Finite Group Databasebeta

← Group #176709

Character table — Group #176709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444442224444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-11111-1-1-111-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111-1-111-1-11111-1-1-111-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-111-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-111-1-1-1-1-1-1-111-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-111-1-1-11-11-111-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-111-1-1-11-11-111-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-1-1-111-1-11-111-1111-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-1-1-111-1-11-111-11-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1111111-1-1-1-11111-1-11-111-1-1-1111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1111111-1-1-1-11111-1-11-111-1-1-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1111111-1-1-1-111-1-11111-1-11-11-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111-1-1-1-111-1-11111-1-11-11-1-1-11111-1-111-1-1-11
χ1722222222222222-2-2-2-222-2-2220000-20000-20000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-200002000020000000000000000
χ192222222222-2-2-2-222-2-2002-20022-2-2000-2200000000000000000
χ202222222222-2-2-2-222-2-2002-200-2-2220002-200000000000000000
χ212222222222-2-2-2-2-2-22200-2200000002-2000-2200000000000000
χ222222222222-2-2-2-2-2-22200-220000000-220002-200000000000000
χ2322222222-2-222-2-222-2-200-22002222000-2-200000000000000000
χ2422222222-2-222-2-222-2-200-2200-2-2-2-20002200000000000000000
χ2522222222-2-222-2-2-2-222002-2000000022000-2-200000000000000
χ2622222222-2-222-2-2-2-222002-20000000-2-20002200000000000000
χ2722222222-2-2-2-222-2-2-2-22222-2-2000020000-20000000000000000
χ2822222222-2-2-2-222-2-2-2-2-2-222220000-2000020000000000000000
χ29444-4-4-4-4400004-4000000004i−4i00000000000000000000000000
χ30444-4-4-4-4400004-400000000−4i4i00000000000000000000000000
χ31444-4-4-4-440000-4400004i−4i000000000000000000000000000000
χ32444-4-4-4-440000-440000−4i4i000000000000000000000000000000
χ3344-4-44-44-4000000004-400000000000000000000002i2−2i200000000
χ3444-4-44-44-4000000004-40000000000000000000000−2i22i200000000
χ3544-4-44-44-400000000-440000000000000000000000002i2−2i2000000
χ3644-4-44-44-400000000-44000000000000000000000000−2i22i2000000
χ374-44-4-444-44i−4i00000000000000000000000000000000002i−2i2-200
χ384-44-4-444-44i−4i0000000000000000000000000000000000−2i2i-2200
χ394-44-4-444-4−4i4i00000000000000000000000000000000002i−2i-2200
χ404-44-4-444-4−4i4i0000000000000000000000000000000000−2i2i2-200
χ414-4-44-4-4440000004-400000000004-40000000000000000000000
χ424-4-44-4-4440000004-40000000000-440000000000000000000000
χ434-4-44-4-444000000-44000000004-4000000000000000000000000
χ444-4-44-4-444000000-4400000000-44000000000000000000000000
χ454-4-4-444-44004-40000000000000000000000002-22-20000000000
χ464-4-4-444-44004-4000000000000000000000000-22-220000000000
χ474-4-4-444-4400-440000000000000000000000002-2-220000000000
χ484-4-4-444-4400-44000000000000000000000000-222-20000000000
χ4988-88-88-8-8000000000000000000000000000000000000000000
χ508-8888-8-8-8000000000000000000000000000000000000000000

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