Finite Group Databasebeta

← Group #316166

Character table — Group #316166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244448888224444448888884488888888888888888888888888884444
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
χ511111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11-11
χ121111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-2-2-222-2-2-2-2-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-20000000000000000000000000000
χ21222222-2-2-2-2000022-2-222-2-2000000-22000000002i2i−2i−2i00002i2i−2i−2i000000000000
χ22222222-2-2-2-2000022-2-222-2-2000000-2200000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ23222222-2-2-2-2000022-2-2-2-2220000002-200002i2i−2i−2i00002i2i−2i−2i0000000000000000
χ24222222-2-2-2-2000022-2-2-2-2220000002-20000−2i−2i2i2i0000−2i−2i2i2i0000000000000000
χ25222222-2-2-2-20000-2-22222-2-20000002-2000000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ26222222-2-2-2-20000-2-22222-2-20000002-200000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ27222222-2-2-2-20000-2-222-2-222000000-2200002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ28222222-2-2-2-20000-2-222-2-222000000-220000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ292222-2-222-2-2222200002-22-2-2-222-2-2000000000000000000000000002i−2i2i−2i0000
χ302222-2-222-2-2222200002-22-2-2-222-2-200000000000000000000000000−2i2i−2i2i0000
χ312222-2-222-2-222220000-22-22-2-2-2-22200000000000000000000002i−2i2i−2i00000000
χ322222-2-222-2-222220000-22-22-2-2-2-2220000000000000000000000−2i2i−2i2i00000000
χ332222-2-222-2-2-2-2-2-200002-22-222-2-222000000000000000000000000002i−2i−2i2i0000
χ342222-2-222-2-2-2-2-2-200002-22-222-2-22200000000000000000000000000−2i2i2i−2i0000
χ352222-2-222-2-2-2-2-2-20000-22-222222-2-200000000000000000000002i−2i−2i2i00000000
χ362222-2-222-2-2-2-2-2-20000-22-222222-2-20000000000000000000000−2i2i2i−2i00000000
χ372-22-22-22-22-200002-22-20000002i−2i2i−2i00002i−2ii2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-22-22-22-22-200002-22-20000002i−2i2i−2i00002i−2i−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-22-22-22-22-200002-22-2000000−2i2i−2i2i0000−2i2ii2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ402-22-22-22-22-200002-22-2000000−2i2i−2i2i0000−2i2i−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ412-22-22-22-22-20000-22-220000002i−2i2i−2i0000−2i2ii2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ422-22-22-22-22-20000-22-220000002i−2i2i−2i0000−2i2i−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ432-22-22-22-22-20000-22-22000000−2i2i−2i2i00002i−2ii2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-22-22-22-22-20000-22-22000000−2i2i−2i2i00002i−2i−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-22-22-2-22-222i2i−2i−2i2-2-2200002i−2i0000002i−2i002−2−22i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ462-22-22-2-22-222i2i−2i−2i2-2-2200002i−2i0000002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ472-22-22-2-22-222i2i−2i−2i-222-200002i−2i000000−2i2i002−2−22i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ482-22-22-2-22-222i2i−2i−2i-222-200002i−2i000000−2i2i00−222−2−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ492-22-22-2-22-22−2i−2i2i2i2-2-220000−2i2i000000−2i2i002−2−22−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ502-22-22-2-22-22−2i−2i2i2i2-2-220000−2i2i000000−2i2i00−222−2i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ512-22-22-2-22-22−2i−2i2i2i-222-20000−2i2i0000002i−2i002−2−22−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ522-22-22-2-22-22−2i−2i2i2i-222-20000−2i2i0000002i−2i00−222−2i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ534444-4-4-4-444000000004-4-440000000000000000000000000000000000000000
χ544444-4-4-4-44400000000-444-40000000000000000000000000000000000000000
χ554-44-4-444-4-44000000000000004i−4i−4i4i0000000000000000000000000000000000
χ564-44-4-444-4-4400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ574-44-4-44-444-44i4i−4i−4i00000000−4i4i00000000000000000000000000000000000000
χ584-44-4-44-444-4−4i−4i4i4i000000004i−4i00000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-880000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-8-88000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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