Finite Group Databasebeta

← Group #325621

Character table — Group #325621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888844444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ91111111111111111-1-111-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ111111111111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-111-1
χ172222222222-2-2-2-22222-2-2-2-22222-2-2-2-22-2000000000000000022-2-20000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-222222-20000000000000000-2-2220000000000000000
χ192222222222-2-2-2-222-2-2-2-2222222-2-2-2-2-220000000000000000-2-2220000000000000000
χ202222222222-2-2-2-222-2-2-2-222-2-2-2-22222-22000000000000000022-2-20000000000000000
χ2122222222-2-22222-2-222-2-22200000000-2-222-2-222-2-20000000000000000000000000000
χ2222222222-2-22222-2-222-2-22200000000-2-2-2-222-2-2220000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000000022-2-22222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-22000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-2200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-22-2-2-220022-2-2002-2002-2i2i2−i2−i2i2i2−i2−i200002i−2i002i−2i00000000i2−i2i2−i22−22−22−22−200000000
χ3022-22-2-2-220022-2-2002-2002-2i2i2−i2−i2i2i2−i2−i20000−2i2i00−2i2i00000000i2−i2i2−i2−22−22−22−2200000000
χ3122-22-2-2-220022-2-2002-2002-2−i2−i2i2i2−i2−i2i2i200002i−2i002i−2i00000000−i2i2−i2i2−22−22−22−2200000000
χ3222-22-2-2-220022-2-2002-2002-2−i2−i2i2i2−i2−i2i2i20000−2i2i00−2i2i00000000−i2i2−i2i22−22−22−22−200000000
χ3322-22-2-2-220022-2-200-2200-22i2i2−i2−i2i2i2−i2−i200002i−2i00−2i2i00000000−i2i2−i2i22−22−2−22−2200000000
χ3422-22-2-2-220022-2-200-2200-22i2i2−i2−i2i2i2−i2−i20000−2i2i002i−2i00000000−i2i2−i2i2−22−222−22−200000000
χ3522-22-2-2-220022-2-200-2200-22−i2−i2i2i2−i2−i2i2i200002i−2i00−2i2i00000000i2−i2i2−i2−22−222−22−200000000
χ3622-22-2-2-220022-2-200-2200-22−i2−i2i2i2−i2−i2i2i20000−2i2i002i−2i00000000i2−i2i2−i22−22−2−22−2200000000
χ3722-22-2-2-2200-2-222002-200-22i2i2−i2−i2−i2−i2i2i2002-2002-20000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ3822-22-2-2-2200-2-222002-200-22i2i2−i2−i2−i2−i2i2i200-2200-220000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ3922-22-2-2-2200-2-222002-200-22−i2−i2i2i2i2i2−i2−i2002-2002-20000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ4022-22-2-2-2200-2-222002-200-22−i2−i2i2i2i2i2−i2−i200-2200-220000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ4122-22-2-2-2200-2-22200-22002-2i2i2−i2−i2−i2−i2i2i2002-200-220000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ4222-22-2-2-2200-2-22200-22002-2i2i2−i2−i2−i2−i2i2i200-22002-20000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ4322-22-2-2-2200-2-22200-22002-2−i2−i2i2i2i2i2−i2−i2002-200-220000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ4422-22-2-2-2200-2-22200-22002-2−i2−i2i2i2i2i2−i2−i200-22002-20000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ452-2-2-222-22222-22-2-2-2002-2002-22-22-22-2000000000000002i2i−2i−2i000000000000002i−2i0000
χ462-2-2-222-22222-22-2-2-2002-2002-22-22-22-200000000000000−2i−2i2i2i00000000000000−2i2i0000
χ472-2-2-222-22222-22-2-2-2002-200-22-22-22-22000000000000002i2i−2i−2i00000000000000−2i2i0000
χ482-2-2-222-22222-22-2-2-2002-200-22-22-22-2200000000000000−2i−2i2i2i000000000000002i−2i0000
χ492-2-2-222-2222-22-22-2-200-22002-22-2-22-2200000000002i2i−2i−2i00000000000000002i−2i000000
χ502-2-2-222-2222-22-22-2-200-22002-22-2-22-220000000000−2i−2i2i2i0000000000000000−2i2i000000
χ512-2-2-222-2222-22-22-2-200-2200-22-222-22-200000000002i2i−2i−2i0000000000000000−2i2i000000
χ522-2-2-222-2222-22-22-2-200-2200-22-222-22-20000000000−2i−2i2i2i00000000000000002i−2i000000
χ53444-44-4-4-44-400004-4000000000000000000000000000022−2222−2200000000000000000000
χ54444-44-4-4-44-400004-40000000000000000000000000000−2222−222200000000000000000000
χ55444-44-4-4-4-440000-4400000000000000000000000022−2222−22000000000000000000000000
χ56444-44-4-4-4-440000-44000000000000000000000000−2222−2222000000000000000000000000
χ574-44-4-4-444004-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-4-4-444004-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-4-4-44400-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-4-4-44400-444-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-44-44-40000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ624-4-444-44-44-40000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ634-4-444-44-4-4400004-40000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ644-4-444-44-4-4400004-4000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ654-4-4-444-44-4-44-44-44400-44000000000000000000000000000000000000000000000000
χ664-4-4-444-44-4-4-44-4444004-4000000000000000000000000000000000000000000000000
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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