Finite Group Databasebeta

← Group #10945074

Character table — Group #10945074

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222222222236666666222444444446666666644446612121212121212121212121212121212222244444444444444121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111111111111111-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-11-111-1-11-11-1
χ101111-1-111111111111111-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-111-1-1-11-11
χ111111-1-111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-111-1-1-11-1-111-11-11
χ121111-1-111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-111-11-1-1111-11-1
χ131111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-1-1-111-1-111-11-1-1111-1-11
χ141111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-11111-1-111-1-1-11-1-111-111-1
χ151111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1111-111-1-1-111-1
χ161111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-11-111-1-11-1-11
χ17222222222222-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ18222222222222-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111-1-1-1-111110000000000000000-2-211110000
χ19222222222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-11111-1-1-1-11111-1-1-1-10000000000000000-2-211110000
χ20222222222222-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ2122222222-2-2-2-2222222222-2-22222-2-2-2-2-2-2-2-222220000-2-222220000-2-2-2-2000000000000000000000000000000
χ2222222222-2-2-2-2222222222-2-2-2-2-2-22222-2-2-2-222220000-2-2-2-2-2-200002222000000000000000000000000000000
χ2322222222-2-2-2-2-1-1-1-1-1-1-1-12-2-22222-2-2-2-21111-1-1-1-1000011-1-1-1-1−i3−i3i3i31111−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ2422222222-2-2-2-2-1-1-1-1-1-1-1-12-2-22222-2-2-2-21111-1-1-1-1000011-1-1-1-1i3i3−i3−i31111i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ2522222222-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-2-2-222221111-1-1-1-10000111111−i3−i3i3i3-1-1-1-1−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ2622222222-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-2-2-222221111-1-1-1-10000111111i3i3−i3−i3-1-1-1-1i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ27222222-2-222-2-22-2-2-2-2222-22-20000000022-2-222-2-200002-20000000000000000000000002222-2-2-2-20000000000
χ28222222-2-222-2-22-2-2-2-2222-22-20000000022-2-222-2-200002-2000000000000000000000000-2-2-2-222220000000000
χ29222222-2-2-2-2222-2-2-2-2222-2-2200000000-2-22222-2-20000-2200000000000000002222-2-2-2-2000000000000000000
χ30222222-2-2-2-2222-2-2-2-2222-2-2200000000-2-22222-2-20000-220000000000000000-2-2-2-22222000000000000000000
χ312222-2-2222222-1-1-1-1-1-1-1-1-2-2-222-2-222-2-2-1-1-1-1111122-2-211-1-111-1-1-1-1-1-111111100000000000000002-2-1-1110000
χ322222-2-2222222-1-1-1-1-1-1-1-1-2-2-222-2-222-2-2-1-1-1-11111-2-22211-1-1111111-1-111-1-1-1-10000000000000000-2211-1-10000
χ332222-2-2222222-1-1-1-1-1-1-1-1-2-2-2-2-222-2-222-1-1-1-1111122-2-21111-1-1-1-1-1-111-1-111110000000000000000-2211-1-10000
χ342222-2-2222222-1-1-1-1-1-1-1-1-2-2-2-2-222-2-222-1-1-1-11111-2-2221111-1-1111111-1-1-1-1-1-100000000000000002-2-1-1110000
χ352222-2-222-2-2-2-222222222-22222-2-2-2-222-2-2-2-2-2-2-2-200002222-2-20000-2-222000000000000000000000000000000
χ362222-2-222-2-2-2-222222222-222-2-22222-2-2-2-2-2-2-2-2-2-2000022-2-222000022-2-2000000000000000000000000000000
χ372222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-22222-2-2-2-222111111110000-1-1-1-111−i3−i3i3i311-1-1i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ382222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-22222-2-2-2-222111111110000-1-1-1-111i3i3−i3−i311-1-1−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ392222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-222-2-22222-2-2111111110000-1-111-1-1−i3−i3i3i3-1-111i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ402222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-222-2-22222-2-2111111110000-1-111-1-1i3i3−i3−i3-1-111−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ412222-2-2-2-222-2-22-2-2-2-22222-220000000022-2-2-2-2220000-2200000000000000000000000022-2-2-2-2220000000000
χ422222-2-2-2-222-2-22-2-2-2-22222-220000000022-2-2-2-2220000-22000000000000000000000000-2-22222-2-20000000000
χ432222-2-2-2-2-2-2222-2-2-2-222222-200000000-2-222-2-22200002-2000000000000000022-2-2-2-222000000000000000000
χ442222-2-2-2-2-2-2222-2-2-2-222222-200000000-2-222-2-22200002-20000000000000000-2-22222-2-2000000000000000000
χ4522-2-2002-22-22-2222-2-22-2-2000002i−2i002i−2i2-22-20000000000002i−2i0000002i−2i0000002-2002-22i−2i002i−2i000000000000
χ4622-2-2002-22-22-2222-2-22-2-2000002i−2i002i−2i2-22-20000000000002i−2i0000002i−2i000000-2200-22−2i2i00−2i2i000000000000
χ4722-2-2002-22-22-2222-2-22-2-200000−2i2i00−2i2i2-22-2000000000000−2i2i000000−2i2i0000002-2002-2−2i2i00−2i2i000000000000
χ4822-2-2002-22-22-2222-2-22-2-200000−2i2i00−2i2i2-22-2000000000000−2i2i000000−2i2i000000-2200-222i−2i002i−2i000000000000
χ4922-2-2002-2-22-22222-2-22-2-2000002i−2i00−2i2i-22-220000000000002i−2i000000−2i2i00002-2002-200002i−2i002i−2i0000000000
χ5022-2-2002-2-22-22222-2-22-2-2000002i−2i00−2i2i-22-220000000000002i−2i000000−2i2i0000-2200-220000−2i2i00−2i2i0000000000
χ5122-2-2002-2-22-22222-2-22-2-200000−2i2i002i−2i-22-22000000000000−2i2i0000002i−2i00002-2002-20000−2i2i00−2i2i0000000000
χ5222-2-2002-2-22-22222-2-22-2-200000−2i2i002i−2i-22-22000000000000−2i2i0000002i−2i0000-2200-2200002i−2i002i−2i0000000000
χ5322-2-200-222-2-222-2-2222-2-20002i−2i002i−2i002-2-2200000000002i−2i0000002i−2i0000002-200-22002i−2i00−2i2i000000000000
χ5422-2-200-222-2-222-2-2222-2-20002i−2i002i−2i002-2-2200000000002i−2i0000002i−2i000000-22002-200−2i2i002i−2i000000000000
χ5522-2-200-222-2-222-2-2222-2-2000−2i2i00−2i2i002-2-220000000000−2i2i000000−2i2i0000002-200-2200−2i2i002i−2i000000000000
χ5622-2-200-222-2-222-2-2222-2-2000−2i2i00−2i2i002-2-220000000000−2i2i000000−2i2i000000-22002-2002i−2i00−2i2i000000000000
χ5722-2-200-22-222-22-2-2222-2-20002i−2i00−2i2i00-222-200000000002i−2i000000−2i2i000000002-200-22002i−2i00−2i2i0000000000
χ5822-2-200-22-222-22-2-2222-2-20002i−2i00−2i2i00-222-200000000002i−2i000000−2i2i00000000-22002-200−2i2i002i−2i0000000000
χ5922-2-200-22-222-22-2-2222-2-2000−2i2i002i−2i00-222-20000000000−2i2i0000002i−2i000000002-200-2200−2i2i002i−2i0000000000
χ6022-2-200-22-222-22-2-2222-2-2000−2i2i002i−2i00-222-20000000000−2i2i0000002i−2i00000000-22002-2002i−2i00−2i2i0000000000
χ61444444-4-444-4-4-22222-2-2-2-44-400000000-2-222-2-2220000-22000000000000000000000000000000000000000000
χ62444444-4-4-4-444-22222-2-2-2-4-440000000022-2-2-2-22200002-2000000000000000000000000000000000000000000
χ634444-4-4-4-444-4-4-22222-2-2-24-4400000000-2-22222-2-200002-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-444-22222-2-2-244-40000000022-2-222-2-20000-22000000000000000000000000000000000000000000
χ6544-4-4004-44-44-4-2-2-222-222000004i−4i004i−4i-22-22000000000000−2i2i000000−2i2i000000000000000000000000000000
χ6644-4-4004-44-44-4-2-2-222-22200000−4i4i00−4i4i-22-220000000000002i−2i0000002i−2i000000000000000000000000000000
χ6744-4-4004-4-44-44-2-2-222-222000004i−4i00−4i4i2-22-2000000000000−2i2i0000002i−2i000000000000000000000000000000
χ6844-4-4004-4-44-44-2-2-222-22200000−4i4i004i−4i2-22-20000000000002i−2i000000−2i2i000000000000000000000000000000
χ6944-4-400-444-4-44-222-2-2-2220004i−4i004i−4i00-222-20000000000−2i2i000000−2i2i00000000000000000000000000000000
χ7044-4-400-444-4-44-222-2-2-222000−4i4i00−4i4i00-222-200000000002i−2i0000002i−2i00000000000000000000000000000000
χ7144-4-400-44-444-4-222-2-2-2220004i−4i00−4i4i002-2-220000000000−2i2i0000002i−2i00000000000000000000000000000000
χ7244-4-400-44-444-4-222-2-2-222000−4i4i004i−4i002-2-2200000000002i−2i000000−2i2i00000000000000000000000000000000
χ734-44-44-400000040000-44-40000000000000004-4002i−2i2i−2i0000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000
χ744-44-44-400000040000-44-40000000000000004-400−2i2i−2i2i000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000
χ754-44-44-4000000-2−2i32i3−2i32i32-22000000000000000-22−2i32i32i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ764-44-44-4000000-2−2i32i3−2i32i32-22000000000000000-22−2i32i3−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ774-44-44-4000000-22i3−2i32i3−2i32-22000000000000000-222i3−2i32i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ784-44-44-4000000-22i3−2i32i3−2i32-22000000000000000-222i3−2i3−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ794-44-4-4400000040000-44-4000000000000000-44002i−2i−2i2i0000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000
χ804-44-4-4400000040000-44-4000000000000000-4400−2i2i2i−2i000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000
χ814-44-4-44000000-2−2i32i3−2i32i32-220000000000000002-22i3−2i32i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ824-44-4-44000000-2−2i32i3−2i32i32-220000000000000002-22i3−2i3−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ834-44-4-44000000-22i3−2i32i3−2i32-220000000000000002-2−2i32i32i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ844-44-4-44000000-22i3−2i32i3−2i32-220000000000000002-2−2i32i3−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ858-8-880000000080000-8-880000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800000000-4−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800000000-44i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000000000

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