Finite Group Databasebeta

← Group #10853310

Character table — Group #10853310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244444412121212121212121212121212121212121244448888888844121212122244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ911111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11-111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111
χ1111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-11-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-11-1-111-1-111-1-1-1-111
χ1211111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-11-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-11111-1-11111-1-1
χ1311111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1111111-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111111-111-1-1-1-1-1-11111-1-1
χ1611111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-111
χ17222222222-2-22222-2-22222222-2-22222-2-2-2-2222200-2-200-2-222220000-2-2-2-200000000000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222002200-2-2-2-2-2-20000222200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-200-22002222-2-20000-2-22200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2002-20022-2-222000022-2-200000000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1-1-11111-1-1-1-11111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-222-1-11111-1-1-1-11111-1-1-1-1000000000000-2-211110000000000
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
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111222-2-2-211-1-111-1-1-1-1-1-11111110000000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-2-22-22211-1-1111111-1-111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111122-22-2-21111-1-1-1-1-1-111-1-11111000000000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2-22221111-1-1111111-1-1-1-1-1-10000000000002-2-1-1110000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-2-20011-1-1-1-1−i3−i3i3i31111−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-2-20011-1-1-1-1i3i3−i3−i31111i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002200111111−i3−i3i3i3-1-1-1-1−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1002200111111i3i3−i3−i3-1-1-1-1i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200-1-1-1-111−i3−i3i3i311-1-1i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200-1-1-1-111i3i3−i3−i311-1-1−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111002-200-1-111-1-1−i3−i3i3i3-1-111i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111002-200-1-111-1-1i3i3−i3−i3-1-111−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ37222-2-22-2-222222-2-2-2-2-2222-2-2-22-2000022-2-222-2-20000002-2000000000000000022-2-2000000000000002-200000000
χ38222-2-22-2-222222-2-2-2-2-2222-2-2-22-2000022-2-222-2-20000002-20000000000000000-2-22200000000000000-2200000000
χ39222-2-22-2-2222-2-222-2-2-2222-2-2-2-22000022-2-2-2-222000000-22000000000000000022-2-200000000000000-2200000000
χ40222-2-22-2-2222-2-222-2-2-2222-2-2-2-22000022-2-2-2-222000000-220000000000000000-2-222000000000000002-200000000
χ41222-2-22-2-22-2-222-2-222-2222-2-2-2-220000-2-22222-2-2000000-220000000000000000000000000000000000002i−2i2i−2i0000
χ42222-2-22-2-22-2-222-2-222-2222-2-2-2-220000-2-22222-2-2000000-22000000000000000000000000000000000000−2i2i−2i2i0000
χ43222-2-22-2-22-2-2-2-22222-2222-2-2-22-20000-2-222-2-2220000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ44222-2-22-2-22-2-2-2-22222-2222-2-2-22-20000-2-222-2-2220000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ4522-22-2-22-222-200002-2-22-2-22-220000002-22-2000000002-2000000000000002-22-22i−2i2i−2i00002i2i−2i−2i0000000000000000
χ4622-22-2-22-222-200002-2-22-2-22-220000002-22-2000000002-2000000000000002-22-2−2i2i−2i2i0000−2i−2i2i2i0000000000000000
χ4722-22-2-22-222-200002-2-22-2-22-220000002-22-200000000-2200000000000000-22-222i−2i2i−2i0000−2i−2i2i2i0000000000000000
χ4822-22-2-22-222-200002-2-22-2-22-220000002-22-200000000-2200000000000000-22-22−2i2i−2i2i00002i2i−2i−2i0000000000000000
χ4922-2-22-2-2222-20000-2222-2-2-22-20000002-2-2200002-200000000002-22-2000000002i−2i−2i2i2i2i−2i−2i00000000000000000000
χ5022-2-22-2-2222-20000-2222-2-2-22-20000002-2-2200002-200000000002-22-200000000−2i2i2i−2i−2i−2i2i2i00000000000000000000
χ5122-2-22-2-2222-20000-2222-2-2-22-20000002-2-220000-220000000000-22-22000000002i−2i−2i2i−2i−2i2i2i00000000000000000000
χ5222-2-22-2-2222-20000-2222-2-2-22-20000002-2-220000-220000000000-22-2200000000−2i2i2i−2i2i2i−2i−2i00000000000000000000
χ532-2-22-22-222002-22-2002-22-22-2-2002-22-200002-22-2000000002-22-20000000000000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2
χ542-2-22-22-222002-22-2002-22-22-2-2002-22-200002-22-2000000002-22-20000000000000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2
χ552-2-22-22-222002-22-2002-22-22-2-200-22-2200002-22-200000000-22-220000000000000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2
χ562-2-22-22-222002-22-2002-22-22-2-200-22-2200002-22-200000000-22-220000000000000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2
χ572-2-22-22-22200-22-22002-22-22-2-2002-2-220000-22-22000000002-2-220000000000000000−i2i2−i2i2i2−i2i2−i2000000000000−i2i2i2−i2
χ582-2-22-22-22200-22-22002-22-22-2-2002-2-220000-22-22000000002-2-220000000000000000i2−i2i2−i2−i2i2−i2i2000000000000i2−i2−i2i2
χ592-2-22-22-22200-22-22002-22-22-2-200-222-20000-22-2200000000-222-20000000000000000−i2i2−i2i2i2−i2i2−i2000000000000i2−i2−i2i2
χ602-2-22-22-22200-22-22002-22-22-2-200-222-20000-22-2200000000-222-20000000000000000i2−i2i2−i2−i2i2−i2i2000000000000−i2i2i2−i2
χ61444-4-44-4-4-24444-4-4-4-42-2-2-22224-40000-2-222-2-222000000-2200000000000000000000000000000000000000000000
χ62444-4-44-4-4-244-4-444-4-42-2-2-2222-440000-2-22222-2-20000002-200000000000000000000000000000000000000000000
χ63444-4-44-4-4-2-4-444-4-4442-2-2-2222-44000022-2-2-2-2220000002-200000000000000000000000000000000000000000000
χ64444-4-44-4-4-2-4-4-4-444442-2-2-22224-4000022-2-222-2-2000000-2200000000000000000000000000000000000000000000
χ6544-44-4-44-44-440000-44-44-4-44-44000000-44-4400000000000000000000000000000000000000000000000000000000
χ6644-44-4-44-4-24-400004-42-222-22-2000000-22-22000000004-400000000000000-22-220000000000000000000000000000
χ6744-44-4-44-4-24-400004-42-222-22-2000000-22-2200000000-44000000000000002-22-20000000000000000000000000000
χ6844-44-4-44-4-2-440000-442-222-22-20000002-22-2000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ6944-44-4-44-4-2-440000-442-222-22-20000002-22-20000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ7044-4-44-4-444-4400004-444-4-4-44-4000000-444-400000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-44-24-40000-44-2-2222-22000000-222-200004-40000000000-22-22000000000000000000000000000000000000
χ7244-4-44-4-44-24-40000-44-2-2222-22000000-222-20000-4400000000002-22-2000000000000000000000000000000000000
χ7344-4-44-4-44-2-4400004-4-2-2222-220000002-2-220000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ7444-4-44-4-44-2-4400004-4-2-2222-220000002-2-2200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ754-4444-4-4-4400000000-4-4-4444-4000000000000000000000000000000000000000000000022−22−22220000000000000000
χ764-4444-4-4-4400000000-4-4-4444-40000000000000000000000000000000000000000000000−222222−220000000000000000
χ774-44-4-4-4444000000004-4-44-4-4400000000000000000000000000000000000000000022−22−222200000000000000000000
χ784-44-4-4-4444000000004-4-44-4-44000000000000000000000000000000000000000000−222222−2200000000000000000000
χ794-4-44-44-44-2004-44-400-22-22-222004-44-40000-22-2200000000-22-220000000000000000000000000000000000000000
χ804-4-44-44-44-2004-44-400-22-22-22200-44-440000-22-22000000002-22-20000000000000000000000000000000000000000
χ814-4-44-44-44-200-44-4400-22-22-222004-4-4400002-22-200000000-222-20000000000000000000000000000000000000000
χ824-4-44-44-44-200-44-4400-22-22-22200-444-400002-22-2000000002-2-220000000000000000000000000000000000000000
χ834-4-4-4444-44004-4-4400-4-44-4-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ844-4-4-4444-4400-444-400-4-44-4-4440000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4-4444-4-2004-4-440022-222-2-20000000000-222-20000000000000000−2i32i3−2i32i300000000000000000000000000000000
χ864-4-4-4444-4-2004-4-440022-222-2-20000000000-222-200000000000000002i3−2i32i3−2i300000000000000000000000000000000
χ874-4-4-4444-4-200-444-40022-222-2-200000000002-2-220000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ884-4-4-4444-4-200-444-40022-222-2-200000000002-2-2200000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ898-8888-8-8-8-400000000444-4-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000

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