Finite Group Databasebeta

← Group #174992

Character table — Group #174992

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111444444444444888888888161616161616161616161616161616161616161616161616
order12222222444444444444222244444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-111-1-1-1-111-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11-1-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1
χ911111111-1-11-1-1-1-11111111-1-1-111-1-111111-1-11-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-11-1-1-1-11111111-1-1-111-1-11-1-111-1-11-1-111-1-111-1-111-1-111
χ1111111111-1-11-1-1-1-11111111-1-1-1-1-111-111-1-1111-11-1-111-1-1-1-111-1-111
χ1211111111-1-11-1-1-1-11111111-1-1-1-1-111-1-1-1-1-1111-1111-1-11111-1-111-1-1
χ1311111111-1-11-1-1-1-111111-1-111-111-1-1111-1-111-11-1-1-1-1-11111-1-1-1-111
χ1411111111-1-11-1-1-1-111111-1-111-111-1-11-1-1-1-111-11-11111-1-1-1-11111-1-1
χ1511111111-1-11-1-1-1-111111-1-111-1-1-111-11111-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-11-1-1-1-111111-1-111-1-1-111-1-1-111-1-1-1111111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-220000-200000002-22-200000000000000000
χ182222222222222-2-2-2-2-2-220000-20000000-22-2200000000000000000
χ192222222222-2-2-22222-2-2-20000-22222-200000000-200000000000000
χ202222222222-2-2-22222-2-2-20000-2-2-2-2-2200000000200000000000000
χ212222222222-2-2-2-2-2-2-222-22222200000000000-2-2000000000000000
χ222222222222-2-2-2-2-2-2-222-2-2-2-2-220000000000022000000000000000
χ2322222222-2-22-2-222-2-2-2-220000200000002-2-2200000000000000000
χ2422222222-2-22-2-222-2-2-2-22000020000000-222-200000000000000000
χ2522222222-2-2-22222-2-222-222-2-2-200000000000-22000000000000000
χ2622222222-2-2-22222-2-222-2-2-222-2000000000002-2000000000000000
χ2722222222-2-2-222-2-222-2-2-20000222-2-2-200000000200000000000000
χ2822222222-2-2-222-2-222-2-2-200002-2-222200000000-200000000000000
χ29444-44-4-4-40000000004-40004-400000000000000000000000000000
χ30444-44-4-4-40000000004-4000-4400000000000000000000000000000
χ31444-44-4-4-4000000000-4404-40000000000000000000000000000000
χ32444-44-4-4-4000000000-440-440000000000000000000000000000000
χ3344-44-4-4-4400000004-400000000004i−4i000000000000000000000000
χ3444-44-4-4-4400000004-40000000000−4i4i000000000000000000000000
χ3544-44-4-4-440000000-44000000004i−4i00000000000000000000000000
χ3644-44-4-4-440000000-4400000000−4i4i00000000000000000000000000
χ3744-4-4-444-44-40000000000000000000000000000000000000002i−2i2i−2i
χ3844-4-4-444-44-4000000000000000000000000000000000000000−2i2i−2i2i
χ3944-4-4-444-4-440000000000000000000000000000000000000002i−2i−2i2i
χ4044-4-4-444-4-44000000000000000000000000000000000000000−2i2i2i−2i
χ414-44-4-44-4400400000000-40000000000000000000000000002i2−2i20000
χ424-44-4-44-4400400000000-4000000000000000000000000000−2i22i20000
χ434-44-4-44-4400-4000000004000000000000000000000000022−22000000
χ444-44-4-44-4400-40000000040000000000000000000000000−2222000000
χ454-4-4444-4-4000004i−4i0000000000000002-200000002i−2i000000000000
χ464-4-4444-4-4000004i−4i000000000000000-220000000−2i2i000000000000
χ474-4-4444-4-400000−4i4i0000000000000002-20000000−2i2i000000000000
χ484-4-4444-4-400000−4i4i000000000000000-2200000002i−2i000000000000
χ494-4-4-44-4440004-400000000000000000000000000002-22-200000000
χ504-4-4-44-4440004-40000000000000000000000000000-22-2200000000
χ514-4-4-44-444000-4400000000000000000000000000002-2-2200000000
χ524-4-4-44-444000-440000000000000000000000000000-222-200000000
χ538-888-8-88-8000000000000000000000000000000000000000000000

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