Finite Group Databasebeta

← Group #323948

Character table — Group #323948

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888822244444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-111-1
χ9111111111111111111-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-11-1
χ10111111111111111111-1-1-1-111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-11-11
χ11111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-11-11
χ12111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1111111-1-1-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ17222222222-2-2-2-2222-2-222-2-22222-2-2-2-2-200200000022000000000000-2-2000000000000
χ18222222222-2-2-2-2222-2-222-2-2-2-2-2-22222-2002000000-2-200000000000022000000000000
χ19222222222-2-2-2-2222-2-2-2-2222222-2-2-2-2200-2000000-2-200000000000022000000000000
χ20222222222-2-2-2-2222-2-2-2-222-2-2-2-22222200-200000022000000000000-2-2000000000000
χ2122222222-22222-2-2-2-2-2222200000000-222-222-2-2-2-20000000000000000000000000000
χ2222222222-22222-2-2-2-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000000002-2-222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000200-2000000002i2i−2i−2i00000000002i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000200-200000000−2i−2i2i2i0000000000−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2002000000002i2i−2i−2i0000000000−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200200000000−2i−2i2i2i00000000002i2i−2i−2i00000000
χ2922-22-2-2-22022-2-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000002i−2i2-22−2i2−i2i2−i2000000002−22−22−200000000
χ3022-22-2-2-22022-2-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000−2i2i-222−2−i2i2−i2i2000000002−2−22−2200000000
χ3122-22-2-2-22022-2-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000002i−2i2-2−22−i2i2−i2i200000000−22−22−2200000000
χ3222-22-2-2-22022-2-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000−2i2i-22−22i2−i2i2−i200000000−222−22−200000000
χ3322-22-2-2-22022-2-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000002i−2i-22−22−i2i2−i2i200000000−222−22−200000000
χ3422-22-2-2-22022-2-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000−2i2i2-2−22i2−i2i2−i200000000−22−22−2200000000
χ3522-22-2-2-22022-2-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000002i−2i-222−2i2−i2i2−i2000000002−2−22−2200000000
χ3622-22-2-2-22022-2-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000−2i2i2-22−2−i2i2−i2i2000000002−22−22−200000000
χ3722-22-2-2-220-2-222000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i202-202i−2i00002−22−2−2200000000−22−i2i2i2−i200000000
χ3822-22-2-2-220-2-222000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20-220−2i2i00002−2−222−200000000−22i2−i2−i2i200000000
χ3922-22-2-2-220-2-222000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i202-202i−2i0000−22−222−2000000002−2i2−i2−i2i200000000
χ4022-22-2-2-220-2-222000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20-220−2i2i0000−222−2−22000000002−2−i2i2i2−i200000000
χ4122-22-2-2-220-2-22200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i202-20−2i2i0000−22−222−2000000002−2−i2i2i2−i200000000
χ4222-22-2-2-220-2-22200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20-2202i−2i0000−222−2−22000000002−2i2−i2−i2i200000000
χ4322-22-2-2-220-2-22200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i202-20−2i2i00002−22−2−2200000000−22i2−i2−i2i200000000
χ4422-22-2-2-220-2-22200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20-2202i−2i00002−2−222−200000000−22−i2i2i2−i200000000
χ452-2-22-222-222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000022-2-2000000002i−2i0000
χ462-2-22-222-222-22-22-2-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000-2-22200000000−2i2i0000
χ472-2-22-222-222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000022-2-200000000−2i2i0000
χ482-2-22-222-222-22-22-2-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000-2-222000000002i−2i0000
χ492-2-22-222-22-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i00000000000000002i2i−2i−2i00000000002-2000000
χ502-2-22-222-22-22-222-2-2-2200002i−2i2i−2i−2i2i−2i2i0000000000000000−2i−2i2i2i0000000000-22000000
χ512-2-22-222-22-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i00000000000000002i2i−2i−2i0000000000-22000000
χ522-2-22-222-22-22-222-2-2-220000−2i2i−2i2i2i−2i2i−2i0000000000000000−2i−2i2i2i00000000002-2000000
χ53444-4-4-44-440000-44-4000000000000000000000000000000000022−2222−2200000000000000
χ54444-4-4-44-440000-44-40000000000000000000000000000000000−2222−222200000000000000
χ55444-4-4-44-4-400004-440000000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ56444-4-4-44-4-400004-44000000000000000000000000000000−2i22i2−2i22i2000000000000000000
χ574-4444-4-4-404-4-4400000000022−22−222222−22−222200000000000000000000000000000000000000
χ584-4444-4-4-404-4-44000000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-4444-4-4-40-444-400000000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-4444-4-4-40-444-4000000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-44-444-4-44-44-4-444-4400000000000000000000000000000000000000000000000000
χ624-4-44-444-4-4-44-44-4444-400000000000000000000000000000000000000000000000000
χ634-4-4-44-44440000-4-44000000000000000000000000000000000022−22−222200000000000000
χ644-4-4-44-44440000-4-440000000000000000000000000000000000−222222−2200000000000000
χ654-4-4-44-444-4000044-400000000000000000000000000000022−22−2222000000000000000000
χ664-4-4-44-444-4000044-4000000000000000000000000000000−222222−22000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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