Finite Group Databasebeta

← Group #102839

Character table — Group #102839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222222244444444444444888888888888888888888888222244444444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ9222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ10222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ11222222222222-2-2-2-2-2-222-2-222-2-200000000000000002222-2-2-2-2000000000000
χ12222222222222-2-2-2-2-2-222-2-222-2-20000000000000000-2-2-2-22222000000000000
χ13222222222222-2-2-2-2-2-2-2-222-2-222000000002222-2-2-2-200000000000000000000
χ14222222222222-2-2-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000000000000000
χ1522222222-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000020-20
χ1622222222-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000-2020
χ1722222222-2-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000020-2
χ1822222222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000-202
χ1922222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000002i2i−2i−2i0000
χ2022222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000−2i−2i2i2i0000
χ2122222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000022-2-200000000
χ2222222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-2-22200000000
χ232222-2-2-2-22-2-222-22-22-200000000000022-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ242222-2-2-2-22-2-222-22-22-200000000000022-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ252222-2-2-2-22-2-222-22-22-2000000000000-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ262222-2-2-2-22-2-222-22-22-2000000000000-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ272222-2-2-2-22-2-22-22-22-220000000022-2-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ282222-2-2-2-22-2-22-22-22-220000000022-2-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ292222-2-2-2-22-2-22-22-22-2200000000-2-2220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ302222-2-2-2-22-2-22-22-22-2200000000-2-2220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3122-2-22-22-222-2-2000000002-2002-2i2−i2i2−i2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i2000000000000
χ3222-2-22-22-222-2-2000000002-2002-2i2−i2i2−i2i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i2000000000000
χ3322-2-22-22-222-2-2000000002-2002-2−i2i2−i2i2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i2000000000000
χ3422-2-22-22-222-2-2000000002-2002-2−i2i2−i2i2−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i2000000000000
χ3522-2-22-22-222-2-200000000-2200-22i2−i2i2−i2−i2i2−i2i22-22-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ3622-2-22-22-222-2-200000000-2200-22i2−i2i2−i2−i2i2−i2i2-22-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ3722-2-22-22-222-2-200000000-2200-22−i2i2−i2i2i2−i2i2−i22-22-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ3822-2-22-22-222-2-200000000-2200-22−i2i2−i2i2i2−i2i2−i2-22-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ3922-2-2-22-222-22-20000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000-222-2000000000000
χ4022-2-2-22-222-22-20000002-2002-200i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200002-2-22000000000000
χ4122-2-2-22-222-22-20000002-2002-200−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200002-2-22000000000000
χ4222-2-2-22-222-22-20000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000-222-2000000000000
χ4322-2-2-22-222-22-2000000-2200-2200i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2-222-20000000000000000
χ4422-2-2-22-222-22-2000000-2200-2200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i22-2-220000000000000000
χ4522-2-2-22-222-22-2000000-2200-2200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i22-2-220000000000000000
χ4622-2-2-22-222-22-2000000-2200-2200−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2-222-20000000000000000
χ474444-4-4-4-4-444-44-44-4-4400000000000000000000000000000000000000000000
χ484444-4-4-4-4-444-4-44-444-400000000000000000000000000000000000000000000
χ4944-4-44-44-4-4-444000000004-400-44000000000000000000000000000000000000
χ5044-4-44-44-4-4-44400000000-44004-4000000000000000000000000000000000000
χ5144-4-4-44-44-44-440000004-400-4400000000000000000000000000000000000000
χ5244-4-4-44-44-44-44000000-44004-400000000000000000000000000000000000000
χ534-4-4444-4-4000044-4-4000000000000000000000000000000000000002i−2i2i−2i0000
χ544-4-4444-4-4000044-4-400000000000000000000000000000000000000−2i2i−2i2i0000
χ554-4-4444-4-40000-4-444000000000000000000000000000000000000002-2-220000
χ564-4-4444-4-40000-4-44400000000000000000000000000000000000000-222-20000
χ574-4-44-4-44400004-4-4400000000000000000000000000000000002-22-200000000
χ584-4-44-4-44400004-4-440000000000000000000000000000000000-22-2200000000
χ594-4-44-4-4440000-444-400000000000000000000000000000000002-2-2200000000
χ604-4-44-4-4440000-444-40000000000000000000000000000000000-222-200000000
χ618-88-88-8-88000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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