Finite Group Databasebeta

← Group #169330

Character table — Group #169330

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ911111111-1-111-1-11111-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-111-1-11111-1-111-1-111-1-11-11-111-1-1-1-111-1-111-1-111-11
χ1111111111-1-111-1-11111-1-111-1-1-1-1111-1-11-1-11111-1-111-1-1-1-111-11
χ1211111111-1-111-1-11111-1-111-1-1-1-1111-1-11-1-111-1-111-1-11111-1-11-1
χ1311111111-1-111-1-11111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-111-1-1111-1
χ1411111111-1-111-1-11111-1-1-1-11111-1-1-111-1-1-111-1-11111-1-111-1-1-11
χ1511111111-1-111-1-11111-1-1-1-111-1-111-11-1111-1-111-1-1-1-11111-1-1-11
χ1611111111-1-111-1-11111-1-1-1-111-1-111-11-1111-1-1-1-11111-1-1-1-1111-1
χ1722222222222-222-2-22-2-2-222220000-2-200000000000000000000
χ1822222222222-222-2-22-2-2-2-2-2-2-200002200000000000000000000
χ192222222222-22-2-2-2-2-22-220000000000002-22-200000000000000
χ202222222222-22-2-2-2-2-22-22000000000000-22-2200000000000000
χ212222222222-2-2-2-222-2-22-20000222200-2-2000000000000000000
χ222222222222-2-2-2-222-2-22-20000-2-2-2-20022000000000000000000
χ2322222222-2-22-2-2-2-2-22-22222-2-20000-2200000000000000000000
χ2422222222-2-22-2-2-2-2-22-222-2-22200002-200000000000000000000
χ2522222222-2-2-2222-2-2-222-20000000000002-2-2200000000000000
χ2622222222-2-2-2222-2-2-222-2000000000000-222-200000000000000
χ2722222222-2-2-2-22222-2-2-22000022-2-200-22000000000000000000
χ2822222222-2-2-2-22222-2-2-220000-2-222002-2000000000000000000
χ2922-222-2-2-22-2-202-20020002i−2i2i−2i0000000000002−22−2i2−i2i2−i2000000
χ3022-222-2-2-22-2-202-20020002i−2i2i−2i000000000000−22−22−i2i2−i2i2000000
χ3122-222-2-2-22-2-202-2002000−2i2i−2i2i0000000000002−22−2−i2i2−i2i2000000
χ3222-222-2-2-22-2-202-2002000−2i2i−2i2i000000000000−22−22i2−i2i2−i2000000
χ3322-222-2-2-2-22-20-220020002i−2i−2i2i0000000000002−2−22i2−i2−i2i2000000
χ3422-222-2-2-2-22-20-220020002i−2i−2i2i000000000000−222−2−i2i2i2−i2000000
χ3522-222-2-2-2-22-20-22002000−2i2i2i−2i0000000000002−2−22−i2i2i2−i2000000
χ3622-222-2-2-2-22-20-22002000−2i2i2i−2i000000000000−222−2i2−i2−i2i2000000
χ37444-4-4-4-440000004-400000000004-40000000000000000000000
χ38444-4-4-4-440000004-40000000000-440000000000000000000000
χ39444-4-4-4-44000000-44000000004-4000000000000000000000000
χ40444-4-4-4-44000000-4400000000-44000000000000000000000000
χ4144-444-4-4-44-440-4400-4000000000000000000000000000000000
χ4244-444-4-4-4-44404-400-4000000000000000000000000000000000
χ434-444-44-4-4000400000-40000000000000000000000000022−220000
χ444-444-44-4-4000400000-400000000000000000000000000−22220000
χ454-444-44-4-4000-400000400000000000000000000000000002i2−2i200
χ464-444-44-4-4000-40000040000000000000000000000000000−2i22i200
χ4788-8-8-888-8000000000000000000000000000000000000000000
χ488-88-88-88-8000000000000000000000000000000000000000000
χ498-8-88-8-888000000000000000000000000000000000000000000
χ508-8-8-888-88000000000000000000000000000000000000000000

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