Finite Group Databasebeta

← Group #330598

Character table — Group #330598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444444444444444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-22222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ182222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-2-222-2-222-2-2-2-222-2-22222-2-20000000000000000000000000000
χ2122222222-2-22222-2-22222-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000
χ2222222222-2-22222-2-22222-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-2220000000022-2-2-2-22200000000000000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-22200000000-2-22222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-22-2-2-222-200002-2002-200002-2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ3022-22-2-2-222-200002-2002-200002-2002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ3122-22-2-2-222-200002-2002-200002-200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ3222-22-2-2-222-200002-2002-200002-200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ3322-22-2-2-222-200002-200-220000-22002i−2i−2i2i00i2−i2−i2i2i2−i2−i2i2−22−222−22−2000000000000
χ3422-22-2-2-222-200002-200-220000-22002i−2i−2i2i00−i2i2i2−i2−i2i2i2−i22−22−2−22−22000000000000
χ3522-22-2-2-222-200002-200-220000-2200−2i2i2i−2i00i2−i2−i2i2i2−i2−i2i22−22−2−22−22000000000000
χ3622-22-2-2-222-200002-200-220000-2200−2i2i2i−2i00−i2i2i2−i2−i2i2i2−i2−22−222−22−2000000000000
χ3722-22-2-2-22-220000-22002-20000-222-200002-2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ3822-22-2-2-22-220000-22002-20000-222-200002-2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ3922-22-2-2-22-220000-22002-20000-22-220000-22i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ4022-22-2-2-22-220000-22002-20000-22-220000-22−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ4122-22-2-2-22-220000-2200-2200002-22-20000-22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-22-2-2-22-220000-2200-2200002-22-20000-22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ4322-22-2-2-22-220000-2200-2200002-2-2200002-2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ4422-22-2-2-22-220000-2200-2200002-2-2200002-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ45444-4-44-4-4004-44-4000000000000000000000000000000000000000022−22000000
χ46444-4-44-4-4004-44-40000000000000000000000000000000000000000−2222000000
χ47444-4-44-4-400-44-4400000000000000000000000000000000000000000022−220000
χ48444-4-44-4-400-44-44000000000000000000000000000000000000000000−22220000
χ494-4444-4-4-44-40000-444-4004-40000000000000000000000000000000000000000
χ504-4444-4-4-44-40000-44-4400-440000000000000000000000000000000000000000
χ514-4444-4-4-4-4400004-44-400-440000000000000000000000000000000000000000
χ524-4444-4-4-4-4400004-4-44004-40000000000000000000000000000000000000000
χ534-4-44-444-4444-4-44-4-40000004-400000000000000000000000000000000000000
χ544-4-44-444-444-444-4-4-4000000-4400000000000000000000000000000000000000
χ554-4-44-444-4-4-44-4-4444000000-4400000000000000000000000000000000000000
χ564-4-44-444-4-4-4-444-4440000004-400000000000000000000000000000000000000
χ574-4-4-444-440044-4-40000000000000000000000000000000000002i2−2i20000000000
χ584-4-4-444-440044-4-4000000000000000000000000000000000000−2i22i20000000000
χ594-4-4-444-4400-4-4440000000000000000000000000000000000000022−2200000000
χ604-4-4-444-4400-4-44400000000000000000000000000000000000000−222200000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-88-8-8-888000000000000000000000000000000000000000000000000000000

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