Finite Group Databasebeta

← Group #351164

Character table — Group #351164

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444444444444224444448888888888888888888888884444
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
χ2122222222-2-22222-2-22222-2-2-2-2-2-20000000022-2-2-2-22200000000000000000000
χ2222222222-2-22222-2-22222-2-2-2-2-2-200000000-2-22222-2-200000000000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-222000000002222-2-2-2-200000000000000000000
χ2422222222-2-22222-2-2-2-2-2-222-2-22200000000-2-2-2-2222200000000000000000000
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
χ2922-2-2-222-22-22-22-22-20000002-200002i−2i002i−2i002i−2i002i−2i2-22-20000000000000000
χ3022-2-2-222-22-22-22-22-20000002-200002i−2i002i−2i00−2i2i00−2i2i-22-220000000000000000
χ3122-2-2-222-22-22-22-22-20000002-20000−2i2i00−2i2i002i−2i002i−2i-22-220000000000000000
χ3222-2-2-222-22-22-22-22-20000002-20000−2i2i00−2i2i00−2i2i00−2i2i2-22-20000000000000000
χ3322-2-2-222-22-2-22-222-2000000-2200002i−2i00−2i2i2i−2i002i−2i0000002-22-2000000000000
χ3422-2-2-222-22-2-22-222-2000000-2200002i−2i00−2i2i−2i2i00−2i2i000000-22-22000000000000
χ3522-2-2-222-22-2-22-222-2000000-220000−2i2i002i−2i2i−2i002i−2i000000-22-22000000000000
χ3622-2-2-222-22-2-22-222-2000000-220000−2i2i002i−2i−2i2i00−2i2i0000002-22-2000000000000
χ3722-2-2-222-2-222-22-2-22000000-22002-2002-200002i−2i00−2i2i00002i−2i−2i2i000000000000
χ3822-2-2-222-2-222-22-2-22000000-22002-2002-20000−2i2i002i−2i0000−2i2i2i−2i000000000000
χ3922-2-2-222-2-222-22-2-22000000-2200-2200-2200002i−2i00−2i2i0000−2i2i2i−2i000000000000
χ4022-2-2-222-2-222-22-2-22000000-2200-2200-220000−2i2i002i−2i00002i−2i−2i2i000000000000
χ4122-2-2-222-2-22-22-22-220000002-2002-200-22002i−2i00−2i2i002i−2i−2i2i0000000000000000
χ4222-2-2-222-2-22-22-22-220000002-2002-200-2200−2i2i002i−2i00−2i2i2i−2i0000000000000000
χ4322-2-2-222-2-22-22-22-220000002-200-22002-2002i−2i00−2i2i00−2i2i2i−2i0000000000000000
χ4422-2-2-222-2-22-22-22-220000002-200-22002-200−2i2i002i−2i002i−2i−2i2i0000000000000000
χ45444-44-4-4-44-40000-444-4004-40000000000000000000000000000000000000000
χ46444-44-4-4-44-40000-44-4400-440000000000000000000000000000000000000000
χ47444-44-4-4-4-4400004-44-400-440000000000000000000000000000000000000000
χ48444-44-4-4-4-4400004-4-44004-40000000000000000000000000000000000000000
χ4944-44-4-4-44440000-4-4004-400004-4000000000000000000000000000000000000
χ5044-44-4-4-44440000-4-400-440000-44000000000000000000000000000000000000
χ5144-44-4-4-44-4-4000044004-40000-44000000000000000000000000000000000000
χ5244-44-4-4-44-4-400004400-4400004-4000000000000000000000000000000000000
χ534-444-4-44-40044-4-40000000000000000000000000000000000000022−2200000000
χ544-444-4-44-40044-4-400000000000000000000000000000000000000−222200000000
χ554-444-4-44-400-4-4440000000000000000000000000000000000002i2−2i20000000000
χ564-444-4-44-400-4-444000000000000000000000000000000000000−2i22i20000000000
χ574-4-4-44-444004-4-44000000000000000000000000000000000000000022−22000000
χ584-4-4-44-444004-4-440000000000000000000000000000000000000000−2222000000
χ594-4-4-44-44400-444-400000000000000000000000000000000000000000022−220000
χ604-4-4-44-44400-444-4000000000000000000000000000000000000000000−22220000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8888-8-8000000000000000000000000000000000000000000000000000000

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