Finite Group Databasebeta

← Group #347893

Character table — Group #347893

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244448888224444448888882222444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1111111-1-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1111111-1-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-111-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-111-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-111-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-2-2-22222220000-20000-2-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-20000200002-2-22200000000000000000000
χ192222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000-20000-2222200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000020000222-2-200000000000000000000
χ21222222-2-2-2-2000022-2-222-2-2000000000020000-200002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222-2-2-2-2000022-2-222-2-2000000000020000-20000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-2-2-2220000002-22-2-22-22-22000000000000000000000000
χ24222222-2-2-2-2000022-2-2-2-222000000-22-22-2-22-222000000000000000000000000
χ25222222-2-2-2-20000-2-22222-2-20000000000-20000200002i2i−2i−2i−2i−2i2i2i000000000000
χ26222222-2-2-2-20000-2-22222-2-20000000000-2000020000−2i−2i2i2i2i2i−2i−2i000000000000
χ27222222-2-2-2-20000-2-222-2-2220000002-2-2222-2-22-2000000000000000000000000
χ28222222-2-2-2-20000-2-222-2-222000000-222-22-222-2-2000000000000000000000000
χ292222-2-222-2-2000000002-22-2002i2i−2i−2i0022000-2-20002i−2i2i−2i2i−2i0000000000000000
χ302222-2-222-2-2000000002-22-2002i2i−2i−2i00-2-2000220002i−2i−2i2i−2i2i0000000000000000
χ312222-2-222-2-2000000002-22-200−2i−2i2i2i0022000-2-2000−2i2i−2i2i−2i2i0000000000000000
χ322222-2-222-2-2000000002-22-200−2i−2i2i2i00-2-200022000−2i2i2i−2i2i−2i0000000000000000
χ332222-2-222-2-200000000-22-22002i2i−2i−2i22000-2-200000−2i2i00002i−2i2i−2i000000000000
χ342222-2-222-2-200000000-22-22002i2i−2i−2i-2-20002200000−2i2i0000−2i2i−2i2i000000000000
χ352222-2-222-2-200000000-22-2200−2i−2i2i2i22000-2-2000002i−2i0000−2i2i−2i2i000000000000
χ362222-2-222-2-200000000-22-2200−2i−2i2i2i-2-200022000002i−2i00002i−2i2i−2i000000000000
χ372222-2-2-2-222222200002-2-22-2-200002-2000-220002-2002-2-220000000000000000
χ382222-2-2-2-222222200002-2-22-2-20000-220002-20002-200-222-20000000000000000
χ392222-2-2-2-22222220000-222-2-2-20000002-2000-220-220000002-2-22000000000000
χ402222-2-2-2-22222220000-222-2-2-2000000-220002-20-22000000-222-2000000000000
χ412222-2-2-2-222-2-2-2-200002-2-222200002-2000-22000-2200-222-20000000000000000
χ422222-2-2-2-222-2-2-2-200002-2-22220000-220002-2000-22002-2-220000000000000000
χ432222-2-2-2-222-2-2-2-20000-222-2220000002-2000-2202-2000000-222-2000000000000
χ442222-2-2-2-222-2-2-2-20000-222-222000000-220002-202-20000002-2-22000000000000
χ452-22-22-22-2-2222-2-22-22-200002-22-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ462-22-22-22-2-2222-2-22-22-200002-22-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ472-22-22-22-2-2222-2-2-22-2200002-2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ482-22-22-22-2-2222-2-2-22-2200002-2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ492-22-22-22-2-22-2-2222-22-20000-22-22-220000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ502-22-22-22-2-22-2-2222-22-20000-22-22-220000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ512-22-22-22-2-22-2-222-22-220000-222-22-20000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ522-22-22-22-2-22-2-222-22-220000-222-22-20000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ534-44-44-4-444-400004-4-4400000000000000000000000000000000000000000000
χ544-44-44-4-444-40000-444-400000000000000000000000000000000000000000000
χ554-44-4-444-44-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ564-44-4-444-44-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ574-44-4-44-44-4444-4-400000000-4400000000000000000000000000000000000000
χ584-44-4-44-44-44-4-444000000004-400000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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