Finite Group Databasebeta

← Group #323902

Character table — Group #323902

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888822444444448888888888882244444488888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-11-1
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-11
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-11111-1-11-1-11
χ1722222222222-2-2-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1822222222222-2-2-2-2222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-222-2-222222222-2-2-2-20000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222220000000000000000000000000000
χ2122222222-2-2-22222-20000000022-2-2-2-2-2-2220000000000002222-2-2-2-200000000000000000000
χ2222222222-2-2-22222-20000000022-2-2-2-2-2-222000000000000-2-2-2-2222200000000000000000000
χ2322222222-2-2-22222-200000000-2-2-2-22222-2-200000000000022-2-2-2-22200000000000000000000
χ2422222222-2-2-22222-200000000-2-2-2-22222-2-2000000000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-200000000222222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-200000000222222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-222-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-22-200022-2-20i2i2i2i2−i2−i2−i2−i200002i−2i2i−2i00i2i2−i2−i222−2−222−2−2002-22i−2i00i2−i2i2−i22−22−2000000000000
χ30222-2-2-22-200022-2-20i2i2i2i2−i2−i2−i2−i200002i−2i2i−2i00i2i2−i2−i222−2−222−2−200-22−2i2i00−i2i2−i2i2−22−22000000000000
χ31222-2-2-22-200022-2-20i2i2i2i2−i2−i2−i2−i20000−2i2i−2i2i00i2i2−i2−i2−2−222−2−222002-2−2i2i00i2−i2i2−i2−22−22000000000000
χ32222-2-2-22-200022-2-20i2i2i2i2−i2−i2−i2−i20000−2i2i−2i2i00i2i2−i2−i2−2−222−2−22200-222i−2i00−i2i2−i2i22−22−2000000000000
χ33222-2-2-22-200022-2-20−i2−i2−i2−i2i2i2i2i200002i−2i2i−2i00−i2−i2i2i2−2−222−2−222002-22i−2i00−i2i2−i2i2−22−22000000000000
χ34222-2-2-22-200022-2-20−i2−i2−i2−i2i2i2i2i200002i−2i2i−2i00−i2−i2i2i2−2−222−2−22200-22−2i2i00i2−i2i2−i22−22−2000000000000
χ35222-2-2-22-200022-2-20−i2−i2−i2−i2i2i2i2i20000−2i2i−2i2i00−i2−i2i2i222−2−222−2−2002-2−2i2i00−i2i2−i2i22−22−2000000000000
χ36222-2-2-22-200022-2-20−i2−i2−i2−i2i2i2i2i20000−2i2i−2i2i00−i2−i2i2i222−2−222−2−200-222i−2i00i2−i2i2−i2−22−22000000000000
χ37222-2-2-22-2000-2-2220i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i00−i2−i2i2i222−2−2−2−2222-200002i−2i2−2−22−i2i2i2−i2000000000000
χ38222-2-2-22-2000-2-2220i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i00−i2−i2i2i222−2−2−2−222-220000−2i2i−222−2i2−i2−i2i2000000000000
χ39222-2-2-22-2000-2-2220i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i00−i2−i2i2i2−2−22222−2−22-20000−2i2i−222−2−i2i2i2−i2000000000000
χ40222-2-2-22-2000-2-2220i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i00−i2−i2i2i2−2−22222−2−2-2200002i−2i2−2−22i2−i2−i2i2000000000000
χ41222-2-2-22-2000-2-2220−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i00i2i2−i2−i2−2−22222−2−22-200002i−2i−222−2i2−i2−i2i2000000000000
χ42222-2-2-22-2000-2-2220−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i00i2i2−i2−i2−2−22222−2−2-220000−2i2i2−2−22−i2i2i2−i2000000000000
χ43222-2-2-22-2000-2-2220−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i00i2i2−i2−i222−2−2−2−2222-20000−2i2i2−2−22i2−i2−i2i2000000000000
χ44222-2-2-22-2000-2-2220−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i00i2i2−i2−i222−2−2−2−222-2200002i−2i−222−2−i2i2i2−i2000000000000
χ452-2-222-22-222-22-22-2-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i00000000000000000000000000002i−2i2-20000
χ462-2-222-22-222-22-22-2-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i0000000000000000000000000000−2i2i-220000
χ472-2-222-22-222-22-22-2-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i00000000000000000000000000002i−2i-220000
χ482-2-222-22-222-22-22-2-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i0000000000000000000000000000−2i2i2-20000
χ492-2-222-22-222-2-22-22-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i0000000000000000000000002-22i−2i00000000
χ502-2-222-22-222-2-22-22-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i000000000000000000000000-22−2i2i00000000
χ512-2-222-22-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i0000000000000000000000002-2−2i2i00000000
χ522-2-222-22-222-2-22-22-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i000000000000000000000000-222i−2i00000000
χ5344-44-4-4-440000000022−2222−2222−2222−22000000004i−4i00002i2−2i22i2−2i200000000000000000000000000000000
χ5444-44-4-4-440000000022−2222−2222−2222−2200000000−4i4i0000−2i22i2−2i22i200000000000000000000000000000000
χ5544-44-4-4-4400000000−2222−2222−2222−2222000000004i−4i0000−2i22i2−2i22i200000000000000000000000000000000
χ5644-44-4-4-4400000000−2222−2222−2222−222200000000−4i4i00002i2−2i22i2−2i200000000000000000000000000000000
χ5744-4-444-4-44-4-40000400000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ5844-4-444-4-44-4-4000040000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ5944-4-444-4-4-4440000-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-444-4-4-4440000-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ614-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i24-400000000000000002i2−2i22i2−2i20000000000000000000000000000
χ624-444-44-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i2-440000000000000000−2i22i2−2i22i20000000000000000000000000000
χ634-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i24-40000000000000000−2i22i2−2i22i20000000000000000000000000000
χ644-444-44-4-400000000−2i22i22i2−2i2−2i22i22i2−2i2-4400000000000000002i2−2i22i2−2i20000000000000000000000000000
χ654-44-44-4-444-440000-4000000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ664-44-44-4-444-440000-400000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ674-44-44-4-44-44-4000044-4-44-444-400000000000000000000000000000000000000000000000000
χ684-44-44-4-44-44-400004-444-44-4-4400000000000000000000000000000000000000000000000000
χ694-4-444-44-4-4-444-44-440000000000-440000000000000000000000000000000000000000000000
χ704-4-444-44-4-4-44-44-44400000000004-40000000000000000000000000000000000000000000000
χ714-4-4-4-44440004-4-4402222−22−22−22−222222000000000022−22−2222000000000000000000000000000000000000
χ724-4-4-4-44440004-4-440−22−2222222222−22−220000000000−222222−22000000000000000000000000000000000000
χ734-4-4-4-4444000-444-402222−22−22−22−2222220000000000−222222−22000000000000000000000000000000000000
χ744-4-4-4-4444000-444-40−22−2222222222−22−22000000000022−22−2222000000000000000000000000000000000000

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