Finite Group Databasebeta

← Group #10943899

Character table — Group #10943899

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222223444444666666622222244444121212121212121244446666661212121212121212121212122222222244444444246612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ91111111-1-111111111111-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-111-1-11-11-1
χ101111111-1-111111111111-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111-111-1-1-11-11
χ111111111-1-111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-11-1-111-11-11
χ121111111-1-111111111111-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-11-1-1111-11-1
χ131111111-1-111111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ141111111-1-111111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ151111111-1-111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ161111111-1-111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-11-111-1-11-1-11
χ17222222222-2-2-2-22222222-2-222-2-2222-2-2-2-2-2-222220000-2-222-2-20000000022-2-200000000000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-2222-2-222-2-2-2-222220000-2-2-2-22200000000-2-22200000000000000000000000000
χ192222222-2-2-2-2-2-222222222222-2-2-2-2-222-2-2-2-2-2-2-2-200002222-2-200000000-2-22200000000000000000000000000
χ202222222-2-2-2-2-2-2222222222-2-222-222-2-2-2-2-2-2-2-2-2-2000022-2-2220000000022-2-200000000000000000000000000
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
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-12222-1-11111-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ25222222-122-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2222-2-21111-1-1-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-1-111000000000000000000−i3i3−i3i30000
χ26222222-122-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2222-2-21111-1-1-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-1-111000000000000000000i3−i3i3−i30000
χ27222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222-2-2221111-1-1-1-100001111-1-1−i3−i3i3i3−i3−i3i3i311-1-1000000000000000000i3−i3i3−i30000
χ28222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2222-2-2221111-1-1-1-100001111-1-1i3i3−i3−i3i3i3−i3−i311-1-1000000000000000000−i3i3−i3i30000
χ29222222-1-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-1-1-1-1111122-2-211-1-1-1-1-1-1-1-11111111100000000000000002-2-1-1110000
χ30222222-1-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-1-1-1-11111-2-22211-1-1-1-11111-1-1-1-111110000000000000000-2211-1-10000
χ31222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-1111122-2-2111111-1-1-1-11111-1-1-1-10000000000000000-2211-1-10000
χ32222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-11111-2-2221111111111-1-1-1-1-1-1-1-100000000000000002-2-1-1110000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-222111111110000-1-1-1-111−i3−i3i3i3i3i3−i3−i311-1-1000000000000000000−i3i3i3−i30000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-2-222111111110000-1-1-1-111i3i3−i3−i3−i3−i3i3i311-1-1000000000000000000i3−i3−i3i30000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-222-2-2111111110000-1-111-1-1−i3−i3i3i3i3i3−i3−i3-1-111000000000000000000i3−i3−i3i30000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-222-2-2111111110000-1-111-1-1i3i3−i3−i3−i3−i3i3i3-1-111000000000000000000−i3i3i3−i30000
χ372222-2-222222-2-22-2-2-2-2222-20000-2000022-2-222-2-200002-20000000000000000000022-2-20000-2-2220000000000
χ382222-2-222222-2-22-2-2-2-2222-20000-2000022-2-222-2-200002-200000000000000000000-2-222000022-2-20000000000
χ392222-2-2222-2-2222-2-2-2-222-220000-20000-2-22222-2-20000-22000000000000000022-2-20000-2-22200000000000000
χ402222-2-2222-2-2222-2-2-2-222-220000-20000-2-22222-2-20000-220000000000000000-2-222000022-2-200000000000000
χ412222-2-22-2-222-2-22-2-2-2-222-2200002000022-2-2-2-2220000-220000000000000000000022220000-2-2-2-20000000000
χ422222-2-22-2-222-2-22-2-2-2-222-2200002000022-2-2-2-2220000-2200000000000000000000-2-2-2-2000022220000000000
χ432222-2-22-2-2-2-2222-2-2-2-2222-2000020000-2-222-2-22200002-2000000000000000022220000-2-2-2-200000000000000
χ442222-2-22-2-2-2-2222-2-2-2-2222-2000020000-2-222-2-22200002-20000000000000000-2-2-2-20000222200000000000000
χ452-2-222-22002-22-2-222-2-2-2200000002-22-22-22-200000000000000000000002-22-2002-22-200002-22-2000000000000
χ462-2-222-22002-22-2-222-2-2-2200000002-22-22-22-200000000000000000000002-22-200-22-220000-22-22000000000000
χ472-2-222-22002-22-2-222-2-2-220000000-22-222-22-20000000000000000000000-22-22002-2-2200002-2-22000000000000
χ482-2-222-22002-22-2-222-2-2-220000000-22-222-22-20000000000000000000000-22-2200-222-20000-222-2000000000000
χ492-2-222-2200-22-22-222-2-2-2200000002-2-22-22-2200000000000000000000002-2-222-200002-22-200002-20000000000
χ502-2-222-2200-22-22-222-2-2-2200000002-2-22-22-2200000000000000000000002-2-22-220000-22-220000-220000000000
χ512-2-222-2200-22-22-222-2-2-220000000-222-2-22-220000000000000000000000-222-22-20000-222-20000-220000000000
χ522-2-222-2200-22-22-222-2-2-220000000-222-2-22-220000000000000000000000-222-2-2200002-2-2200002-20000000000
χ532-2-22-222002-2-22-2-2-222-22002-22-2000002-2-2200000000002-22-20000000000002-2002-200-2200-22000000000000
χ542-2-22-222002-2-22-2-2-222-22002-22-2000002-2-2200000000002-22-2000000000000-2200-22002-2002-2000000000000
χ552-2-22-222002-2-22-2-2-222-2200-22-22000002-2-220000000000-22-220000000000002-200-2200-22002-2000000000000
χ562-2-22-222002-2-22-2-2-222-2200-22-22000002-2-220000000000-22-22000000000000-22002-2002-200-22000000000000
χ572-2-22-22200-222-2-2-2-222-22002-2-2200000-222-200000000002-2-22000000000000002-2002-200-2200-220000000000
χ582-2-22-22200-222-2-2-2-222-22002-2-2200000-222-200000000002-2-2200000000000000-2200-22002-2002-20000000000
χ592-2-22-22200-222-2-2-2-222-2200-222-200000-222-20000000000-222-2000000000000002-200-2200-22002-20000000000
χ602-2-22-22200-222-2-2-2-222-2200-222-200000-222-20000000000-222-200000000000000-22002-2002-200-220000000000
χ614444-4-4-24444-4-4-22222-2-24-40000-40000-2-222-2-2220000-22000000000000000000000000000000000000000000
χ624444-4-4-244-4-444-22222-2-2-440000-4000022-2-2-2-22200002-2000000000000000000000000000000000000000000
χ634444-4-4-2-4-444-4-4-22222-2-2-44000040000-2-22222-2-200002-2000000000000000000000000000000000000000000
χ644444-4-4-2-4-4-4-444-22222-2-24-400004000022-2-222-2-20000-22000000000000000000000000000000000000000000
χ6544-4-40044i−4i000040000-4-40000000000000004i−4i002-22i−2i0000002-22-22i−2i2i−2i000000000000000000000000000000
χ6644-4-40044i−4i000040000-4-40000000000000004i−4i00-22−2i2i000000-22-22−2i2i−2i2i000000000000000000000000000000
χ6744-4-4004−4i4i000040000-4-4000000000000000−4i4i002-2−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000000000
χ6844-4-4004−4i4i000040000-4-4000000000000000−4i4i00-222i−2i000000-22-222i−2i2i−2i000000000000000000000000000000
χ6944-4-400-24i−4i0000-2−2i32i3−2i32i322000000000000000−2i2i23−232-22i−2i000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ7044-4-400-24i−4i0000-2−2i32i3−2i32i322000000000000000−2i2i23−23-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ7144-4-400-24i−4i0000-22i3−2i32i3−2i322000000000000000−2i2i−23232-22i−2i000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ7244-4-400-24i−4i0000-22i3−2i32i3−2i322000000000000000−2i2i−2323-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ7344-4-400-2−4i4i0000-2−2i32i3−2i32i3220000000000000002i−2i−23232-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ7444-4-400-2−4i4i0000-2−2i32i3−2i32i3220000000000000002i−2i−2323-222i−2i0000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ7544-4-400-2−4i4i0000-22i3−2i32i3−2i3220000000000000002i−2i23−232-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ7644-4-400-2−4i4i0000-22i3−2i32i3−2i3220000000000000002i−2i23−23-222i−2i0000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ774-4-444-4-2004-44-42-2-2222-200000004-44-4-22-220000000000000000000000-22-2200000000000000000000000000
χ784-4-444-4-2004-44-42-2-2222-20000000-44-44-22-2200000000000000000000002-22-200000000000000000000000000
χ794-4-444-4-200-44-442-2-2222-200000004-4-442-22-20000000000000000000000-222-200000000000000000000000000
χ804-4-444-4-200-44-442-2-2222-20000000-444-42-22-200000000000000000000002-2-2200000000000000000000000000
χ814-4-44-44-2004-4-44222-2-22-2004-44-400000-222-20000000000-22-2200000000000000000000000000000000000000
χ824-4-44-44-2004-4-44222-2-22-200-44-4400000-222-200000000002-22-200000000000000000000000000000000000000
χ834-4-44-44-200-444-4222-2-22-2004-4-44000002-2-220000000000-222-200000000000000000000000000000000000000
χ844-4-44-44-200-444-4222-2-22-200-444-4000002-2-2200000000002-2-2200000000000000000000000000000000000000
χ858-88-8008000000-800008-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-40000004−4i34i34i3−4i3-440000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-400000044i3−4i3−4i34i3-440000000000000000000000000000000000000000000000000000000000000000000

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