Finite Group Databasebeta

← Group #329995

Character table — Group #329995

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444442244444444444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-2-2-22200000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000
χ192222222222-2-2-2-222-2-2-2-22222-2-2000000002222-2-2-2-200000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-200000000-2-2-2-2222200000000000000000000
χ2122222222-2-22222-2-222-2-222-2-2-2-222-2-2-2-2220000000000000000000000000000
χ2222222222-2-22222-2-222-2-222-2-2-2-2-2-22222-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-22-2-20022-2-2002-2002-20000002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ30222-2-22-2-20022-2-2002-2002-20000002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ31222-2-22-2-20022-2-2002-2002-2000000−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ32222-2-22-2-20022-2-2002-2002-2000000−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ33222-2-22-2-20022-2-200-2200-220000002i−2i−2i2i00i2−i2−i2i2i2−i2−i2i2−22−222−22−2000000000000
χ34222-2-22-2-20022-2-200-2200-220000002i−2i−2i2i00−i2i2i2−i2−i2i2i2−i22−22−2−22−22000000000000
χ35222-2-22-2-20022-2-200-2200-22000000−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i22−22−2−22−22000000000000
χ36222-2-22-2-20022-2-200-2200-22000000−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i2−22−222−22−2000000000000
χ37222-2-22-2-200-2-222002-200-2200002-200002-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ38222-2-22-2-200-2-222002-200-2200002-200002-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ39222-2-22-2-200-2-222002-200-220000-220000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ40222-2-22-2-200-2-222002-200-220000-220000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ41222-2-22-2-200-2-22200-22002-200002-20000-22i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ42222-2-22-2-200-2-22200-22002-200002-20000-22−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ43222-2-22-2-200-2-22200-22002-20000-2200002-2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ44222-2-22-2-200-2-22200-22002-20000-2200002-2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4544-44-4-44-4004-44-4000000004i−4i4i−4i000000000000000000000000000000000000
χ4644-44-4-44-4004-44-400000000−4i4i−4i4i000000000000000000000000000000000000
χ4744-44-4-44-400-44-44000000004i−4i−4i4i000000000000000000000000000000000000
χ4844-44-4-44-400-44-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ4944-4-44-4-44444-4-44-4-4004-4000000000000000000000000000000000000000000
χ5044-4-44-4-4444-444-4-4-400-44000000000000000000000000000000000000000000
χ5144-4-44-4-44-4-44-4-444400-44000000000000000000000000000000000000000000
χ5244-4-44-4-44-4-4-444-444004-4000000000000000000000000000000000000000000
χ534-44-4-4-4444-400004-40000000000000000000000000000000000002i2−2i200000000
χ544-44-4-4-4444-400004-4000000000000000000000000000000000000−2i22i200000000
χ554-44-4-4-444-440000-44000000000000000000000000000000000022−220000000000
χ564-44-4-4-444-440000-440000000000000000000000000000000000−22220000000000
χ574-4-44-44-444-40000-44000000000000000000000000000000000000000022−220000
χ584-4-44-44-444-40000-440000000000000000000000000000000000000000−22220000
χ594-4-44-44-44-4400004-4000000000000000000000000000000000000002i2−2i2000000
χ604-4-44-44-44-4400004-400000000000000000000000000000000000000−2i22i2000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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