Finite Group Databasebeta

← Group #321749

Character table — Group #321749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1111-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-11-1-11
χ1722222222222-2-2-2-2222-2-2-2-22222-2-2-2-2002-200000022-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-22222002-2000000-2-222000000000000000000000000
χ1922222222222-2-2-2-22-2-222-2-22222-2-2-2-200-22000000-2-222000000000000000000000000
χ2022222222222-2-2-2-22-2-222-2-2-2-2-2-2222200-2200000022-2-2000000000000000000000000
χ2122222222-2-2-22222-22222-2-20000000022-2-2-2-222-2-20000000000000000000000000000
χ2222222222-2-2-22222-22222-2-200000000-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000000000-220000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000000-22000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200000000002-20000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200000000002-2000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ29222-2-2-22-200022-2-202-22-200i2i2−i2−i2i2i2−i2−i200002i−2i002i−2ii2−i2i2−i2000000002−22−22−22−200000000
χ30222-2-2-22-200022-2-202-22-200i2i2−i2−i2i2i2−i2−i20000−2i2i00−2i2ii2−i2i2−i200000000−22−22−22−2200000000
χ31222-2-2-22-200022-2-202-22-200−i2−i2i2i2−i2−i2i2i200002i−2i002i−2i−i2i2−i2i200000000−22−22−22−2200000000
χ32222-2-2-22-200022-2-202-22-200−i2−i2i2i2−i2−i2i2i20000−2i2i00−2i2i−i2i2−i2i2000000002−22−22−22−200000000
χ33222-2-2-22-200022-2-20-22-2200i2i2−i2−i2i2i2−i2−i200002i−2i00−2i2i−i2i2−i2i2000000002−22−2−22−2200000000
χ34222-2-2-22-200022-2-20-22-2200i2i2−i2−i2i2i2−i2−i20000−2i2i002i−2i−i2i2−i2i200000000−22−222−22−200000000
χ35222-2-2-22-200022-2-20-22-2200−i2−i2i2i2−i2−i2i2i200002i−2i00−2i2ii2−i2i2−i200000000−22−222−22−200000000
χ36222-2-2-22-200022-2-20-22-2200−i2−i2i2i2−i2−i2i2i20000−2i2i002i−2ii2−i2i2−i2000000002−22−2−22−2200000000
χ37222-2-2-22-2000-2-22202-2-2200i2i2−i2−i2−i2−i2i2i22-200002-200i2−i2−i2i200000000i2−i2−i2i2i2−i2−i2i200000000
χ38222-2-2-22-2000-2-22202-2-2200i2i2−i2−i2−i2−i2i2i2-220000-2200i2−i2−i2i200000000−i2i2i2−i2−i2i2i2−i200000000
χ39222-2-2-22-2000-2-22202-2-2200−i2−i2i2i2i2i2−i2−i22-200002-200−i2i2i2−i200000000−i2i2i2−i2−i2i2i2−i200000000
χ40222-2-2-22-2000-2-22202-2-2200−i2−i2i2i2i2i2−i2−i2-220000-2200−i2i2i2−i200000000i2−i2−i2i2i2−i2−i2i200000000
χ41222-2-2-22-2000-2-2220-222-200i2i2−i2−i2−i2−i2i2i22-20000-2200−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i200000000
χ42222-2-2-22-2000-2-2220-222-200i2i2−i2−i2−i2−i2i2i2-2200002-200−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i200000000
χ43222-2-2-22-2000-2-2220-222-200−i2−i2i2i2i2i2−i2−i22-20000-2200i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i200000000
χ44222-2-2-22-2000-2-2220-222-200−i2−i2i2i2i2i2−i2−i2-2200002-200i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i200000000
χ452-2-2-2-22222-2-22-22-2200002-22-22-22-22-200000000000000000022-2-200000000002-20000
χ462-2-2-2-22222-2-22-22-2200002-22-22-22-22-2000000000000000000-2-2220000000000-220000
χ472-2-2-2-22222-2-22-22-2200002-2-22-22-22-2200000000000000000022-2-20000000000-220000
χ482-2-2-2-22222-2-22-22-2200002-2-22-22-22-22000000000000000000-2-22200000000002-20000
χ492-2-2-2-22222-2-2-22-2220000-222-22-2-22-220000000000000022-2-20000000000002-2000000
χ502-2-2-2-22222-2-2-22-2220000-222-22-2-22-2200000000000000-2-222000000000000-22000000
χ512-2-2-2-22222-2-2-22-2220000-22-22-222-22-20000000000000022-2-2000000000000-22000000
χ522-2-2-2-22222-2-2-22-2220000-22-22-222-22-200000000000000-2-2220000000000002-2000000
χ5344-44-44-4-444-40000-4000000000000000000000000000022−2222−2200000000000000000000
χ5444-44-44-4-444-40000-40000000000000000000000000000−2222−222200000000000000000000
χ5544-44-44-4-4-4-4400004000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5644-44-44-4-4-4-440000400000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ574-44-444-4-44-440000-4000000000000000000000000000022−22−222200000000000000000000
χ584-44-444-4-44-440000-40000000000000000000000000000−222222−2200000000000000000000
χ594-44-444-4-4-44-400004000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-44-444-4-4-44-40000400000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ614-4-444-44-40004-4-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ624-4-444-44-40004-4-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-4-444-44-4000-444-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ644-4-444-44-4000-444-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ654-4-4-4-4444-4444-44-4-40000-440000000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-44-44-400004-40000000000000000000000000000000000000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-8-88000000000000000000000000000000000000000000000000000000000000

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