Finite Group Databasebeta

← Group #10944217

Character table — Group #10944217

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222222234466666662244444444466661212121244446612121212121212121212121212121212222244444444444444121212124444
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
χ511111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111111111-1-1
χ911111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-11-11-1
χ1011111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-1-11-11
χ1111111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-11-11
χ1211111111111-1-1111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-1111-11-1
χ1311111111111-1-11111111-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-11-1-1111-1-11
χ1411111111111-1-11111111-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-11-1-111-111-1
χ1511111111111-1-11111111-1-111-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11-111-1-1-111-1
χ1611111111111-1-11111111-1-111-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111-111-1-11-1-11
χ172222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ182222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ192222222222-122-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-11111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ202222222222-122-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111111111111000000000000000022-1-1-1-10000
χ212222222222-1-2-2-1-1-1-1-1-1-122-2-2-2-2-2-2-222-1-1-1-1111122-2-2-1-1111111-1-1-1-1-1-1111100000000000000002-2-1-1110000
χ222222222222-1-2-2-1-1-1-1-1-1-122-2-2-2-2-2-2-222-1-1-1-11111-2-222-1-1111111-1-11111-1-1-1-10000000000000000-2211-1-10000
χ232222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-222-2-2-1-1-1-1111122-2-211-1-111-1-111-1-1-1-111110000000000000000-2211-1-10000
χ242222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-222-2-2-1-1-1-11111-2-22211-1-111-1-1111111-1-1-1-100000000000000002-2-1-1110000
χ2522222-2-22-2-2222222222222-2-22-2-222-2-2-2-2-2-22222000022-2-2-2-222-2-20000000000000000000000000000000000
χ2622222-2-22-2-22222222222-2-2222-2-2-2-222-2-2-2-222220000-2-222-2-2-2-2220000000000000000000000000000000000
χ2722222-2-22-2-22-2-222222222222-222-2-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-20000000000000000000000000000000000
χ2822222-2-22-2-22-2-22222222-2-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-2-2-22222220000000000000000000000000000000000
χ2922222-2-22-2-2-122-1-1-1-1-1-1-122-2-22-2-222-2-21111-1-1-1-10000-1-11111-1-111−i3−i3i3i3−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ3022222-2-22-2-2-122-1-1-1-1-1-1-122-2-22-2-222-2-21111-1-1-1-10000-1-11111-1-111i3i3−i3−i3i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ3122222-2-22-2-2-122-1-1-1-1-1-1-1-2-2222-2-2-2-2221111-1-1-1-1000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ3222222-2-22-2-2-122-1-1-1-1-1-1-1-2-2222-2-2-2-2221111-1-1-1-1000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ3322222-2-22-2-2-1-2-2-1-1-1-1-1-1-12222-222-2-2-2-2111111110000-1-1-1-1-1-11111−i3−i3i3i3i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ3422222-2-22-2-2-1-2-2-1-1-1-1-1-1-12222-222-2-2-2-2111111110000-1-1-1-1-1-11111i3i3−i3−i3−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ3522222-2-22-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-2-22222221111111100001111-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ3622222-2-22-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-2-22222221111111100001111-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ372222-22-2-22-2222-2-22-2-2220000-22-2000022-2-222-2-2000000002-2000000000000002200-2-2002200-2-20000000000
χ382222-22-2-22-2222-2-22-2-2220000-22-2000022-2-222-2-2000000002-200000000000000-2-2002200-2-200220000000000
χ392222-22-2-22-22-2-2-2-22-2-22200002-22000022-2-2-2-22200000000-220000000000000022002200-2-200-2-20000000000
χ402222-22-2-22-22-2-2-2-22-2-22200002-22000022-2-2-2-22200000000-2200000000000000-2-200-2-2002200220000000000
χ412222-2-22-2-22222-2-22-2-2220000-2-220000-2-22222-2-200000000-220000000000002200-2-2002200-2-2000000000000
χ422222-2-22-2-22222-2-22-2-2220000-2-220000-2-22222-2-200000000-22000000000000-2-2002200-2-20022000000000000
χ432222-2-22-2-222-2-2-2-22-2-222000022-20000-2-222-2-222000000002-200000000000022002200-2-200-2-2000000000000
χ442222-2-22-2-222-2-2-2-22-2-222000022-20000-2-222-2-222000000002-2000000000000-2-200-2-200220022000000000000
χ452-2-2222-2-2-2220022-2-2-2-22002i−2i0002i−2i002-22-200000000002i−2i002i−2i00000000002-200002i−2i002i−2i2-2000000000000
χ462-2-2222-2-2-2220022-2-2-2-22002i−2i0002i−2i002-22-200000000002i−2i002i−2i0000000000-220000−2i2i00−2i2i-22000000000000
χ472-2-2222-2-2-2220022-2-2-2-2200−2i2i000−2i2i002-22-20000000000−2i2i00−2i2i00000000002-20000−2i2i00−2i2i2-2000000000000
χ482-2-2222-2-2-2220022-2-2-2-2200−2i2i000−2i2i002-22-20000000000−2i2i00−2i2i0000000000-2200002i−2i002i−2i-22000000000000
χ492-2-222-22-22-220022-2-2-2-22002i−2i000−2i2i00-22-2200000000002i−2i00−2i2i0000000000002-22i−2i002i−2i00002-20000000000
χ502-2-222-22-22-220022-2-2-2-22002i−2i000−2i2i00-22-2200000000002i−2i00−2i2i000000000000-22−2i2i00−2i2i0000-220000000000
χ512-2-222-22-22-220022-2-2-2-2200−2i2i0002i−2i00-22-220000000000−2i2i002i−2i0000000000002-2−2i2i00−2i2i00002-20000000000
χ522-2-222-22-22-220022-2-2-2-2200−2i2i0002i−2i00-22-220000000000−2i2i002i−2i000000000000-222i−2i002i−2i0000-220000000000
χ532-2-22-2222-2-2200-2-2-222-222-200000002-22-2-22000000002-20000002-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ542-2-22-2222-2-2200-2-2-222-222-200000002-22-2-22000000002-20000002-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ552-2-22-2222-2-2200-2-2-222-22-220000000-222-2-2200000000-22000000-220000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ562-2-22-2222-2-2200-2-2-222-22-220000000-222-2-2200000000-22000000-22000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ572-2-22-2-2-2222200-2-2-222-222-20000000-22-222-2000000002-2000000-22000000002-2-2200000000-222-20000000000
χ582-2-22-2-2-2222200-2-2-222-222-20000000-22-222-2000000002-2000000-2200000000-222-2000000002-2-220000000000
χ592-2-22-2-2-2222200-2-2-222-22-2200000002-2-222-200000000-220000002-2000000002-22-200000000-22-220000000000
χ602-2-22-2-2-2222200-2-2-222-22-2200000002-2-222-200000000-220000002-200000000-22-22000000002-22-20000000000
χ614444-44-4-44-4-24422-222-2-20000-44-40000-2-222-2-22200000000-2200000000000000000000000000000000000000
χ624444-44-4-44-4-2-4-422-222-2-200004-440000-2-22222-2-2000000002-200000000000000000000000000000000000000
χ634444-4-44-4-44-24422-222-2-20000-4-44000022-2-2-2-222000000002-200000000000000000000000000000000000000
χ644444-4-44-4-44-2-4-422-222-2-2000044-4000022-2-222-2-200000000-2200000000000000000000000000000000000000
χ654-44-400000044-400-4004-40000000000000004-4002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ664-44-400000044-400-4004-40000000000000004-400−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ674-44-40000004-4400-4004-4000000000000000-44002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ684-44-40000004-4400-4004-4000000000000000-4400−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ694-44-4000000-24-4−2i32i32−2i32i3-22000000000000000-22−2i32i32i−2i2i−2i00000000002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ704-44-4000000-24-4−2i32i32−2i32i3-22000000000000000-22−2i32i3−2i2i−2i2i0000000000−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ714-44-4000000-24-42i3−2i322i3−2i3-22000000000000000-222i3−2i32i−2i2i−2i00000000002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ724-44-4000000-24-42i3−2i322i3−2i3-22000000000000000-222i3−2i3−2i2i−2i2i0000000000−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ734-44-4000000-2-44−2i32i32−2i32i3-220000000000000002-22i3−2i32i−2i−2i2i00000000002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ744-44-4000000-2-44−2i32i32−2i32i3-220000000000000002-22i3−2i3−2i2i2i−2i0000000000−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ754-44-4000000-2-442i3−2i322i3−2i3-220000000000000002-2−2i32i32i−2i−2i2i00000000002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ764-44-4000000-2-442i3−2i322i3−2i3-220000000000000002-2−2i32i3−2i2i2i−2i0000000000−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ774-4-4444-4-4-44-200-2-22222-2004i−4i0004i−4i00-22-220000000000−2i2i00−2i2i000000000000000000000000000000000000
χ784-4-4444-4-4-44-200-2-22222-200−4i4i000−4i4i00-22-2200000000002i−2i002i−2i000000000000000000000000000000000000
χ794-4-444-44-44-4-200-2-22222-2004i−4i000−4i4i002-22-20000000000−2i2i002i−2i000000000000000000000000000000000000
χ804-4-444-44-44-4-200-2-22222-200−4i4i0004i−4i002-22-200000000002i−2i00−2i2i000000000000000000000000000000000000
χ814-4-44-4444-4-4-200222-2-22-24-400000004-4-222-200000000-22000000-220000000000000000000000000000000000
χ824-4-44-4444-4-4-200222-2-22-2-440000000-44-222-2000000002-20000002-20000000000000000000000000000000000
χ834-4-44-4-4-4444-200222-2-22-24-40000000-442-2-2200000000-220000002-20000000000000000000000000000000000
χ844-4-44-4-4-4444-200222-2-22-2-4400000004-42-2-22000000002-2000000-220000000000000000000000000000000000
χ8588-8-800000080000800-8-80000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-400−4i34i3-44i3−4i3440000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4004i3−4i3-4−4i34i3440000000000000000000000000000000000000000000000000000000000000000000

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