Finite Group Databasebeta

← Group #10868020

Character table — Group #10868020

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222222234444444466666664444441212121212121212244444661212121212121212121212121212121244448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-111-1-1-1-11111-1-1
χ10111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1111111-1-1-1-111
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-111-1-111
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11111-1-111-1-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111-111-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-111-1-111-1-1-1-1-1-111
χ14111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1111111-1-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-1-1-111-1-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1-1-111111-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-11111-1-111
χ172222222222222-2-2-2-222222222222-2-22222-2-2-2-2-2-20000-2-222220000-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-222000022-2-2-2-20000-2-22200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-22-200002222-2-2000022-2-200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2-220000-2-2-2-2220000222200000000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-11111-1-1-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22222111111-1-1-1-1-1-111-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111111-1-111111100000000000022-1-1-1-10000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-2-2000011-1-1-1-1−i3−i3i3i31111−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-2-1-1-1-11111-2-2000011-1-1-1-1i3i3−i3−i31111i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111220000-1-11111−i3−i3i3i311-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-11111220000-1-11111i3i3−i3−i311-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1-2222-2-211-1-111111111-1-1-1-1-1-1000000000000-2211-1-10000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-21111-1-1-1-1-22-2-22211-1-111-1-1-1-111-1-111110000000000002-2-1-1110000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-12-222-2-2-1-111-1-111111111-1-1-1-10000000000002-2-1-1110000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-12-2-2-222-1-111-1-1-1-1-1-111111111000000000000-2211-1-10000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222111111112-20000-1-1-1-111−i3−i3i3i3-1-111i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222111111112-20000-1-1-1-111i3i3−i3−i3-1-111−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-2200001111-1-1−i3−i3i3i3-1-1-1-1i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2222211111111-2200001111-1-1i3i3−i3−i3-1-1-1-1−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3722-22-22-2-220000-22-222-22-2-22-2000000000022-2-200002i−2i0000002i−2i2i−2i000000002i2i−2i−2i000022-2-20000000000000000
χ3822-22-22-2-220000-22-222-22-2-22-2000000000022-2-200002i−2i0000002i−2i2i−2i00000000−2i−2i2i2i0000-2-2220000000000000000
χ3922-22-22-2-220000-22-222-22-2-22-2000000000022-2-20000−2i2i000000−2i2i−2i2i000000002i2i−2i−2i0000-2-2220000000000000000
χ4022-22-22-2-220000-22-222-22-2-22-2000000000022-2-20000−2i2i000000−2i2i−2i2i00000000−2i−2i2i2i000022-2-20000000000000000
χ412-22-2-222-222i2i−2i−2i2-2-22-2-2222-2-200002i−2i2i2i−2i−2i2-22-200000000000000002i−2i0000000000000000000000002i−2i002-20000
χ422-22-2-222-222i2i−2i−2i2-2-22-2-2222-2-200002i−2i2i2i−2i−2i2-22-200000000000000002i−2i000000000000000000000000−2i2i00-220000
χ432-22-2-222-222i2i−2i−2i-222-2-2-2222-2-20000−2i2i2i2i−2i−2i-22-220000000000000000−2i2i0000002i−2i2i−2i00000000000000002-2000000
χ442-22-2-222-222i2i−2i−2i-222-2-2-2222-2-20000−2i2i2i2i−2i−2i-22-220000000000000000−2i2i000000−2i2i−2i2i0000000000000000-22000000
χ452-22-2-222-22−2i−2i2i2i2-2-22-2-2222-2-20000−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i0000000000000000000000002i−2i00-220000
χ462-22-2-222-22−2i−2i2i2i2-2-22-2-2222-2-20000−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i000000000000000000000000−2i2i002-20000
χ472-22-2-222-22−2i−2i2i2i-222-2-2-2222-2-200002i−2i−2i−2i2i2i-22-2200000000000000002i−2i0000002i−2i2i−2i0000000000000000-22000000
χ482-22-2-222-22−2i−2i2i2i-222-2-2-2222-2-200002i−2i−2i−2i2i2i-22-2200000000000000002i−2i000000−2i2i−2i2i00000000000000002-2000000
χ492-2-222-22-222-22-20000-22-22-22-22i−2i2i−2i002-22-20000000000002i−2i2i−2i0000000000000000−i2−i2i2i2−i2i2−i2i20000000000002−22−2
χ502-2-222-22-222-22-20000-22-22-22-22i−2i2i−2i002-22-20000000000002i−2i2i−2i0000000000000000i2i2−i2−i2i2−i2i2−i2000000000000−22−22
χ512-2-222-22-222-22-20000-22-22-22-2−2i2i−2i2i002-22-2000000000000−2i2i−2i2i0000000000000000−i2−i2i2i2−i2i2−i2i2000000000000−22−22
χ522-2-222-22-222-22-20000-22-22-22-2−2i2i−2i2i002-22-2000000000000−2i2i−2i2i0000000000000000i2i2−i2−i2i2−i2i2−i20000000000002−22−2
χ532-2-222-22-22-22-220000-22-22-22-22i−2i−2i2i00-22-220000000000002i−2i−2i2i0000000000000000−i2−i2i2i2i2−i2i2−i20000000000002−2−22
χ542-2-222-22-22-22-220000-22-22-22-22i−2i−2i2i00-22-220000000000002i−2i−2i2i0000000000000000i2i2−i2−i2−i2i2−i2i2000000000000−222−2
χ552-2-222-22-22-22-220000-22-22-22-2−2i2i2i−2i00-22-22000000000000−2i2i2i−2i0000000000000000−i2−i2i2i2i2−i2i2−i2000000000000−222−2
χ562-2-222-22-22-22-220000-22-22-22-2−2i2i2i−2i00-22-22000000000000−2i2i2i−2i0000000000000000i2i2−i2−i2−i2i2−i2i20000000000002−2−22
χ572-2-2-222-222000022-2-2-222-2-2-220000000000-222-2002i−2i00000000000000002i−2i2i−2i2-2-222i−2i2i−2i00000000000000000000
χ582-2-2-222-222000022-2-2-222-2-2-220000000000-222-2002i−2i00000000000000002i−2i2i−2i-222-2−2i2i−2i2i00000000000000000000
χ592-2-2-222-222000022-2-2-222-2-2-220000000000-222-200−2i2i0000000000000000−2i2i−2i2i2-2-22−2i2i−2i2i00000000000000000000
χ602-2-2-222-222000022-2-2-222-2-2-220000000000-222-200−2i2i0000000000000000−2i2i−2i2i-222-22i−2i2i−2i00000000000000000000
χ61444-44-4-4-440000000044-4-44-4-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ62444-44-4-4-440000000044-4-44-4-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ6344-44-44-4-4400004-44-44-44-4-44-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ6444-44-44-4-4-200004-44-4-22-222-22000000000022-2-200000000000023−23−2323000000000000000000000000000000000000
χ6544-44-44-4-4-200004-44-4-22-222-22000000000022-2-2000000000000−232323−23000000000000000000000000000000000000
χ6644-44-44-4-4-20000-44-44-22-222-220000000000-2-22200004i−4i000000−2i2i−2i2i000000000000000000000000000000000000
χ6744-44-44-4-4-20000-44-44-22-222-220000000000-2-2220000−4i4i0000002i−2i2i−2i000000000000000000000000000000000000
χ6844-4-4-4-44444i−4i−4i4i00004-4-44-4-440000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6944-4-4-4-4444−4i4i4i−4i00004-4-44-4-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7044-4-4-4-444-24i−4i−4i4i0000-222-222-2000000−2i2i2i−2i0000000000−2i32i3000000000023−2300000000000000000000000000000000
χ7144-4-4-4-444-24i−4i−4i4i0000-222-222-2000000−2i2i2i−2i00000000002i3−2i30000000000−232300000000000000000000000000000000
χ7244-4-4-4-444-2−4i4i4i−4i0000-222-222-20000002i−2i−2i2i0000000000−2i32i30000000000−232300000000000000000000000000000000
χ7344-4-4-4-444-2−4i4i4i−4i0000-222-222-20000002i−2i−2i2i00000000002i3−2i3000000000023−2300000000000000000000000000000000
χ744-444-4-4-44400000000-4-4-4-44440000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ754-444-4-4-44400000000-4-4-4-444400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ764-44-4-444-4-24i4i−4i−4i4-4-4422-2-2-22200004i−4i−2i−2i2i2i-22-220000000000000000−2i2i0000000000000000000000000000000000
χ774-44-4-444-4-24i4i−4i−4i-444-422-2-2-2220000−4i4i−2i−2i2i2i2-22-200000000000000002i−2i0000000000000000000000000000000000
χ784-44-4-444-4-2−4i−4i4i4i4-4-4422-2-2-2220000−4i4i2i2i−2i−2i-22-2200000000000000002i−2i0000000000000000000000000000000000
χ794-44-4-444-4-2−4i−4i4i4i-444-422-2-2-22200004i−4i2i2i−2i−2i2-22-20000000000000000−2i2i0000000000000000000000000000000000
χ804-4-444-44-4-24-44-400002-22-22-224i−4i4i−4i00-22-22000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ814-4-444-44-4-24-44-400002-22-22-22−4i4i−4i4i00-22-220000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ824-4-444-44-4-2-44-4400002-22-22-224i−4i−4i4i002-22-2000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ834-4-444-44-4-2-44-4400002-22-22-22−4i4i4i−4i002-22-20000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ844-4-4-444-4440000-4-444-444-4-4-4400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-2000044-4-42-2-2222-200000000002-2-22004i−4i0000000000000000−2i2i−2i2i0000000000000000000000000000
χ864-4-4-444-44-2000044-4-42-2-2222-200000000002-2-2200−4i4i00000000000000002i−2i2i−2i0000000000000000000000000000
χ874-4-4-444-44-20000-4-4442-2-2222-20000000000-222-20000000000000000000023−23−23230000000000000000000000000000
χ884-4-4-444-44-20000-4-4442-2-2222-20000000000-222-200000000000000000000−232323−230000000000000000000000000000
χ89888-88-8-8-8-400000000-4-444-444000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-8-88-4000000004444-4-4-4000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).