Finite Group Databasebeta

← Group #329985

Character table — Group #329985

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444442244444444444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
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
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111111111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
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
χ131111111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
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
χ1722222222222-2-2-2-2222-2-222-2-2-2-20000000022-2-2-2-22200000000000000000000
χ1822222222222-2-2-2-2222-2-222-2-2-2-200000000-2-22222-2-200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-22222000000002222-2-2-2-200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2222200000000-2-2-2-2222200000000000000000000
χ2122222222-2-2-22222-222-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000
χ2222222222-2-2-22222-222-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000
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
χ29222-2-2-2-2200022-2-2000002i−2i2i−2i00002-22i−2i002−2i2−i22−2i2−i2i2−i2i2−i22−22−2000000000000
χ30222-2-2-2-2200022-2-2000002i−2i2i−2i00002-22i−2i00−22−i2i2−22−i2i2−i2i2−i2i2−22−22000000000000
χ31222-2-2-2-2200022-2-2000002i−2i2i−2i0000-22−2i2i002−2i2−i22−2i2−i2−i2i2−i2i2−22−22000000000000
χ32222-2-2-2-2200022-2-2000002i−2i2i−2i0000-22−2i2i00−22−i2i2−22−i2i2i2−i2i2−i22−22−2000000000000
χ33222-2-2-2-2200022-2-200000−2i2i−2i2i00002-2−2i2i002−2−i2i22−2−i2i2−i2i2−i2i22−22−2000000000000
χ34222-2-2-2-2200022-2-200000−2i2i−2i2i00002-2−2i2i00−22i2−i2−22i2−i2i2−i2i2−i2−22−22000000000000
χ35222-2-2-2-2200022-2-200000−2i2i−2i2i0000-222i−2i002−2−i2i22−2−i2i2i2−i2i2−i2−22−22000000000000
χ36222-2-2-2-2200022-2-200000−2i2i−2i2i0000-222i−2i00−22i2−i2−22i2−i2−i2i2−i2i22−22−2000000000000
χ37222-2-2-2-22000-2-222000002i−2i−2i2i002-200002i−2i2−2−i2i2−22i2−i22−2−22i2−i2−i2i2000000000000
χ38222-2-2-2-22000-2-222000002i−2i−2i2i002-200002i−2i−22i2−i22−2−i2i2−222−2−i2i2i2−i2000000000000
χ39222-2-2-2-22000-2-222000002i−2i−2i2i00-220000−2i2i2−2−i2i2−22i2−i2−222−2−i2i2i2−i2000000000000
χ40222-2-2-2-22000-2-222000002i−2i−2i2i00-220000−2i2i−22i2−i22−2−i2i22−2−22i2−i2−i2i2000000000000
χ41222-2-2-2-22000-2-22200000−2i2i2i−2i002-20000−2i2i2−2i2−i2−22−i2i22−2−22−i2i2i2−i2000000000000
χ42222-2-2-2-22000-2-22200000−2i2i2i−2i002-20000−2i2i−22−i2i22−2i2−i2−222−2i2−i2−i2i2000000000000
χ43222-2-2-2-22000-2-22200000−2i2i2i−2i00-2200002i−2i2−2i2−i2−22−i2i2−222−2i2−i2−i2i2000000000000
χ44222-2-2-2-22000-2-22200000−2i2i2i−2i00-2200002i−2i−22−i2i22−2i2−i22−2−22−i2i2i2−i2000000000000
χ4544-44-44-4-44-440000-40000000000000000000000000000000000000022−22000000
χ4644-44-44-4-44-440000-400000000000000000000000000000000000000−2222000000
χ4744-44-44-4-4-44-40000400000000000000000000000000000000000000002i2−2i20000
χ4844-44-44-4-4-44-4000040000000000000000000000000000000000000000−2i22i20000
χ494-444-4-44-44-4-40000400000000000000000000000000000000002i2−2i20000000000
χ504-444-4-44-44-4-4000040000000000000000000000000000000000−2i22i20000000000
χ514-444-4-44-4-4440000-400000000000000000000000000000000000022−2200000000
χ524-444-4-44-4-4440000-4000000000000000000000000000000000000−222200000000
χ534-4-444-4-4444-44-44-4-4004-4000000000000000000000000000000000000000000
χ544-4-444-4-4444-4-44-44-400-44000000000000000000000000000000000000000000
χ554-4-444-4-44-4-444-44-4400-44000000000000000000000000000000000000000000
χ564-4-444-4-44-4-44-44-444004-4000000000000000000000000000000000000000000
χ574-4-4-4-44440004-4-4404-40000004-4000000000000000000000000000000000000
χ584-4-4-4-44440004-4-440-44000000-44000000000000000000000000000000000000
χ594-4-4-4-4444000-444-404-4000000-44000000000000000000000000000000000000
χ604-4-4-4-4444000-444-40-440000004-4000000000000000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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