Finite Group Databasebeta

← Group #10828716

Character table — Group #10828716

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order12222222344446666666244666612121212444444444444121212121212121212121212121212121212444412121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11-11-11111-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-11-1-1-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111111-1-1
χ91111-1-111111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-11-1111-1-11-1
χ101111-1-111111111111111-1-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-11
χ111111-1-111111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-11-11-1-111-11
χ121111-1-111111111111111-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-111-1-11-1
χ131111-1-111111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-11
χ141111-1-111111111111111-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1
χ151111-1-111111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111-1
χ161111-1-111111111111111-1-1-1-1-1-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-11
χ17222222222-2-2-2-222222222-2-22222-2-2-2-22-22-20000000000000000-2-20000000000002-22-2000000000000
χ18222222222-2-2-2-222222222-2-22222-2-2-2-2-22-220000000000000000-2-2000000000000-22-22000000000000
χ1922222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-211111111-1-1111111110000-1-1-1-1000000000000
χ2122222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-100001111000000000000
χ2222222222-12222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ2322222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000−i3−i3i3i3−i3−i3i3i311−i3−i3i3i3−i3−i3i3i30000-11-11000000000000
χ2422222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-111112-22-200000000i3i3−i3−i3i3i3−i3−i311i3i3−i3−i3i3i3−i3−i30000-11-11000000000000
χ2522222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000−i3−i3i3i3−i3−i3i3i311i3i3−i3−i3i3i3−i3−i300001-11-1000000000000
χ2622222222-1-2-2-2-2-1-1-1-1-1-1-12-2-2-1-1-1-11111-22-2200000000i3i3−i3−i3i3i3−i3−i311−i3−i3i3i3−i3−i3i3i300001-11-1000000000000
χ27222222-2-222-2-22-2-2-2-2222-22-222-2-222-2-2000000000000000000002-20000000022-2-200000020-20000000
χ28222222-2-222-2-22-2-2-2-2222-22-222-2-222-2-2000000000000000000002-200000000-2-222000000-2020000000
χ29222222-2-22-222-2-2-2-2-2222-2-2222-2-2-2-22200000000000000000000-2200000000000000002-20-202000000
χ30222222-2-22-222-2-2-2-2-2222-2-2222-2-2-2-22200000000000000000000-220000000000000000-22020-2000000
χ312222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-22-2-22000000000000000022000000000000-222-2000000000000
χ322222-2-2222-2-2-2-22222222-222-2-2-2-2-2-2-2-2-222-20000000000000000220000000000002-2-22000000000000
χ332222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-222-2-222-2-2-1-1-1-1111111-1-1-1-11111000011-1-1000000000000
χ342222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-122-2-2-2-222-2-2221111-1-1-1-1111111-1-1-1-1000011-1-1000000000000
χ352222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-111-1-1-1-111110000-1-111000000000000
χ362222-2-222-12222-1-1-1-1-1-1-1-2-2-21111-1-1-1-1-2-222-2-22222-2-2-1-1-1-11111111111-1-1-1-10000-1-111000000000000
χ372222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000−i3−i3i3i3i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i300001-1-11000000000000
χ382222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-222111111112-2-2200000000i3i3−i3−i3−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i300001-1-11000000000000
χ392222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000−i3−i3i3i3i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i30000-111-1000000000000
χ402222-2-222-1-2-2-2-2-1-1-1-1-1-1-1-22211111111-222-200000000i3i3−i3−i3−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i30000-111-1000000000000
χ412222-2-2-2-222-2-22-2-2-2-22222-22-2-22222-2-200000000000000000000-220000000022-2-2000000-2020000000
χ422222-2-2-2-222-2-22-2-2-2-22222-22-2-22222-2-200000000000000000000-2200000000-2-22200000020-20000000
χ432222-2-2-2-22-222-2-2-2-2-222222-2-2-222-2-222000000000000000000002-200000000000000002-2020-2000000
χ442222-2-2-2-22-222-2-2-2-2-222222-2-2-222-2-222000000000000000000002-20000000000000000-220-202000000
χ4522-2-2002-22-22-2222-2-2-22-200000002-22-20000002i−2i0000000000000000002i−2i2i−2i2i−2i2i−2i0000000000002-200
χ4622-2-2002-22-22-2222-2-2-22-200000002-22-20000002i−2i0000000000000000002i−2i2i−2i−2i2i−2i2i000000000000-2200
χ4722-2-2002-22-22-2222-2-2-22-200000002-22-2000000−2i2i000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000-2200
χ4822-2-2002-22-22-2222-2-2-22-200000002-22-2000000−2i2i000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000002-200
χ4922-2-200-222-2-222-2-222-22-200000002-2-2200002i−2i00000000000000002i−2i2i−2i00002i−2i−2i2i00000000002-20000
χ5022-2-200-222-2-222-2-222-22-200000002-2-2200002i−2i00000000000000002i−2i2i−2i0000−2i2i2i−2i0000000000-220000
χ5122-2-200-222-2-222-2-222-22-200000002-2-220000−2i2i0000000000000000−2i2i−2i2i00002i−2i−2i2i0000000000-220000
χ5222-2-200-222-2-222-2-222-22-200000002-2-220000−2i2i0000000000000000−2i2i−2i2i0000−2i2i2i−2i00000000002-20000
χ53444444-4-4-24-4-442222-2-2-2-44-4-2-222-2-22200000000000000000000-220000000000000000000000000000
χ54444444-4-4-2-444-42222-2-2-2-4-44-2-22222-2-2000000000000000000002-20000000000000000000000000000
χ554444-4-4-4-4-24-4-442222-2-2-24-4422-2-2-2-222000000000000000000002-20000000000000000000000000000
χ564444-4-4-4-4-2-444-42222-2-2-244-422-2-222-2-200000000000000000000-220000000000000000000000000000
χ5744-4-4004-444-44-444-4-4-44-40000000-44-4400000000000000000000000000000000000000000000000000
χ5844-4-4004-4-24-44-4-2-2222-2200000002-22-20000000000000000000000000023−23−232300000000000000000000
χ5944-4-4004-4-24-44-4-2-2222-2200000002-22-200000000000000000000000000−232323−2300000000000000000000
χ6044-4-4004-4-2-44-44-2-2222-220000000-22-220000004i−4i000000000000000000−2i2i−2i2i00000000000000000000
χ6144-4-4004-4-2-44-44-2-2222-220000000-22-22000000−4i4i0000000000000000002i−2i2i−2i00000000000000000000
χ6244-4-400-44444-4-4-4-444-44-40000000-444-400000000000000000000000000000000000000000000000000
χ6344-4-400-44-244-4-422-2-22-2200000002-2-22000000000000000000000023−23−2323000000000000000000000000
χ6444-4-400-44-244-4-422-2-22-2200000002-2-220000000000000000000000−232323−23000000000000000000000000
χ6544-4-400-44-2-4-44422-2-22-220000000-222-200004i−4i0000000000000000−2i2i−2i2i000000000000000000000000
χ6644-4-400-44-2-4-44422-2-22-220000000-222-20000−4i4i00000000000000002i−2i2i−2i000000000000000000000000
χ674-4-444-400400000000-4-440004-4000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ684-4-444-400400000000-4-440004-400000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ694-4-444-400-20000−2i32i3−2i32i322-2000-22−2i32i30000000000002i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ704-4-444-400-20000−2i32i3−2i32i322-2000-22−2i32i3000000000000−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ714-4-444-400-200002i3−2i32i3−2i322-2000-222i3−2i30000000000002i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ724-4-444-400-200002i3−2i32i3−2i322-2000-222i3−2i3000000000000−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ734-4-44-4400400000000-4-44000-44000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ744-4-44-4400400000000-4-44000-4400000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ754-4-44-4400-20000−2i32i3−2i32i322-20002-22i3−2i30000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ764-4-44-4400-20000−2i32i3−2i32i322-20002-22i3−2i3000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ774-4-44-4400-200002i3−2i32i3−2i322-20002-2−2i32i30000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ784-4-44-4400-200002i3−2i32i3−2i322-20002-2−2i32i3000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ798-88-800008000000008-8-80000000000000000000000000000000000000000000000000000000000000
χ808-88-80000-40000−4i34i34i3−4i3-4440000000000000000000000000000000000000000000000000000000000000
χ818-88-80000-400004i3−4i3−4i34i3-4440000000000000000000000000000000000000000000000000000000000000

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