121212121212121212121212222222222222444488242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111111111111111-111-1-1-1-111-1-1-1-11111-1-111-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-11-11-1
χ101111-1-111111111111111-111-1-1-1-111-1-1-1-11111-1-111-1-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111-111-1-1-11-11
χ111111-1-111111111111111-111-1-1-1-111-1-1-1-11111-1-1-1-111-111-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11-1-111-11-11
χ121111-1-111111111111111-111-1-1-1-111-1-1-1-11111-1-1-1-111-111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11-1-1111-11-1
χ131111-1-111111111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-11-1-1111-1-11
χ141111-1-111111111111111-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-1-111-111-1
χ151111-1-111111111111111-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1111-111-1-1-111-1
χ161111-1-111111111111111-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-11-111-1-11-1-11
χ17222222222-2-2-2-2222-2-2-2-220000-2-200002222-2-2-2-2000020000-200000000000022-2-222-2-2000000000000000000
χ18222222222-2-2-2-2222-2-2-2-220000-2-200002222-2-2-2-2000020000-2000000000000-2-222-2-222000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-12222-11111-11111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ2222222222-12222-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111111111111000000000000000022-1-1-1-10000
χ23222222-2-2222-2-22222222-200002-2000022-2-2-2-2220000-20000-2000000000000000000002222-2-2-2-20000000000
χ24222222-2-2222-2-22222222-200002-2000022-2-2-2-2220000-20000-200000000000000000000-2-2-2-222220000000000
χ25222222-2-22-2-222222-2-2-2-2-22222-22-2-2-2-222-2-222-2-20000-222222-2-2-2-20000000000000000000000000000000000
χ26222222-2-22-2-222222-2-2-2-2-2-2-2-2-2-22222222-2-222-2-20000-2-2-2-2-2222220000000000000000000000000000000000
χ27222222-2-2-1-2-222-1-1-11111-22222-22-2-2-2-2-1-111-1-11100001-1-1-1-1-1111133−3−333−3−30000000000000000003−33−30000
χ28222222-2-2-1-2-222-1-1-11111-22222-22-2-2-2-2-1-111-1-11100001-1-1-1-1-11111−3−333−3−333000000000000000000−33−330000
χ29222222-2-2-1-2-222-1-1-11111-2-2-2-2-2-222222-1-111-1-111000011111-1-1-1-1-133−3−333−3−3000000000000000000−33−330000
χ30222222-2-2-1-2-222-1-1-11111-2-2-2-2-2-222222-1-111-1-111000011111-1-1-1-1-1−3−333−3−3330000000000000000003−33−30000
χ312222-2-2222-2-2-2-2222-2-2-2-2-20000220000-2-222-2-2220000-20000200000000000022-2-2-2-222000000000000000000
χ322222-2-2222-2-2-2-2222-2-2-2-2-20000220000-2-222-2-2220000-200002000000000000-2-22222-2-2000000000000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-222-2-2-2-222-2-211-1-1-1-11122-2-21-1-1111-1-111-1-1-1-1111100000000000000002-2-1-1110000
χ342222-2-222-12222-1-1-1-1-1-1-1-222-2-2-2-222-2-211-1-1-1-111-2-2221-1-1111-1-1111111-1-1-1-10000000000000000-2211-1-10000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-222-2-2-2-22211-1-1-1-11122-2-2111-1-1111-1-1-1-1-1-111110000000000000000-2211-1-10000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-222-2-2-2-22211-1-1-1-111-2-222111-1-1111-1-11111-1-1-1-100000000000000002-2-1-1110000
χ372222-2-2-2-2222-2-2222222220000-220000-2-2-2-2-2-2-2-200002000020000000000000000000022-2-2-2-2220000000000
χ382222-2-2-2-2222-2-2222222220000-220000-2-2-2-2-2-2-2-2000020000200000000000000000000-2-22222-2-20000000000
χ392222-2-2-2-22-2-222222-2-2-2-2222-2-22-2-2-222-2-2-2-222220000222-2-2-2-2-2220000000000000000000000000000000000
χ402222-2-2-2-22-2-222222-2-2-2-22-2-2222-222-2-2-2-2-2-2222200002-2-222-222-2-20000000000000000000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-11111222-2-22-2-2-2221111-1-1-1-10000-1-1-111111-1-133−3−3−3−3330000000000000000003−3−330000
χ422222-2-2-2-2-1-2-222-1-1-11111222-2-22-2-2-2221111-1-1-1-10000-1-1-111111-1-1−3−33333−3−3000000000000000000−333−30000
χ432222-2-2-2-2-1-2-222-1-1-111112-2-2222-222-2-21111-1-1-1-10000-111-1-11-1-11133−3−3−3−333000000000000000000−333−30000
χ442222-2-2-2-2-1-2-222-1-1-111112-2-2222-222-2-21111-1-1-1-10000-111-1-11-1-111−3−33333−3−30000000000000000003−3−330000
χ452-2-22002-222-22-2-2-2222-2-20002-200002-2002-22-20000000002-20002-20000000000002-22-22-2002-2000000000000
χ462-2-22002-222-22-2-2-2222-2-20002-200002-2002-22-20000000002-20002-2000000000000-22-22-2200-22000000000000
χ472-2-22002-222-22-2-2-2222-2-2000-220000-22002-22-2000000000-22000-220000000000002-22-2-2200-22000000000000
χ482-2-22002-222-22-2-2-2222-2-2000-220000-22002-22-2000000000-22000-22000000000000-22-222-2002-2000000000000
χ492-2-22002-22-22-22-2-22-2-22202-200002-200002-2-2200000002-20002-2000000000000002-2-22002-2002-20000000000
χ502-2-22002-22-22-22-2-22-2-22202-200002-200002-2-2200000002-20002-200000000000000-222-200-2200-220000000000
χ512-2-22002-22-22-22-2-22-2-2220-220000-2200002-2-220000000-22000-22000000000000002-2-2200-2200-220000000000
χ522-2-22002-22-22-22-2-22-2-2220-220000-2200002-2-220000000-22000-2200000000000000-222-2002-2002-20000000000
χ532-2-2200-2222-2-22-2-2222-2-202-20000-220000-22-2200000002-2000-2200000000002-22-200002-200-22000000000000
χ542-2-2200-2222-2-22-2-2222-2-202-20000-220000-22-2200000002-2000-220000000000-22-220000-22002-2000000000000
χ552-2-2200-2222-2-22-2-2222-2-20-2200002-20000-22-220000000-220002-200000000002-22-20000-22002-2000000000000
χ562-2-2200-2222-2-22-2-2222-2-20-2200002-20000-22-220000000-220002-20000000000-22-2200002-200-22000000000000
χ572-2-2200-222-222-2-2-22-2-2220002-20000-2200-222-20000000002-2000-22000000002-2-220000002-200-220000000000
χ582-2-2200-222-222-2-2-22-2-2220002-20000-2200-222-20000000002-2000-2200000000-222-2000000-22002-20000000000
χ592-2-2200-222-222-2-2-22-2-222000-2200002-200-222-2000000000-220002-2000000002-2-22000000-22002-20000000000
χ602-2-2200-222-222-2-2-22-2-222000-2200002-200-222-2000000000-220002-200000000-222-20000002-200-220000000000
χ6144444444-2-4-4-4-4-2-2-2222240000-4-40000-2-2-2-222220000-20000200000000000000000000000000000000000000
χ62444444-4-4-244-4-4-2-2-2-2-2-2-2-400004-40000-2-22222-2-2000020000200000000000000000000000000000000000000
χ634444-4-444-2-4-4-4-4-2-2-22222-4000044000022-2-222-2-2000020000-200000000000000000000000000000000000000
χ644444-4-4-4-4-244-4-4-2-2-2-2-2-2-240000-440000222222220000-20000-200000000000000000000000000000000000000
χ6544-4-44-400400004-4-40000000000000004-40000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ6644-4-44-400400004-4-40000000000000004-4000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ6744-4-44-400-20000-22223−2323−2300000000000-22000023−232i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ6844-4-44-400-20000-22223−2323−2300000000000-22000023−23−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ6944-4-44-400-20000-222−2323−232300000000000-220000−23232i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ7044-4-44-400-20000-222−2323−232300000000000-220000−2323−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7144-4-4-4400400004-4-4000000000000000-440000002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ7244-4-4-4400400004-4-4000000000000000-44000000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ7344-4-4-4400-20000-22223−2323−23000000000002-20000−23232i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ7444-4-4-4400-20000-22223−2323−23000000000002-20000−2323−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ7544-4-4-4400-20000-222−2323−2323000000000002-2000023−232i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7644-4-4-4400-20000-222−2323−2323000000000002-2000023−23−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ774-4-44004-4-24-44-422-2-2-2220004-400004-400-22-22000000000-22000-220000000000000000000000000000000000
χ784-4-44004-4-24-44-422-2-2-222000-440000-4400-22-220000000002-20002-20000000000000000000000000000000000
χ794-4-44004-4-2-44-4422-222-2-204-400004-40000-222-20000000-22000-22000000000000000000000000000000000000
χ804-4-44004-4-2-44-4422-222-2-20-440000-440000-222-200000002-20002-2000000000000000000000000000000000000
χ814-4-4400-44-24-4-4422-2-2-22204-40000-4400002-22-20000000-220002-2000000000000000000000000000000000000
χ824-4-4400-44-24-4-4422-2-2-2220-4400004-400002-22-200000002-2000-22000000000000000000000000000000000000
χ834-4-4400-44-2-444-422-222-2-20004-40000-44002-2-22000000000-220002-20000000000000000000000000000000000
χ844-4-4400-44-2-444-422-222-2-2000-4400004-4002-2-220000000002-2000-220000000000000000000000000000000000
χ858-88-8000080000-88-800000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-80000-400004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-88-80000-400004-44−434343−430000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.