Finite Group Databasebeta

← Group #10853321

Character table — Group #10853321

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
χ311111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ911111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-111111-111-1-1-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-111
χ1111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-111-1-111-1-1-1-111
χ1211111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-11111-1-11111-1-1
χ1311111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-11-1-111-1-1-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-11-1-1111111-1-111-1-1
χ1511111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-11-111-1-1-1-1-1-11111-1-1
χ1611111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-111-1-11111-1-1-1-111
χ17222222222-2-22222-2-22222222-2-22222-2-2-2-2222200-2-200-2-2000022220000-2-2-2-20000000000000000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-22222002200-2-20000-2-2-2-2000022220000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-200-220022000022-2-20000-2-2220000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2002-200220000-2-222000022-2-20000000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-222-2-2-1-11111-1-1-1-11111-1-1-1-1000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-222-1-1-1-1-1-11111-1-1-1-11111000000000000-2-211110000000000
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
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111222-2-2-2111111-1-111-1-1-1-1-1-1110000000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-2-22-22211-1-1-1-1-1-1111111-1-111000000000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1111122-22-2-211111111-1-1-1-1-1-111-1-1000000000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-11111-2-2-222211-1-1-1-111-1-1111111-1-10000000000002-2-1-1110000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-2-20011−i3−i3i3i3-1-1-1-1−i3−i3i3i3111100000000000000−i3i3−i3i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-222221111-1-1-1-100-2-20011i3i3−i3−i3-1-1-1-1i3i3−i3−i3111100000000000000i3−i3i3−i30000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-100220011−i3−i3i3i31111−i3−i3i3i3-1-1-1-100000000000000i3−i3i3−i30000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-100220011i3i3−i3−i31111i3i3−i3−i3-1-1-1-100000000000000−i3i3−i3i30000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200-1-1−i3−i3i3i3-1-111i3i3−i3−i311-1-100000000000000i3−i3−i3i30000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12222-2-21111111100-2200-1-1i3i3−i3−i3-1-111−i3−i3i3i311-1-100000000000000−i3i3i3−i30000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111002-200-1-1−i3−i3i3i311-1-1i3i3−i3−i3-1-11100000000000000−i3i3i3−i30000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-22211111111002-200-1-1i3i3−i3−i311-1-1−i3−i3i3i3-1-11100000000000000i3−i3−i3i30000000000
χ37222-2-2-2-2222-20000-2222-2-22-2-200000022-2-2000000002-2002-22-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ38222-2-2-2-2222-20000-2222-2-22-2-200000022-2-2000000002-2002-22-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ39222-2-2-2-2222-20000-2222-2-22-2-200000022-2-200000000-2200-22-220000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ40222-2-2-2-2222-20000-2222-2-22-2-200000022-2-200000000-2200-22-22000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4122-2-2-222-220022-2-2002-22-2-2-22002i−2i2i−2i000022-2-20000000000002i−2i2i−2i000000000000−i2i2−i2i2−i2−i2i2i20000000000002−22−2
χ4222-2-2-222-220022-2-2002-22-2-2-22002i−2i2i−2i000022-2-20000000000002i−2i2i−2i000000000000i2−i2i2−i2i2i2−i2−i2000000000000−22−22
χ4322-2-2-222-220022-2-2002-22-2-2-2200−2i2i−2i2i000022-2-2000000000000−2i2i−2i2i000000000000−i2i2−i2i2−i2−i2i2i2000000000000−22−22
χ4422-2-2-222-220022-2-2002-22-2-2-2200−2i2i−2i2i000022-2-2000000000000−2i2i−2i2i000000000000i2−i2i2−i2i2i2−i2−i20000000000002−22−2
χ4522-2-2-222-2200-2-222002-22-2-2-22002i−2i−2i2i0000-2-2220000000000002i−2i−2i2i000000000000−i2i2−i2i2i2i2−i2−i2000000000000−222−2
χ4622-2-2-222-2200-2-222002-22-2-2-22002i−2i−2i2i0000-2-2220000000000002i−2i−2i2i000000000000i2−i2i2−i2−i2−i2i2i20000000000002−2−22
χ4722-2-2-222-2200-2-222002-22-2-2-2200−2i2i2i−2i0000-2-222000000000000−2i2i2i−2i000000000000−i2i2−i2i2i2i2−i2−i20000000000002−2−22
χ4822-2-2-222-2200-2-222002-22-2-2-2200−2i2i2i−2i0000-2-222000000000000−2i2i2i−2i000000000000i2−i2i2−i2−i2−i2i2i2000000000000−222−2
χ492-222-2-22-22222-22-2-2-2-2222-2-2-22-200002-22-22-22-20000002-200000000000000002-22-2000000000000002-200000000
χ502-222-2-22-22222-22-2-2-2-2222-2-2-22-200002-22-22-22-20000002-20000000000000000-22-2200000000000000-2200000000
χ512-222-2-22-2222-22-22-2-2-2222-2-2-2-2200002-22-2-22-22000000-2200000000000000002-22-200000000000000-2200000000
χ522-222-2-22-2222-22-22-2-2-2222-2-2-2-2200002-22-2-22-22000000-220000000000000000-22-22000000000000002-200000000
χ532-222-2-22-22-2-22-22-222-2222-2-2-2-220000-22-222-22-2000000-220000000000000000000000000000000000002i−2i2i−2i0000
χ542-222-2-22-22-2-22-22-222-2222-2-2-2-220000-22-222-22-2000000-22000000000000000000000000000000000000−2i2i−2i2i0000
χ552-222-2-22-22-2-2-22-2222-2222-2-2-22-20000-22-22-22-220000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ562-222-2-22-22-2-2-22-2222-2222-2-2-22-20000-22-22-22-220000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ572-22-222-2-222-200002-2-22-2-2-2220000002-2-2200002-2000000000000002-22-200002i−2i−2i2i00002i−2i2i−2i0000000000000000
χ582-22-222-2-222-200002-2-22-2-2-2220000002-2-2200002-2000000000000002-22-20000−2i2i2i−2i0000−2i2i−2i2i0000000000000000
χ592-22-222-2-222-200002-2-22-2-2-2220000002-2-220000-2200000000000000-22-2200002i−2i−2i2i0000−2i2i−2i2i0000000000000000
χ602-22-222-2-222-200002-2-22-2-2-2220000002-2-220000-2200000000000000-22-220000−2i2i2i−2i00002i−2i2i−2i0000000000000000
χ61444-4-4-4-444-4400004-444-4-44-4-4000000-4-44400000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-24-40000-44-2-222-222000000-2-222000000004-400-22-220000000000000000000000000000000000000000
χ63444-4-4-4-44-24-40000-44-2-222-222000000-2-22200000000-44002-22-20000000000000000000000000000000000000000
χ64444-4-4-4-44-2-4400004-4-2-222-22200000022-2-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ65444-4-4-4-44-2-4400004-4-2-222-22200000022-2-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ6644-444-4-4-44000000004-4-44-44-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ6744-444-4-4-44000000004-4-44-44-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ6844-4-4-444-4-20044-4-400-22-2222-2004i−4i4i−4i0000-2-222000000000000−2i2i−2i2i000000000000000000000000000000000000
χ6944-4-4-444-4-20044-4-400-22-2222-200−4i4i−4i4i0000-2-2220000000000002i−2i2i−2i000000000000000000000000000000000000
χ7044-4-4-444-4-200-4-44400-22-2222-2004i−4i−4i4i000022-2-2000000000000−2i2i2i−2i000000000000000000000000000000000000
χ7144-4-4-444-4-200-4-44400-22-2222-200−4i4i4i−4i000022-2-20000000000002i−2i−2i2i000000000000000000000000000000000000
χ724-444-4-44-4-2444-44-4-4-42-2-2-22224-40000-22-22-22-22000000-2200000000000000000000000000000000000000000000
χ734-444-4-44-4-244-44-44-4-42-2-2-2222-440000-22-222-22-20000002-200000000000000000000000000000000000000000000
χ744-444-4-44-4-2-4-44-44-4442-2-2-2222-4400002-22-2-22-220000002-200000000000000000000000000000000000000000000
χ754-444-4-44-4-2-4-4-44-44442-2-2-22224-400002-22-22-22-2000000-2200000000000000000000000000000000000000000000
χ764-44-444-4-44-440000-44-44-4-4-444000000-444-400000000000000000000000000000000000000000000000000000000
χ774-44-444-4-4-24-400004-42-2222-2-2000000-222-200004-400000000000000-22-2200000000000000000000000000000000
χ784-44-444-4-4-24-400004-42-2222-2-2000000-222-20000-44000000000000002-22-200000000000000000000000000000000
χ794-44-444-4-4-2-440000-442-2222-2-20000002-2-2200000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ804-44-444-4-4-2-440000-442-2222-2-20000002-2-22000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ814-4-44-44-44400000000-4-4-444-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ824-4-44-44-44400000000-4-4-444-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ834-4-4-44-4444004-4-4400-4-44-444-400000000004-4-440000000000000000000000000000000000000000000000000000
χ844-4-4-44-444400-444-400-4-44-444-40000000000-444-40000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-2004-4-440022-22-2-220000000000-222-20000000000000000000023−2323−230000000000000000000000000000
χ864-4-4-44-444-2004-4-440022-22-2-220000000000-222-200000000000000000000−2323−23230000000000000000000000000000
χ874-4-4-44-444-200-444-40022-22-2-2200000000002-2-220000000000000000000023−23−23230000000000000000000000000000
χ884-4-4-44-444-200-444-40022-22-2-2200000000002-2-2200000000000000000000−232323−230000000000000000000000000000
χ8988-888-8-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000

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