Finite Group Databasebeta

← Group #349553

Character table — Group #349553

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244448888888888888888888888888888888888816161616161616163232
order12222222444444444444224444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-1-1-111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ611111111111111111111-1-111-1-1-1-111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111111-1-1111-1-111-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111111111111-1-1111-1-111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111111111111-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-11
χ1211111111111111111-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-11-1
χ1311111111111111111-1-11-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111111111111-1-11-1-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111111-1-11-1-1-1-1-1-111-1-111-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ1611111111111111111-1-11-1-1-1-1-1-111-1-111-111-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2-222-222-22-2-2-2-20000-222000000000000000000000000000000
χ182222222222-2-222-2-2-222-2-2-2-2222220000-2-2-2000000000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-2222-2-2-22200002-2-2000000000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22-222-2-20000222000000000000000000000000000000
χ2122222222-2-222-2-222-222-2002-200002222-200-2-200000000-2-2000000000000000000
χ2222222222-2-222-2-222-222-2002-20000-2-2-2-2-200220000000022000000000000000000
χ2322222222-2-222-2-222-2-2-2-200-22000022-2-2200-2-20000000022000000000000000000
χ2422222222-2-222-2-222-2-2-2-200-220000-2-2222002200000000-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222200-2-2000000002000022-2-222-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222200-2-20000000020000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-22002200000000-2000022-2-2-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-22002200000000-20000-2-22222-2-200000000000000000000
χ2922-22-22-2-22222-2-2-2-2200-22-2002-2002-2000002-22-22-2000000000000000000000000
χ3022-22-22-2-22222-2-2-2-2200-22-2002-200-2200000-22-22-22000000000000000000000000
χ3122-22-22-2-22222-2-2-2-2200-2-2200-22002-2000002-2-22-22000000000000000000000000
χ3222-22-22-2-22222-2-2-2-2200-2-2200-2200-2200000-222-22-2000000000000000000000000
χ3322-22-22-2-222-2-2-2-222-20022-200-2200002i−2i0000000002i−2i2i−2i2i−2i000000000000000000
χ3422-22-22-2-222-2-2-2-222-20022-200-220000−2i2i000000000−2i2i−2i2i−2i2i000000000000000000
χ3522-22-22-2-222-2-2-2-222-2002-22002-200002i−2i000000000−2i2i−2i2i2i−2i000000000000000000
χ3622-22-22-2-222-2-2-2-222-2002-22002-20000−2i2i0000000002i−2i2i−2i−2i2i000000000000000000
χ3722-22-22-2-2-2-22222-2-2-20020000002i−2i2-20002i−2i-2200002i−2i−2i2i00000000000000000000
χ3822-22-22-2-2-2-22222-2-2-20020000002i−2i-220002i−2i2-20000−2i2i2i−2i00000000000000000000
χ3922-22-22-2-2-2-22222-2-2-2002000000−2i2i2-2000−2i2i-220000−2i2i2i−2i00000000000000000000
χ4022-22-22-2-2-2-22222-2-2-2002000000−2i2i-22000−2i2i2-200002i−2i−2i2i00000000000000000000
χ4122-22-22-2-2-2-2-2-22222200-20000002i−2i002i−2i0−2i2i00-222-20000−2i2i000000000000000000
χ4222-22-22-2-2-2-2-2-22222200-20000002i−2i00−2i2i0−2i2i002-2-2200002i−2i000000000000000000
χ4322-22-22-2-2-2-2-2-22222200-2000000−2i2i002i−2i02i−2i002-2-220000−2i2i000000000000000000
χ4422-22-22-2-2-2-2-2-22222200-2000000−2i2i00−2i2i02i−2i00-222-200002i−2i000000000000000000
χ45444-4-4-44-44-4004-4000000000000000000000000000000000000000000022−22000000
χ46444-4-4-44-44-4004-40000000000000000000000000000000000000000000−2222000000
χ47444-4-4-44-4-4400-440000000000000000000000000000000000000000022−2200000000
χ48444-4-4-44-4-4400-4400000000000000000000000000000000000000000−222200000000
χ4944-4-44-4-444-400-4400000000000000000000000000000000000002i22i2−2i2−2i20000000000
χ5044-4-44-4-444-400-440000000000000000000000000000000000000−2i2−2i22i22i20000000000
χ5144-4-44-4-44-44004-40000000000000000000000000000000002i22i2−2i2−2i200000000000000
χ5244-4-44-4-44-44004-4000000000000000000000000000000000−2i2−2i22i22i200000000000000
χ534-444-4-4-44004-4004-4000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ544-444-4-4-44004-4004-400000000000000000000000000000000000−2i22i2−2i22i20000000000
χ554-444-4-4-4400-4400-4400000000000000000000000000000002i2−2i22i2−2i200000000000000
χ564-444-4-4-4400-4400-440000000000000000000000000000000−2i22i2−2i22i200000000000000
χ574-4-444-44-4004-400-440000000000000000000000000000000000000000000002i2−2i200
χ584-4-444-44-4004-400-44000000000000000000000000000000000000000000000−2i22i200
χ594-4-444-44-400-44004-400000000000000000000000000000000000000000002i2−2i20000
χ604-4-444-44-400-44004-40000000000000000000000000000000000000000000−2i22i20000
χ614-4-4-4-44440000000004-400000000000000000000000000002-2-222-2-220000000000
χ624-4-4-4-44440000000004-40000000000000000000000000000-222-2-222-20000000000
χ634-4-4-4-4444000000000-4400000000000000000000000000002-2-22-222-20000000000
χ644-4-4-4-4444000000000-440000000000000000000000000000-222-22-2-220000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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