Finite Group Databasebeta

← Group #278167

Character table — Group #278167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888822444444448888888888884444444488888888888888882444
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
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-11
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1
χ17222222222-2-2222-2-2222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222-2-2222-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000000000000000
χ2122222222-222-2-2-2220000000022-2-2-2-2-2-22200000000000022-2-2-2-22200000000000000000000
χ2222222222-222-2-2-2220000000022-2-2-2-2-2-222000000000000-2-22222-2-200000000000000000000
χ2322222222-222-2-2-22200000000-2-222-2-222-2-20000000000002222-2-2-2-200000000000000000000
χ2422222222-222-2-2-22200000000-2-222-2-222-2-2000000000000-2-2-2-2222200000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-20000000022-2-22222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-2-2-2-2202-20002-22222−2−2−2−2002i−2i002i−2i00i2i2−i2−i222−2−2i2i2−i2−i200002i−2i2-2i2−i2i2−i22−22−2000000000000
χ30222-2-2-2-2202-20002-22222−2−2−2−2002i−2i002i−2i00i2i2−i2−i222−2−2i2i2−i2−i20000−2i2i-22−i2i2−i2i2−22−22000000000000
χ31222-2-2-2-2202-20002-22222−2−2−2−200−2i2i00−2i2i00−i2−i2i2i222−2−2−i2−i2i2i200002i−2i-22i2−i2i2−i2−22−22000000000000
χ32222-2-2-2-2202-20002-22222−2−2−2−200−2i2i00−2i2i00−i2−i2i2i222−2−2−i2−i2i2i20000−2i2i2-2−i2i2−i2i22−22−2000000000000
χ33222-2-2-2-2202-20002-2−2−2−2−22222002i−2i002i−2i00−i2−i2i2i2−2−222−i2−i2i2i200002i−2i2-2−i2i2−i2i2−22−22000000000000
χ34222-2-2-2-2202-20002-2−2−2−2−22222002i−2i002i−2i00−i2−i2i2i2−2−222−i2−i2i2i20000−2i2i-22i2−i2i2−i22−22−2000000000000
χ35222-2-2-2-2202-20002-2−2−2−2−2222200−2i2i00−2i2i00i2i2−i2−i2−2−222i2i2−i2−i200002i−2i-22−i2i2−i2i22−22−2000000000000
χ36222-2-2-2-2202-20002-2−2−2−2−2222200−2i2i00−2i2i00i2i2−i2−i2−2−222i2i2−i2−i20000−2i2i2-2i2−i2i2−i2−22−22000000000000
χ37222-2-2-2-220-22000-222222−2−2−2−2002i−2i00−2i2i00i2i2−i2−i2−2−222−i2−i2i2i22-22i−2i00002−2−22i2−i2−i2i2000000000000
χ38222-2-2-2-220-22000-222222−2−2−2−2002i−2i00−2i2i00i2i2−i2−i2−2−222−i2−i2i2i2-22−2i2i0000−222−2−i2i2i2−i2000000000000
χ39222-2-2-2-220-22000-222222−2−2−2−200−2i2i002i−2i00−i2−i2i2i2−2−222i2i2−i2−i22-2−2i2i00002−2−22−i2i2i2−i2000000000000
χ40222-2-2-2-220-22000-222222−2−2−2−200−2i2i002i−2i00−i2−i2i2i2−2−222i2i2−i2−i2-222i−2i0000−222−2i2−i2−i2i2000000000000
χ41222-2-2-2-220-22000-22−2−2−2−22222002i−2i00−2i2i00−i2−i2i2i222−2−2i2i2−i2−i22-22i−2i0000−222−2−i2i2i2−i2000000000000
χ42222-2-2-2-220-22000-22−2−2−2−22222002i−2i00−2i2i00−i2−i2i2i222−2−2i2i2−i2−i2-22−2i2i00002−2−22i2−i2−i2i2000000000000
χ43222-2-2-2-220-22000-22−2−2−2−2222200−2i2i002i−2i00i2i2−i2−i222−2−2−i2−i2i2i22-2−2i2i0000−222−2i2−i2−i2i2000000000000
χ44222-2-2-2-220-22000-22−2−2−2−2222200−2i2i002i−2i00i2i2−i2−i222−2−2−i2−i2i2i2-222i−2i00002−2−22−i2i2i2−i2000000000000
χ452-2-222-2-22-2222-22-2-222-2-222-2-200002-2000000002-22-2000000000000000000002i−2i2i−2i00000000
χ462-2-222-2-22-2222-22-2-222-2-222-2-200002-2000000002-22-200000000000000000000−2i2i−2i2i00000000
χ472-2-222-2-22-2222-22-2-2-2-222-2-22200002-200000000-22-22000000000000000000002i−2i−2i2i00000000
χ482-2-222-2-22-2222-22-2-2-2-222-2-22200002-200000000-22-2200000000000000000000−2i2i2i−2i00000000
χ492-2-222-2-22-2-2-22-222222-2-222-2-20000-2200000000-22-220000000000000000000000002-22-20000
χ502-2-222-2-22-2-2-22-222222-2-222-2-20000-2200000000-22-22000000000000000000000000-22-220000
χ512-2-222-2-22-2-2-22-2222-2-222-2-2220000-22000000002-22-20000000000000000000000002-2-220000
χ522-2-222-2-22-2-2-22-2222-2-222-2-2220000-22000000002-22-2000000000000000000000000-222-20000
χ5344-44-44-4-44004-4-4000000000000000000004-44-4000000000000000000000000000000000000
χ5444-44-44-4-44004-4-400000000000000000000-44-44000000000000000000000000000000000000
χ5544-44-44-4-4-400-444004i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ5644-44-44-4-4-400-44400−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ5744-4-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i24-4000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ5844-4-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2-4400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ5944-4-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i24-400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6044-4-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2-44000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ614-444-4-44-4400-4-44004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ624-444-4-44-4400-4-4400−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ634-444-4-44-4-40044-400000000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ644-444-4-44-4-40044-40000000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ654-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000004i−4i0000000022−22−22220000000000000000000000000000
χ664-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000−4i4i00000000−222222−220000000000000000000000000000
χ674-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000004i−4i00000000−222222−220000000000000000000000000000
χ684-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000−4i4i0000000022−22−22220000000000000000000000000000
χ694-4-444-4-44444-44-4-4-4000000000000-4400000000000000000000000000000000000000000000
χ704-4-444-4-444-4-4-44-4440000000000004-400000000000000000000000000000000000000000000
χ714-4-4-4-444404-4000-442222−22−22−22−2222220000000000000022−22−222200000000000000000000000000000000
χ724-4-4-4-444404-4000-44−22−2222222222−22−2200000000000000−222222−2200000000000000000000000000000000
χ734-4-4-4-44440-440004-42222−22−22−22−22222200000000000000−222222−2200000000000000000000000000000000
χ744-4-4-4-44440-440004-4−22−2222222222−22−220000000000000022−22−222200000000000000000000000000000000

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