Finite Group Databasebeta

← Group #10943902

Character table — Group #10943902

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222223444444666121212122222224444466661212121244446666612121212121212121212121212222222224444444488242424242488
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
χ51111111111111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ91111111-1-111111111111-1-111-1-1-111-1-1-1-11111-1-111-1-1-111-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11-111-1-11-11-1
χ101111111-1-111111111111-1-111-1-1-111-1-1-1-11111-1-111-1-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111-111-1-1-11-11
χ111111111-1-111111111111-1-111-1-1-111-1-1-1-11111-1-1-1-111-111-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11-1-111-11-11
χ121111111-1-111111111111-1-111-1-1-111-1-1-1-11111-1-1-1-111-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-11-1-1111-11-1
χ131111111-1-111111111111-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111-11-1-1111-1-11
χ141111111-1-111111111111-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-111-1-1111111-1-1-11-1-111-111-1
χ151111111-1-111111111111-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1111-111-1-1-111-1
χ161111111-1-111111111111-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-111-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-11-111-1-11-1-11
χ17222222222-2-2-2-2222-2-2-2-2-2-2000020000-2-222-2-2220000-20000200000000000022-2-2000022-2-200000000000000
χ18222222222-2-2-2-2222-2-2-2-2-2-2000020000-2-222-2-2220000-200002000000000000-2-2220000-2-22200000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-2220000-200002222-2-2-2-2000020000-200000000000022-2-20000-2-22200000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-2220000-200002222-2-2-2-2000020000-2000000000000-2-222000022-2-200000000000000
χ21222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-12222-11111-11111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-11111-1111111111111000000000000000022-1-1-1-10000
χ25222222-1-2-22222-1-1-1-1-1-1-1-2-222-2-2-222-2-211-1-1-1-11122-2-21-1-1111-1-111-1-1-1-1111100000000000000002-2-1-1110000
χ26222222-1-2-22222-1-1-1-1-1-1-1-2-222-2-2-222-2-211-1-1-1-111-2-2221-1-1111-1-1111111-1-1-1-10000000000000000-2211-1-10000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-222-2-2-22211-1-1-1-11122-2-2111-1-1111-1-1-1-1-1-111110000000000000000-2211-1-10000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-222-2-2-22211-1-1-1-111-2-222111-1-1111-1-11111-1-1-1-100000000000000002-2-1-1110000
χ292222-2-222222-2-222222222-20000-2000022-2-2-2-2220000-20000-2000000000000000022-2-20000-2-2220000000000
χ302222-2-222222-2-222222222-20000-2000022-2-2-2-2220000-20000-20000000000000000-2-222000022-2-20000000000
χ312222-2-2222-2-222222-2-2-2-2-2222-2-2-2-2-222-2-2-2-222220000222-2-2-2-2-2220000000000000000000000000000000000
χ322222-2-2222-2-222222-2-2-2-2-22-2-222-222-2-2-2-2-2-2222200002-2-222-222-2-20000000000000000000000000000000000
χ332222-2-22-2-222-2-22222222-22000020000-2-2-2-2-2-2-2-20000200002000000000000000022220000-2-2-2-20000000000
χ342222-2-22-2-222-2-22222222-22000020000-2-2-2-2-2-2-2-200002000020000000000000000-2-2-2-2000022220000000000
χ352222-2-22-2-2-2-222222-2-2-2-22-222222-2-2-2-222-2-222-2-20000-222222-2-2-2-20000000000000000000000000000000000
χ362222-2-22-2-2-2-222222-2-2-2-22-2-2-2-2-22222222-2-222-2-20000-2-2-2-2-2222220000000000000000000000000000000000
χ372222-2-2-122-2-222-1-1-11111-2222-2-2-2-2-2221111-1-1-1-10000-1-1-111111-1-133−3−333−3−30000000000000000003−33−30000
χ382222-2-2-122-2-222-1-1-11111-2222-2-2-2-2-2221111-1-1-1-10000-1-1-111111-1-1−3−333−3−333000000000000000000−33−330000
χ392222-2-2-122-2-222-1-1-11111-22-2-222-222-2-21111-1-1-1-10000-111-1-11-1-11133−3−333−3−3000000000000000000−33−330000
χ402222-2-2-122-2-222-1-1-11111-22-2-222-222-2-21111-1-1-1-10000-111-1-11-1-111−3−333−3−3330000000000000000003−33−30000
χ412222-2-2-1-2-2-2-222-1-1-111112-222222-2-2-2-2-1-111-1-11100001-1-1-1-1-1111133−3−3−3−3330000000000000000003−3−330000
χ422222-2-2-1-2-2-2-222-1-1-111112-222222-2-2-2-2-1-111-1-11100001-1-1-1-1-11111−3−33333−3−3000000000000000000−333−30000
χ432222-2-2-1-2-2-2-222-1-1-111112-2-2-2-2-222222-1-111-1-111000011111-1-1-1-1-133−3−3−3−333000000000000000000−333−30000
χ442222-2-2-1-2-2-2-222-1-1-111112-2-2-2-2-222222-1-111-1-111000011111-1-1-1-1-1−3−33333−3−30000000000000000003−3−330000
χ452-2-222-22002-22-2-2-2222-2-200002-20002-2002-22-20000000002-20002-2000000002-22-2002-20000002-20000000000
χ462-2-222-22002-22-2-2-2222-2-200002-20002-2002-22-20000000002-20002-200000000-22-2200-22000000-220000000000
χ472-2-222-22002-22-2-2-2222-2-20000-22000-22002-22-2000000000-22000-22000000002-22-200-22000000-220000000000
χ482-2-222-22002-22-2-2-2222-2-20000-22000-22002-22-2000000000-22000-2200000000-22-22002-20000002-20000000000
χ492-2-222-2200-22-22-2-22-2-222002-20002-200002-2-2200000002-20002-200000000002-2-222-20000002-2000000000000
χ502-2-222-2200-22-22-2-22-2-222002-20002-200002-2-2200000002-20002-20000000000-222-2-22000000-22000000000000
χ512-2-222-2200-22-22-2-22-2-22200-22000-2200002-2-220000000-22000-2200000000002-2-22-22000000-22000000000000
χ522-2-222-2200-22-22-2-22-2-22200-22000-2200002-2-220000000-22000-220000000000-222-22-20000002-2000000000000
χ532-2-22-222002-2-22-2-2222-2-2002-2000-220000-22-2200000002-2000-2200000000000000002-22-22-200-220000000000
χ542-2-22-222002-2-22-2-2222-2-2002-2000-220000-22-2200000002-2000-220000000000000000-22-22-22002-20000000000
χ552-2-22-222002-2-22-2-2222-2-200-220002-20000-22-220000000-220002-200000000000000002-2-22-2200-220000000000
χ562-2-22-222002-2-22-2-2222-2-200-220002-20000-22-220000000-220002-20000000000000000-222-22-2002-20000000000
χ572-2-22-22200-222-2-2-22-2-22200002-2000-2200-222-20000000002-2000-220000000000002-2002-2-22-22000000000000
χ582-2-22-22200-222-2-2-22-2-22200002-2000-2200-222-20000000002-2000-22000000000000-2200-222-22-2000000000000
χ592-2-22-22200-222-2-2-22-2-2220000-220002-200-222-2000000000-220002-20000000000002-200-222-2-22000000000000
χ602-2-22-22200-222-2-2-22-2-2220000-220002-200-222-2000000000-220002-2000000000000-22002-2-222-2000000000000
χ61444444-244-4-4-4-4-2-2-22222-4-400004000022-2-222-2-2000020000-200000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-22222440000-40000-2-2-2-222220000-20000200000000000000000000000000000000000000
χ634444-4-4-24444-4-4-2-2-2-2-2-2-24-40000-40000-2-22222-2-2000020000200000000000000000000000000000000000000
χ644444-4-4-2-4-444-4-4-2-2-2-2-2-2-2-44000040000222222220000-20000-200000000000000000000000000000000000000
χ6544-4-40044i−4i00004-4-40000000000000000000004i−4i2-22i−2i00000000002-22-22i−2i2i−2i00000000000000000000000000
χ6644-4-40044i−4i00004-4-40000000000000000000004i−4i-22−2i2i0000000000-22-22−2i2i−2i2i00000000000000000000000000
χ6744-4-4004−4i4i00004-4-4000000000000000000000−4i4i2-2−2i2i00000000002-22-2−2i2i−2i2i00000000000000000000000000
χ6844-4-4004−4i4i00004-4-4000000000000000000000−4i4i-222i−2i0000000000-22-222i−2i2i−2i00000000000000000000000000
χ6944-4-400-24i−4i0000-22223−2323−2300000000000−2i32i30000−2i2i2-22i−2i0000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ7044-4-400-24i−4i0000-22223−2323−2300000000000−2i32i30000−2i2i-22−2i2i00000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7144-4-400-24i−4i0000-222−2323−2323000000000002i3−2i30000−2i2i2-22i−2i0000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ7244-4-400-24i−4i0000-222−2323−2323000000000002i3−2i30000−2i2i-22−2i2i00000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ7344-4-400-2−4i4i0000-22223−2323−23000000000002i3−2i300002i−2i2-2−2i2i0000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ7444-4-400-2−4i4i0000-22223−2323−23000000000002i3−2i300002i−2i-222i−2i00000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ7544-4-400-2−4i4i0000-222−2323−232300000000000−2i32i300002i−2i2-2−2i2i0000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ7644-4-400-2−4i4i0000-222−2323−232300000000000−2i32i300002i−2i-222i−2i00000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ774-4-444-4-2004-44-422-2-2-22200004-40004-400-22-22000000000-22000-220000000000000000000000000000000000
χ784-4-444-4-2004-44-422-2-2-2220000-44000-4400-22-220000000002-20002-20000000000000000000000000000000000
χ794-4-444-4-200-44-4422-222-2-2004-40004-40000-222-20000000-22000-22000000000000000000000000000000000000
χ804-4-444-4-200-44-4422-222-2-200-44000-440000-222-200000002-20002-2000000000000000000000000000000000000
χ814-4-44-44-2004-4-4422-2-2-222004-4000-4400002-22-20000000-220002-2000000000000000000000000000000000000
χ824-4-44-44-2004-4-4422-2-2-22200-440004-400002-22-200000002-2000-22000000000000000000000000000000000000
χ834-4-44-44-200-444-422-222-2-200004-4000-44002-2-22000000000-220002-20000000000000000000000000000000000
χ844-4-44-44-200-444-422-222-2-20000-440004-4002-2-220000000002-2000-220000000000000000000000000000000000
χ858-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000000

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