Finite Group Databasebeta

← Group #329167

Character table — Group #329167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-1111111-1-11-1-111111-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-11-1-111111-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-11-1-1111-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-11
χ121111111111-1-1-1-1111111-1-11-1-1111-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-11-1-11-1-111-111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-11-1-11-1-111-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-11-1-11-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-11-1-11-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-11
χ1722222222222222-2-222-2-222-2-2-2-22200-22200-2-2-2-200000000000000000000000000
χ1822222222222222-2-222-2-222-2-2-2-2-2-200-2-2-200222200000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2-222-222002-2-200-2-22200000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-222-2-2-2002220022-2-200000000000000000000000000
χ2122222222-2-2222222-2-222-2-2-222-20022-200220000-2-2-2-20000000000000000000000
χ2222222222-2-2222222-2-222-2-2-222-200-2-2-200-2-2000022220000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-22-2-2200002000000000000000000002-22-20000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-22-2-220000200000000000000000000-22-220000000000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-20022200-2-20000-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-200-2-220022000022-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200000000000000000000-222-20000000000
χ2922-2-22-22-2002i2i−2i−2i2-2002-20002i−2i0002i−2i0002-200000000i2i2−i2−i222−2−2000000002−2i2−i200
χ3022-2-22-22-2002i2i−2i−2i2-2002-20002i−2i0002i−2i0002-200000000−i2−i2i2i2−2−22200000000−22−i2i200
χ3122-2-22-22-2002i2i−2i−2i2-2002-20002i−2i000−2i2i000-2200000000i2i2−i2−i222−2−200000000−22−i2i200
χ3222-2-22-22-2002i2i−2i−2i2-2002-20002i−2i000−2i2i000-2200000000−i2−i2i2i2−2−222000000002−2i2−i200
χ3322-2-22-22-200−2i−2i2i2i2-2002-2000−2i2i0002i−2i000-2200000000i2i2−i2−i2−2−222000000002−2−i2i200
χ3422-2-22-22-200−2i−2i2i2i2-2002-2000−2i2i0002i−2i000-2200000000−i2−i2i2i222−2−200000000−22i2−i200
χ3522-2-22-22-200−2i−2i2i2i2-2002-2000−2i2i000−2i2i0002-200000000i2i2−i2−i2−2−22200000000−22i2−i200
χ3622-2-22-22-200−2i−2i2i2i2-2002-2000−2i2i000−2i2i0002-200000000−i2−i2i2i222−2−2000000002−2−i2i200
χ372-22-22-2-222-22i−2i2i−2i002-2002i−2i00000000000002i−2i2-200002−22−2i2−i2i2−i20000i2−i22−2000000
χ382-22-22-2-222-22i−2i2i−2i002-2002i−2i00000000000002i−2i2-20000−22−22−i2i2−i2i20000−i2i2−22000000
χ392-22-22-2-222-22i−2i2i−2i002-2002i−2i0000000000000−2i2i-2200002−22−2i2−i2i2−i20000−i2i2−22000000
χ402-22-22-2-222-22i−2i2i−2i002-2002i−2i0000000000000−2i2i-220000−22−22−i2i2−i2i20000i2−i22−2000000
χ412-22-22-2-222-2−2i2i−2i2i002-200−2i2i00000000000002i−2i-2200002−22−2−i2i2−i2i20000i2−i2−22000000
χ422-22-22-2-222-2−2i2i−2i2i002-200−2i2i00000000000002i−2i-220000−22−22i2−i2i2−i20000−i2i22−2000000
χ432-22-22-2-222-2−2i2i−2i2i002-200−2i2i0000000000000−2i2i2-200002−22−2−i2i2−i2i20000−i2i22−2000000
χ442-22-22-2-222-2−2i2i−2i2i002-200−2i2i0000000000000−2i2i2-20000−22−22i2−i2i2−i20000i2−i2−22000000
χ45444-4-44-4-44-4000000-4400000000000004-400000000000000000000000000000000
χ46444-4-44-4-44-4000000-440000000000000-4400000000000000000000000000000000
χ47444-4-44-4-4-440000004-4000000004-40000000000000000000000000000000000000
χ48444-4-44-4-4-440000004-400000000-440000000000000000000000000000000000000
χ4944-4-44-44-4004i4i−4i−4i-4400-44000−4i4i0000000000000000000000000000000000000000
χ5044-4-44-44-400−4i−4i4i4i-4400-440004i−4i0000000000000000000000000000000000000000
χ514-444-4-44-444000044-4-4-4-400-4004000000000000000000000000000000000000000
χ524-444-4-44-4440000-4-4-4-44400400-4000000000000000000000000000000000000000
χ534-444-4-44-4-4-400004444-4-400400-4000000000000000000000000000000000000000
χ544-444-4-44-4-4-40000-4-4444400-4004000000000000000000000000000000000000000
χ554-44-44-4-44-444i−4i4i−4i00-4400−4i4i0000000000000000000000000000000000000000000
χ564-44-44-4-44-44−4i4i−4i4i00-44004i−4i0000000000000000000000000000000000000000000
χ574-4-4444-4-4004-4-44000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ584-4-4444-4-4004-4-4400000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-4-4444-4-400-444-4000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ604-4-4444-4-400-444-400000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-4-4-4-44440000004-400-440000000000000000000004-40000000000000000000000
χ624-4-4-4-44440000004-400-44000000000000000000000-440000000000000000000000
χ634-4-4-4-4444000000-44004-400000000000000000004-4000000000000000000000000
χ644-4-4-4-4444000000-44004-40000000000000000000-44000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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