Finite Group Databasebeta

← Group #175241

Character table — Group #175241

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222224444444444444444444222244444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11-1-11111-1-1-1-11-11-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111
χ511111111111111111111-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-111111-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-11-1-111111-1-11-11-111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-11-11-11-1-1-1-111111111
χ911111111-1-1-1-11-1-11111111-1-111-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11111111-1-111-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-11111-1-1-1-111-111-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-111-1-111-1-111-111-111-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-111111-1-11111-1-1-111-1-1-11-1111-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-111111-1-11111-1-1-1-1-111-11-1111-1-111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-111111-1-111-1-1-11111-1-11-11-11-1-1111-1-1-1-111-1-111
χ1611111111-1-1-1-11-1-111111-1-111-1-1-111-1-1111-11-11-1-11-1-11111-1-111-1-1
χ17222222222222-2-2-2-222-2-2000000-2000000200-2020-2000000000000
χ18222222222222-2-2-2-222-2-2000000-2000000-20020-202000000000000
χ192222222222-2-2222-2-2-22-2000022-2-2-200000-2200000000000000000
χ202222222222-2-2222-2-2-22-20000-2-2-222000002-200000000000000000
χ212222222222-2-2-2-2-22-2-2-2222-2-2002000000000020-20000000000000
χ222222222222-2-2-2-2-22-2-2-22-2-2220020000000000-2020000000000000
χ2322222222-2-2222-2-2-2-2-22-200002222200000-2-200000000000000000
χ2422222222-2-2222-2-2-2-2-22-20000-2-22-2-2000002200000000000000000
χ2522222222-2-222-2222-2-2-22222200-20000000000-20-20000000000000
χ2622222222-2-222-2222-2-2-22-2-2-2-200-200000000002020000000000000
χ2722222222-2-2-2-2-222-222-2-2000000200000020020-20-2000000000000
χ2822222222-2-2-2-2-222-222-2-20000002000000-200-20202000000000000
χ29444-4-4-44-44-40000000000000000000000000000000000000002i−2i2i−2i
χ30444-4-4-44-44-4000000000000000000000000000000000000000−2i2i−2i2i
χ31444-4-4-44-4-440000000000000000000000000000000000000002i−2i−2i2i
χ32444-4-4-44-4-44000000000000000000000000000000000000000−2i2i2i−2i
χ3344-444-4-4-4000000004-4000000000000000000000000000002i2−2i20000
χ3444-444-4-4-4000000004-400000000000000000000000000000−2i22i20000
χ3544-444-4-4-400000000-440000000000000000000000000002i2−2i2000000
χ3644-444-4-4-400000000-44000000000000000000000000000−2i22i2000000
χ3744-4-4-44-4400000004000-44i−4i0000000000000000000000000000000
χ3844-4-4-44-4400000004000-4−4i4i0000000000000000000000000000000
χ3944-4-4-44-440000000-40004004-400000000000000000000000000000
χ4044-4-4-44-440000000-4000400-4400000000000000000000000000000
χ414-444-44-4-4004-4000000000000000000000000000002i−2i2i−2i00000000
χ424-444-44-4-4004-400000000000000000000000000000−2i2i−2i2i00000000
χ434-444-44-4-400-44000000000000000000000000000002i−2i−2i2i00000000
χ444-444-44-4-400-4400000000000000000000000000000−2i2i2i−2i00000000
χ454-4-44-4-444000004-4000000000000002-22-200000000000000000000
χ464-4-44-4-444000004-400000000000000-22-2200000000000000000000
χ474-4-44-4-44400000-44000000000000002-2-2200000000000000000000
χ484-4-44-4-44400000-4400000000000000-222-200000000000000000000
χ494-4-4-4444-40000400000-4000000004i−4i000000000000000000000000
χ504-4-4-4444-40000400000-400000000−4i4i000000000000000000000000
χ514-4-4-4444-40000-4000004000004-4000000000000000000000000000
χ524-4-4-4444-40000-400000400000-44000000000000000000000000000
χ538-88-88-8-88000000000000000000000000000000000000000000000

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