Finite Group Databasebeta

← Group #173716

Character table — Group #173716

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444222244444444444444488888888888824
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-11-1-11111111-1-1-111-1-111-1-11-11-11-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-11111111-1-1-111-1-111-1-11-11-11-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-111-1-111-11-111-111-1-111-1-1-1-111-11
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-111-1-111-11-111-1-1-111-1-11111-1-11-1
χ1311111111-1-1-1-11-1-111111-1-111-111-1-1-1-1111-1-11-1111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-11-1-111111-1-111-111-1-1-1-1111-1-11-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-11-1-111111-1-111-1-1-11111-1-1-111-1-1111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11-1-111111-1-111-1-1-11111-1-1-111-1-11-1-11111-1-111-1-1-11
χ172222222222222-2-2-2-2-2-222222-2000000000000-2-200000000000000
χ182222222222222-2-2-2-2-2-22-2-2-2-2-20000000000002200000000000000
χ192222222222-2-2-22222-2-2-20000-20000222200-2-20000000000000000
χ202222222222-2-2-22222-2-2-20000-20000-2-2-2-200220000000000000000
χ212222222222-2-2-2-2-2-2-222-20000222-2-20000-22000000000000000000
χ222222222222-2-2-2-2-2-2-222-200002-2-22200002-2000000000000000000
χ2322222222-2-222-222-2-222-20000-222220000-2-2000000000000000000
χ2422222222-2-222-222-2-222-20000-2-2-2-2-2000022000000000000000000
χ2522222222-2-222-2-2-222-2-2-200002000022-2-200-220000000000000000
χ2622222222-2-222-2-2-222-2-2-2000020000-2-222002-20000000000000000
χ2722222222-2-2-2-2222-2-2-2-2222-2-22000000000000-2200000000000000
χ2822222222-2-2-2-2222-2-2-2-22-2-22220000000000002-200000000000000
χ29222-22-2-2-22-22-2-200000022-22-2000000000000000i2−i2i2−i2i2−i2i2−i2000000
χ30222-22-2-2-22-22-2-200000022-22-2000000000000000−i2i2−i2i2−i2i2−i2i2000000
χ31222-22-2-2-22-22-2-20000002-22-22000000000000000i2−i2i2−i2−i2i2−i2i2000000
χ32222-22-2-2-22-22-2-20000002-22-22000000000000000−i2i2−i2i2i2−i2i2−i2000000
χ33222-22-2-2-2-22-22-200000022-2-22000000000000000i2−i2−i2i2i2−i2−i2i2000000
χ34222-22-2-2-2-22-22-200000022-2-22000000000000000−i2i2i2−i2−i2i2i2−i2000000
χ35222-22-2-2-2-22-22-20000002-222-2000000000000000i2−i2−i2i2−i2i2i2−i2000000
χ36222-22-2-2-2-22-22-20000002-222-2000000000000000−i2i2i2−i2i2−i2−i2i2000000
χ37444-44-4-4-44-4-444000000-4000000000000000000000000000000000
χ38444-44-4-4-4-444-44000000-4000000000000000000000000000000000
χ3944-4-4-44-4400000004-4000000000000004-400000000000000000000
χ4044-4-4-44-4400000004-400000000000000-4400000000000000000000
χ4144-4-4-44-440000000-440000000000004-40000000000000000000000
χ4244-4-4-44-440000000-44000000000000-440000000000000000000000
χ434-44-4-4-4440000000004-4000000004-4000000000000000000000000
χ444-44-4-4-4440000000004-400000000-44000000000000000000000000
χ454-44-4-4-444000000000-440000004-400000000000000000000000000
χ464-44-4-4-444000000000-44000000-4400000000000000000000000000
χ474-4-444-4-44000004-4000000000000000000000000000000002-22-200
χ484-4-444-4-44000004-400000000000000000000000000000000-22-2200
χ494-4-444-4-4400000-44000000000000000000000000000000002-2-2200
χ504-4-444-4-4400000-4400000000000000000000000000000000-222-200
χ5188-88-8-88-8000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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