Finite Group Databasebeta

← Group #10943891

Character table — Group #10943891

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222223444466666662444444444466661212121244441212121212121212121212121212121212122222222244444444246612128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ91111-1-111111111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-11-111-1-11-11-1
χ101111-1-111111111111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1111-111-1-1-11-11
χ111111-1-111111111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-11-1-111-11-11
χ121111-1-111111111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-11-1-1111-11-1
χ131111-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-11-1-1111-1-11
χ141111-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-11-1-111-111-1
χ151111-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111-111-1-1-111-1
χ161111-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11-111-1-11-1-11
χ17222222222-2-2-2-222222222-2-222-2-222-2-22222-2-2-2-2000000000000-2-222-2-222-2-200000000000000000000000000
χ18222222222-2-2-2-222222222-2-2-2-222-2-2222222-2-2-2-2000000000000-2-2-2-222-2-22200000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ2222222222-12222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-10000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-12-2-222-2-222-2-2-1-1-1-111110000−i3−i3i3i3−i3−i3i3i311-1-111-1-111000000000000000000−i3i3−i3i30000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-12-2-222-2-222-2-2-1-1-1-111110000i3i3−i3−i3i3i3−i3−i311-1-111-1-111000000000000000000i3−i3i3−i30000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-222-2-222-1-1-1-111110000−i3−i3i3i3−i3−i3i3i31111-1-111-1-1000000000000000000i3−i3i3−i30000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-2-222-2-222-1-1-1-111110000i3i3−i3−i3i3i3−i3−i31111-1-111-1-1000000000000000000−i3i3−i3i30000
χ27222222-2-2222-2-22-2-2-2-222-22-20000000022-2-222-2-20000000000002-200000000000022220000-2-2-2-20000000000
χ28222222-2-2222-2-22-2-2-2-222-22-20000000022-2-222-2-20000000000002-2000000000000-2-2-2-2000022220000000000
χ29222222-2-22-2-2222-2-2-2-222-2-220000000022-2-2-2-222000000000000-220000000022220000-2-2-2-200000000000000
χ30222222-2-22-2-2222-2-2-2-222-2-220000000022-2-2-2-222000000000000-2200000000-2-2-2-20000222200000000000000
χ312222-2-2222-2-2-2-22222222-22222-2-2-2-222-2-2-2-2-2-2-2-20000000000002222-2-2-2-22200000000000000000000000000
χ322222-2-2222-2-2-2-22222222-222-2-22222-2-2-2-2-2-2-2-2-2-200000000000022-2-22222-2-200000000000000000000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-2-2-22222-2-2-2-21111-1-1-1-122-2-2-1-1-1-1111111-1-1-1-1111100000000000000002-2-1-1110000
χ342222-2-222-12222-1-1-1-1-1-1-1-2-2-22222-2-2-2-21111-1-1-1-1-2-2221111-1-1-1-111-1-1-1-111110000000000000000-2211-1-10000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-122-2-2-1-1-1-11111111111-1-1-1-10000000000000000-2211-1-10000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-222221111-1-1-1-1-2-2221111-1-1-1-1111111-1-1-1-100000000000000002-2-1-1110000
χ372222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22222-2-2-2-222111111110000−i3−i3i3i3i3i3−i3−i3-1-1-1-11111-1-1000000000000000000−i3i3i3−i30000
χ382222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22222-2-2-2-222111111110000i3i3−i3−i3−i3−i3i3i3-1-1-1-11111-1-1000000000000000000i3−i3−i3i30000
χ392222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-2111111110000−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-111000000000000000000i3−i3−i3i30000
χ402222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222-2-22222-2-2111111110000i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-111000000000000000000−i3i3i3−i30000
χ412222-2-2-2-2222-2-22-2-2-2-2222-2200000000-2-22222-2-2000000000000-2200000000000022-2-20000-2-2220000000000
χ422222-2-2-2-2222-2-22-2-2-2-2222-2200000000-2-22222-2-2000000000000-22000000000000-2-222000022-2-20000000000
χ432222-2-2-2-22-2-2222-2-2-2-22222-200000000-2-222-2-2220000000000002-20000000022-2-20000-2-22200000000000000
χ442222-2-2-2-22-2-2222-2-2-2-22222-200000000-2-222-2-2220000000000002-200000000-2-222000022-2-200000000000000
χ452-2-22002-222-22-2-222-2-2-2200000002-22-200002-22-20000000000000000002-22-2002-22-200002-22-2000000000000
χ462-2-22002-222-22-2-222-2-2-2200000002-22-200002-22-20000000000000000002-22-200-22-220000-22-22000000000000
χ472-2-22002-222-22-2-222-2-2-220000000-22-2200002-22-2000000000000000000-22-22002-2-2200002-2-22000000000000
χ482-2-22002-222-22-2-222-2-2-220000000-22-2200002-22-2000000000000000000-22-2200-222-20000-222-2000000000000
χ492-2-22002-22-22-22-222-2-2-2200000002-2-220000-22-220000000000000000002-2-222-200002-22-200002-20000000000
χ502-2-22002-22-22-22-222-2-2-2200000002-2-220000-22-220000000000000000002-2-22-220000-22-220000-220000000000
χ512-2-22002-22-22-22-222-2-2-220000000-222-20000-22-22000000000000000000-222-22-20000-222-20000-220000000000
χ522-2-22002-22-22-22-222-2-2-220000000-222-20000-22-22000000000000000000-222-2-2200002-2-2200002-20000000000
χ532-2-2200-2222-2-22-2-2-222-220002-22-2000000002-2-22000000000000002-22-200002-2002-200-2200-22000000000000
χ542-2-2200-2222-2-22-2-2-222-220002-22-2000000002-2-22000000000000002-22-20000-2200-22002-2002-2000000000000
χ552-2-2200-2222-2-22-2-2-222-22000-22-22000000002-2-2200000000000000-22-2200002-200-2200-22002-2000000000000
χ562-2-2200-2222-2-22-2-2-222-22000-22-22000000002-2-2200000000000000-22-220000-22002-2002-200-22000000000000
χ572-2-2200-222-222-2-2-2-222-220002-2-2200000000-222-2000000000000002-2-220000002-2002-200-2200-220000000000
χ582-2-2200-222-222-2-2-2-222-220002-2-2200000000-222-2000000000000002-2-22000000-2200-22002-2002-20000000000
χ592-2-2200-222-222-2-2-2-222-22000-222-200000000-222-200000000000000-222-20000002-200-2200-22002-20000000000
χ602-2-2200-222-222-2-2-2-222-22000-222-200000000-222-200000000000000-222-2000000-22002-2002-200-220000000000
χ61444444-4-4-244-4-4-22222-2-2-44-400000000-2-222-2-222000000000000-220000000000000000000000000000000000
χ62444444-4-4-2-4-444-22222-2-2-4-4400000000-2-22222-2-20000000000002-20000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-22222-2-24-440000000022-2-2-2-2220000000000002-20000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-22222-2-244-40000000022-2-222-2-2000000000000-220000000000000000000000000000000000
χ654-44-44-40040000-400004-4000000000004-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ664-44-44-40040000-400004-4000000000004-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ674-44-44-400-200002−2i32i3−2i32i3-2200000000000-22−2i32i300002i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000000000
χ684-44-44-400-200002−2i32i3−2i32i3-2200000000000-22−2i32i30000−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000000000
χ694-44-44-400-2000022i3−2i32i3−2i3-2200000000000-222i3−2i300002i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000000000
χ704-44-44-400-2000022i3−2i32i3−2i3-2200000000000-222i3−2i30000−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000000000
χ714-44-4-440040000-400004-400000000000-440000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ724-44-4-440040000-400004-400000000000-44000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ734-44-4-4400-200002−2i32i3−2i32i3-22000000000002-22i3−2i300002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000000000
χ744-44-4-4400-200002−2i32i3−2i32i3-22000000000002-22i3−2i30000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000000000
χ754-44-4-4400-2000022i3−2i32i3−2i3-22000000000002-2−2i32i300002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000000000
χ764-44-4-4400-2000022i3−2i32i3−2i3-22000000000002-2−2i32i30000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000000000
χ774-4-44004-4-24-44-42-2-2222-200000004-44-40000-22-22000000000000000000-22-2200000000000000000000000000
χ784-4-44004-4-24-44-42-2-2222-20000000-44-440000-22-220000000000000000002-22-200000000000000000000000000
χ794-4-44004-4-2-44-442-2-2222-200000004-4-4400002-22-2000000000000000000-222-200000000000000000000000000
χ804-4-44004-4-2-44-442-2-2222-20000000-444-400002-22-20000000000000000002-2-2200000000000000000000000000
χ814-4-4400-44-24-4-44222-2-22-20004-44-400000000-222-200000000000000-22-22000000000000000000000000000000
χ824-4-4400-44-24-4-44222-2-22-2000-44-4400000000-222-2000000000000002-22-2000000000000000000000000000000
χ834-4-4400-44-2-444-4222-2-22-20004-4-44000000002-2-2200000000000000-222-2000000000000000000000000000000
χ844-4-4400-44-2-444-4222-2-22-2000-444-4000000002-2-22000000000000002-2-22000000000000000000000000000000
χ8588-8-800008000080000-8-80000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-80000-40000-4−4i34i34i3−4i3440000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-80000-40000-44i3−4i3−4i34i3440000000000000000000000000000000000000000000000000000000000000000000

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