Finite Group Databasebeta

← Group #10858839

Character table — Group #10858839

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222222234444444466666662244441212121212121212444444661212121212121212121212121212121244448888888844121212124444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-11-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111111111-111-111-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111-111-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ911111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-111
χ1111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111111-1-1-11111-1-1-1-1-1-111
χ1211111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-1111111-1-1
χ1311111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-1-1-11-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-1-1-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1111-1-1-1-1-1-11111-1-1
χ1611111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-11111-1-1-1-111
χ17222222222-2-22222-2-22222222-2-22222-2-2-2-2222200-200-2-2-22222-2-20000-2-200000000000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222002002-2-2-2-2-2-22200002200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-200-200222-2-222220000-2-200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-200200-22222-2-2-2-200002200000000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-22-2-22-1-1-1-1-1-1-1-11111-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-222-2-1-1111111-1-1-1-111-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111222-2-2-21111-1-111-1-1-1-1-1-11111000000000000-22-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-2-2222-21111-1-1111111-1-1-1-1-1-10000000000002-211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111122-2-2-2211-1-111-1-1-1-1-1-11111110000000000002-211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2-222211-1-111-1-1111111-1-1-1-1000000000000-22-1-1110000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-200-211-1-1-1-111−i3−i3i3i311−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-200-211-1-1-1-111i3i3−i3−i311i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002002111111-1-1−i3−i3i3i3-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002002111111-1-1i3i3−i3−i3-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2002-1-111-1-1-1-1−i3−i3i3i311i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2002-1-111-1-1-1-1i3i3−i3−i311−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2221111111100200-2-1-1-1-11111−i3−i3i3i3-1-1i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-2221111111100200-2-1-1-1-11111i3i3−i3−i3-1-1−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ3722-2-22-22-222222-2-2-2-222-22-2-2-22-2000022-2-222-2-20000002-200000000000000000000000000000000002-2002-20000
χ3822-2-22-22-222222-2-2-2-222-22-2-2-22-2000022-2-222-2-20000002-20000000000000000000000000000000000-2200-220000
χ3922-2-22-22-2222-2-222-2-222-22-2-2-2-22000022-2-2-2-222000000-2200000000000000000000000000000000002-200-220000
χ4022-2-22-22-2222-2-222-2-222-22-2-2-2-22000022-2-2-2-222000000-220000000000000000000000000000000000-22002-20000
χ4122-2-22-22-22-2-222-2-22222-22-2-2-2-220000-2-22222-2-2000000-2200000000000000002i2i−2i−2i00000000000000002i−2i000000
χ4222-2-22-22-22-2-222-2-22222-22-2-2-2-220000-2-22222-2-2000000-220000000000000000−2i−2i2i2i0000000000000000−2i2i000000
χ4322-2-22-22-22-2-2-2-2222222-22-2-2-22-20000-2-222-2-2220000002-200000000000000002i2i−2i−2i0000000000000000−2i2i000000
χ4422-2-22-22-22-2-2-2-2222222-22-2-2-22-20000-2-222-2-2220000002-20000000000000000−2i−2i2i2i00000000000000002i−2i000000
χ452-222-2-22-222-200002-2-2-2-222-220000002-22-200000002-20000000000000002-22-22i−2i2i−2i00002i2i−2i−2i0000000000000000
χ462-222-2-22-222-200002-2-2-2-222-220000002-22-200000002-20000000000000002-22-2−2i2i−2i2i0000−2i−2i2i2i0000000000000000
χ472-222-2-22-222-200002-2-2-2-222-220000002-22-20000000-22000000000000000-22-222i−2i2i−2i0000−2i−2i2i2i0000000000000000
χ482-222-2-22-222-200002-2-2-2-222-220000002-22-20000000-22000000000000000-22-22−2i2i−2i2i00002i2i−2i−2i0000000000000000
χ492-22-22-2-222002i−2i2i−2i002-2-2-222-2002-22i−2i00002i−2i2i−2i000000002i−2i2-2000000000000000022−2−2−i2i2−i2i20000000000002−2−i2i2
χ502-22-22-2-222002i−2i2i−2i002-2-2-222-2002-22i−2i00002i−2i2i−2i000000002i−2i2-20000000000000000−2−222i2−i2i2−i2000000000000−22i2−i2
χ512-22-22-2-222002i−2i2i−2i002-2-2-222-200-22−2i2i00002i−2i2i−2i00000000−2i2i-22000000000000000022−2−2−i2i2−i2i2000000000000−22i2−i2
χ522-22-22-2-222002i−2i2i−2i002-2-2-222-200-22−2i2i00002i−2i2i−2i00000000−2i2i-220000000000000000−2−222i2−i2i2−i20000000000002−2−i2i2
χ532-22-22-2-22200−2i2i−2i2i002-2-2-222-2002-2−2i2i0000−2i2i−2i2i00000000−2i2i2-2000000000000000022−2−2i2−i2i2−i20000000000002−2i2−i2
χ542-22-22-2-22200−2i2i−2i2i002-2-2-222-2002-2−2i2i0000−2i2i−2i2i00000000−2i2i2-20000000000000000−2−222−i2i2−i2i2000000000000−22−i2i2
χ552-22-22-2-22200−2i2i−2i2i002-2-2-222-200-222i−2i0000−2i2i−2i2i000000002i−2i-22000000000000000022−2−2i2−i2i2−i2000000000000−22−i2i2
χ562-22-22-2-22200−2i2i−2i2i002-2-2-222-200-222i−2i0000−2i2i−2i2i000000002i−2i-220000000000000000−2−222−i2i2−i2i20000000000002−2i2−i2
χ572-2-2-2-22222-2200002-2-2-222-22-2000000-222-200002i−2i0000000000002i−2i2i−2i0000002-2-222i−2i2i−2i00000000000000000000
χ582-2-2-2-22222-2200002-2-2-222-22-2000000-222-200002i−2i0000000000002i−2i2i−2i000000-222-2−2i2i−2i2i00000000000000000000
χ592-2-2-2-22222-2200002-2-2-222-22-2000000-222-20000−2i2i000000000000−2i2i−2i2i0000002-2-22−2i2i−2i2i00000000000000000000
χ602-2-2-2-22222-2200002-2-2-222-22-2000000-222-20000−2i2i000000000000−2i2i−2i2i000000-222-22i−2i2i−2i00000000000000000000
χ61444-4-44-4-4400000000-444-44-4-4000000000000000000000000000000000000000000000022−22−22220000000000000000
χ62444-4-44-4-4400000000-444-44-4-40000000000000000000000000000000000000000000000−222222−220000000000000000
χ6344-44-4-4-44400000000-44-4-4-444000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6444-44-4-4-44400000000-44-4-4-4440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6544-4-44-44-4-24444-4-4-4-4-2-22-22224-40000-2-222-2-222000000-2200000000000000000000000000000000000000000000
χ6644-4-44-44-4-244-4-444-4-4-2-22-2222-440000-2-22222-2-20000002-200000000000000000000000000000000000000000000
χ6744-4-44-44-4-2-4-444-4-444-2-22-2222-44000022-2-2-2-2220000002-200000000000000000000000000000000000000000000
χ6844-4-44-44-4-2-4-4-4-44444-2-22-22224-4000022-2-222-2-2000000-2200000000000000000000000000000000000000000000
χ694-444-4-44-44-440000-44-4-4-444-44000000-44-4400000000000000000000000000000000000000000000000000000000
χ704-444-4-44-4-24-400004-4222-2-22-2000000-22-2200000004-4000000000000000-22-220000000000000000000000000000
χ714-444-4-44-4-24-400004-4222-2-22-2000000-22-220000000-440000000000000002-22-20000000000000000000000000000
χ724-444-4-44-4-2-440000-44222-2-22-20000002-22-2000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ734-444-4-44-4-2-440000-44222-2-22-20000002-22-20000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ744-44-44-4-44-2004i−4i4i−4i00-2222-2-22004-44i−4i0000−2i2i−2i2i00000000−2i2i-220000000000000000000000000000000000000000
χ754-44-44-4-44-2004i−4i4i−4i00-2222-2-2200-44−4i4i0000−2i2i−2i2i000000002i−2i2-20000000000000000000000000000000000000000
χ764-44-44-4-44-200−4i4i−4i4i00-2222-2-22004-4−4i4i00002i−2i2i−2i000000002i−2i-220000000000000000000000000000000000000000
χ774-44-44-4-44-200−4i4i−4i4i00-2222-2-2200-444i−4i00002i−2i2i−2i00000000−2i2i2-20000000000000000000000000000000000000000
χ784-4-4444-4-44004i−4i−4i4i004-44-4-4-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ794-4-4444-4-4400−4i4i4i−4i004-44-4-4-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-2004i−4i−4i4i00-22-2222-20000000000−2i2i2i−2i00000000000023−230000−2i32i300000000000000000000000000000000
χ814-4-4444-4-4-2004i−4i−4i4i00-22-2222-20000000000−2i2i2i−2i000000000000−232300002i3−2i300000000000000000000000000000000
χ824-4-4444-4-4-200−4i4i4i−4i00-22-2222-200000000002i−2i−2i2i00000000000023−2300002i3−2i300000000000000000000000000000000
χ834-4-4444-4-4-200−4i4i4i−4i00-22-2222-200000000002i−2i−2i2i000000000000−23230000−2i32i300000000000000000000000000000000
χ844-4-4-4-444444-40000-44-4-444-44-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-24-40000-4422-2-22-22000000-222-200000000000000000023−23−23230000000000000000000000000000000000
χ864-4-4-4-4444-24-40000-4422-2-22-22000000-222-2000000000000000000−232323−230000000000000000000000000000000000
χ874-4-4-4-4444-2-4400004-422-2-22-220000002-2-2200004i−4i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ884-4-4-4-4444-2-4400004-422-2-22-220000002-2-220000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ89888-8-88-8-8-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-8-88-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000

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