Finite Group Databasebeta

← Group #10943967

Character table — Group #10943967

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222222222223666666622222224444666666664444666666121212121212121212121212222222224444444444121212124444
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
χ511111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
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
χ131111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ141111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ151111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ161111-1-111111111111111-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-11-111-1-11-1-11
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
χ27222222-2-222-2-222-2-2-2-222-22-20000000022-2-222-2-200002-20000000000000000000022220000-2-2-2-20000000000
χ28222222-2-222-2-222-2-2-2-222-22-20000000022-2-222-2-200002-200000000000000000000-2-2-2-2000022220000000000
χ29222222-2-2-2-22222-2-2-2-222-2-2200000000-2-22222-2-20000-22000000000000000022220000-2-2-2-200000000000000
χ30222222-2-2-2-22222-2-2-2-222-2-2200000000-2-22222-2-20000-220000000000000000-2-2-2-20000222200000000000000
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
χ412222-2-2-2-222-2-222-2-2-2-2222-220000000022-2-2-2-2220000-220000000000000000000022-2-20000-2-2220000000000
χ422222-2-2-2-222-2-222-2-2-2-2222-220000000022-2-2-2-2220000-2200000000000000000000-2-222000022-2-20000000000
χ432222-2-2-2-2-2-22222-2-2-2-22222-200000000-2-222-2-22200002-2000000000000000022-2-20000-2-22200000000000000
χ442222-2-2-2-2-2-22222-2-2-2-22222-200000000-2-222-2-22200002-20000000000000000-2-222000022-2-200000000000000
χ452-2-22002-22-22-22-222-2-2-22000002-2002-22-22-20000000000002-20000002-20000002-22-200002-22-2000000000000
χ462-2-22002-22-22-22-222-2-2-22000002-2002-22-22-20000000000002-20000002-2000000-22-220000-22-22000000000000
χ472-2-22002-22-22-22-222-2-2-2200000-2200-222-22-2000000000000-22000000-220000002-2-2200002-2-22000000000000
χ482-2-22002-22-22-22-222-2-2-2200000-2200-222-22-2000000000000-22000000-22000000-222-20000-222-2000000000000
χ492-2-22002-2-22-222-222-2-2-22000002-200-22-22-220000000000002-2000000-2200002-200002-22-200002-20000000000
χ502-2-22002-2-22-222-222-2-2-22000002-200-22-22-220000000000002-2000000-220000-220000-22-220000-220000000000
χ512-2-22002-2-22-222-222-2-2-2200000-22002-2-22-22000000000000-220000002-200002-20000-222-20000-220000000000
χ522-2-22002-2-22-222-222-2-2-2200000-22002-2-22-22000000000000-220000002-20000-2200002-2-2200002-20000000000
χ532-2-2200-222-2-222-2-2-222-220002-2002-2002-2-2200000000002-20000002-20000002-2002-200-2200-22000000000000
χ542-2-2200-222-2-222-2-2-222-220002-2002-2002-2-2200000000002-20000002-2000000-2200-22002-2002-2000000000000
χ552-2-2200-222-2-222-2-2-222-22000-2200-22002-2-220000000000-22000000-220000002-200-2200-22002-2000000000000
χ562-2-2200-222-2-222-2-2-222-22000-2200-22002-2-220000000000-22000000-22000000-22002-2002-200-22000000000000
χ572-2-2200-22-222-22-2-2-222-220002-200-2200-222-200000000002-2000000-22000000002-2002-200-2200-220000000000
χ582-2-2200-22-222-22-2-2-222-220002-200-2200-222-200000000002-2000000-2200000000-2200-22002-2002-20000000000
χ592-2-2200-22-222-22-2-2-222-22000-22002-200-222-20000000000-220000002-2000000002-200-2200-22002-20000000000
χ602-2-2200-22-222-22-2-2-222-22000-22002-200-222-20000000000-220000002-200000000-22002-2002-200-220000000000
χ61444444-4-444-4-4-2-22222-2-2-44-400000000-2-222-2-2220000-22000000000000000000000000000000000000000000
χ62444444-4-4-4-444-2-22222-2-2-4-440000000022-2-2-2-22200002-2000000000000000000000000000000000000000000
χ634444-4-4-4-444-4-4-2-22222-2-24-4400000000-2-22222-2-200002-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-444-2-22222-2-244-40000000022-2-222-2-20000-22000000000000000000000000000000000000000000
χ6544-4-44-4000000440000-4-40000000000000004-4002i−2i2i−2i0000002i−2i2i−2i00002i−2i2i−2i00000000000000000000000000
χ6644-4-44-4000000440000-4-40000000000000004-400−2i2i−2i2i000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000
χ6744-4-44-4000000-2-2−2i32i3−2i32i322000000000000000-22−2i32i32i−2i2i−2i0000002ζ7−2ζ72ζ11−2ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ6844-4-44-4000000-2-2−2i32i3−2i32i322000000000000000-22−2i32i3−2i2i−2i2i000000−2ζ72ζ7−2ζ112ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ6944-4-44-4000000-2-22i3−2i32i3−2i322000000000000000-222i3−2i32i−2i2i−2i0000002ζ11−2ζ112ζ7−2ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ7044-4-44-4000000-2-22i3−2i32i3−2i322000000000000000-222i3−2i3−2i2i−2i2i000000−2ζ112ζ11−2ζ72ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ7144-4-4-44000000440000-4-4000000000000000-44002i−2i−2i2i0000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000000000
χ7244-4-4-44000000440000-4-4000000000000000-4400−2i2i2i−2i000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000
χ7344-4-4-44000000-2-2−2i32i3−2i32i3220000000000000002-22i3−2i32i−2i−2i2i0000002ζ7−2ζ72ζ11−2ζ110000−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ7444-4-4-44000000-2-2−2i32i3−2i32i3220000000000000002-22i3−2i3−2i2i2i−2i000000−2ζ72ζ7−2ζ112ζ1100002ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ7544-4-4-44000000-2-22i3−2i32i3−2i3220000000000000002-2−2i32i32i−2i−2i2i0000002ζ11−2ζ112ζ7−2ζ70000−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ7644-4-4-44000000-2-22i3−2i32i3−2i3220000000000000002-2−2i32i3−2i2i2i−2i000000−2ζ112ζ11−2ζ72ζ700002ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ774-4-44004-44-44-4-22-2-2222-2000004-4004-4-22-22000000000000-22000000-22000000000000000000000000000000
χ784-4-44004-44-44-4-22-2-2222-200000-4400-44-22-220000000000002-20000002-2000000000000000000000000000000
χ794-4-44004-4-44-44-22-2-2222-2000004-400-442-22-2000000000000-220000002-2000000000000000000000000000000
χ804-4-44004-4-44-44-22-2-2222-200000-44004-42-22-20000000000002-2000000-22000000000000000000000000000000
χ814-4-4400-444-4-44-2222-2-22-20004-4004-400-222-20000000000-22000000-2200000000000000000000000000000000
χ824-4-4400-444-4-44-2222-2-22-2000-4400-4400-222-200000000002-20000002-200000000000000000000000000000000
χ834-4-4400-44-444-4-2222-2-22-20004-400-44002-2-220000000000-220000002-200000000000000000000000000000000
χ844-4-4400-44-444-4-2222-2-22-2000-44004-4002-2-2200000000002-2000000-2200000000000000000000000000000000
χ858-88-8000000008-800008-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800000000-44−4i34i34i3−4i3-440000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800000000-444i3−4i3−4i34i3-440000000000000000000000000000000000000000000000000000000000000000000

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