Finite Group Databasebeta

← Group #169341

Character table — Group #169341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444442444444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-11-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-11-1-1-1-1-11-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-11-1-11111-1-1-111-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-11-1-11111-1-1-111-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-11-1-1-1-1-1-11-11-1-111-11111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-11-1-1-1-1-1-11-11-1-111-1-1-1-1-111111111-1-1
χ911111111-1-11-1-111111-111-1-1-111-1-1-1111-11-1-111-1-111-1-111-1-11-1
χ1011111111-1-11-1-111111-111-1-1-111-1-1-1111-11-1-1-1-111-1-111-1-111-11
χ1111111111-1-11-1-111111-111-1-1-1-1-11111-1-11-11-111-1-111-1-1-1-111-11
χ1211111111-1-11-1-111111-111-1-1-1-1-11111-1-11-11-1-1-111-1-11111-1-11-1
χ1311111111-1-11-1-111111-1-1-1-11111-1-11-1-11-1-11111-1-1-1-11111-1-1-11
χ1411111111-1-11-1-111111-1-1-1-11111-1-11-1-11-1-111-1-11111-1-1-1-1111-1
χ1511111111-1-11-1-111111-1-1-1-111-1-111-1-11-111-1111-1-1-1-111-1-1111-1
χ1611111111-1-11-1-111111-1-1-1-111-1-111-1-11-111-11-1-11111-1-111-1-1-11
χ172222222222222-2-2-22-2-200-2002222000-2-200000000000000000
χ182222222222222-2-2-22-2-200-200-2-2-2-20002200000000000000000
χ192222222222-2-2-22-2-2-22-22222200000-200000-200000000000000
χ202222222222-2-2-22-2-2-22-2-2-22-2-200000200000200000000000000
χ212222222222-2-2-2-222-2-2200-200000020-2002-2000000000000000
χ222222222222-2-2-2-222-2-2200-2000000-20200-22000000000000000
χ2322222222-2-22-2-2-2-2-22-220020022-2-2000-2200000000000000000
χ2422222222-2-22-2-2-2-2-22-2200200-2-2220002-200000000000000000
χ2522222222-2-2-2222-2-2-22222-2-2-200000-200000200000000000000
χ2622222222-2-2-2222-2-2-222-2-2-22200000200000-200000000000000
χ2722222222-2-2-222-222-2-2-200200000020200-2-2000000000000000
χ2822222222-2-2-222-222-2-2-2002000000-20-20022000000000000000
χ2922-2-222-2-22-2-22-2000200000002i−2i2i−2i00000000i2−i2i2−i200002−22−200
χ3022-2-222-2-22-2-22-2000200000002i−2i2i−2i00000000−i2i2−i2i20000−22−2200
χ3122-2-222-2-22-2-22-200020000000−2i2i−2i2i00000000i2−i2i2−i20000−22−2200
χ3222-2-222-2-22-2-22-200020000000−2i2i−2i2i00000000−i2i2−i2i200002−22−200
χ3322-2-222-2-2-22-2-22000200000002i−2i−2i2i00000000i2−i2−i2i200002−2−2200
χ3422-2-222-2-2-22-2-22000200000002i−2i−2i2i00000000−i2i2i2−i20000−222−200
χ3522-2-222-2-2-22-2-2200020000000−2i2i2i−2i00000000i2−i2−i2i20000−222−200
χ3622-2-222-2-2-22-2-2200020000000−2i2i2i−2i00000000−i2i2i2−i200002−2−2200
χ374444-4-4-4-40000004-400000000000000000000000022−2200000000
χ384444-4-4-4-40000004-4000000000000000000000000−222200000000
χ394444-4-4-4-4000000-440000000000000000000000000022−22000000
χ404444-4-4-4-4000000-4400000000000000000000000000−2222000000
χ4144-4-444-4-44-44-44000-4000000000000000000000000000000000
χ4244-4-444-4-4-4444-4000-4000000000000000000000000000000000
χ434-44-44-4-44000004000-400004i−4i00000000000000000000000000
χ444-44-44-4-44000004000-40000−4i4i00000000000000000000000000
χ454-44-44-4-4400000-4000404-400000000000000000000000000000
χ464-44-44-4-4400000-400040-4400000000000000000000000000000
χ4788-8-8-8-888000000000000000000000000000000000000000000
χ488-88-8-888-8000000000000000000000000000000000000000000
χ498-8-888-88-8000000000000000000000000000000000000000000
χ508-8-88-88-88000000000000000000000000000000000000000000

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