Finite Group Databasebeta

← Group #173805

Character table — Group #173805

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444224444444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-111-1-111-1-11-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-11-1-111-1-111-1-11-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-11-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-11-1-1-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-111-1-1111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-111-1-11-1-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-11-111-1-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-11-1-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1-1111-111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-111-1-1111-1-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-11-1-11-1111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-11111-1-11-1-11-11-1-11111-1-111-1-1-11
χ17222222222222-2-2-2-222-2-200-20022002200-20-200000000000000000
χ18222222222222-2-2-2-222-2-200-200-2-200-2-20020200000000000000000
χ192222222222-2-222-2-2-2-22222-222000000000-20-20000000000000000
χ202222222222-2-222-2-2-2-222-2-2-2-2-20000000002020000000000000000
χ212222222222-2-2-2-222-2-2-2-200200002200-2-200002-200000000000000
χ222222222222-2-2-2-222-2-2-2-20020000-2-200220000-2200000000000000
χ2322222222-2-2222222-2-2-2-200-200002200220000-2-200000000000000
χ2422222222-2-2222222-2-2-2-200-20000-2-200-2-200002200000000000000
χ2522222222-2-222-2-2-2-2-2-222222-2-2000000000-2020000000000000000
χ2622222222-2-222-2-2-2-2-2-222-2-222200000000020-20000000000000000
χ2722222222-2-2-2-222-2-222-2-2002002200-2-20020-200000000000000000
χ2822222222-2-2-2-222-2-222-2-200200-2-2002200-20200000000000000000
χ292-222-2-2-22002i−2i2i−2i2-2000000000002i−2i002-200000000002−2i2−i2i2−i22−200
χ302-222-2-2-22002i−2i2i−2i2-2000000000002i−2i002-20000000000−22−i2i2−i2i2−2200
χ312-222-2-2-22002i−2i2i−2i2-200000000000−2i2i00-2200000000002−2i2−i2−i2i2−2200
χ322-222-2-2-22002i−2i2i−2i2-200000000000−2i2i00-220000000000−22−i2i2i2−i22−200
χ332-222-2-2-2200−2i2i−2i2i2-2000000000002i−2i00-2200000000002−2−i2i2i2−i2−2200
χ342-222-2-2-2200−2i2i−2i2i2-2000000000002i−2i00-220000000000−22i2−i2−i2i22−200
χ352-222-2-2-2200−2i2i−2i2i2-200000000000−2i2i002-200000000002−2−i2i2−i2i22−200
χ362-222-2-2-2200−2i2i−2i2i2-200000000000−2i2i002-20000000000−22i2−i2i2−i2−2200
χ37444-44-4-4-44-4000000000000000000000000000002-22-20000000000
χ38444-44-4-4-44-400000000000000000000000000000-22-220000000000
χ39444-44-4-4-4-44000000000000000000000000000002-2-220000000000
χ40444-44-4-4-4-4400000000000000000000000000000-222-20000000000
χ414-444-4-4-44004i−4i−4i4i-440000000000000000000000000000000000000
χ424-444-4-4-4400−4i4i4i−4i-440000000000000000000000000000000000000
χ434-4-4444-4-4000000004-4000000000004i−4i0000000000000000000000
χ444-4-4444-4-4000000004-400000000000−4i4i0000000000000000000000
χ454-4-4444-4-400000000-4400000004i−4i00000000000000000000000000
χ464-4-4444-4-400000000-440000000−4i4i00000000000000000000000000
χ474-4-4-44-44400000000004-40004-40000000000000000000000000000
χ484-4-4-44-44400000000004-4000-440000000000000000000000000000
χ494-4-4-44-4440000000000-444-40000000000000000000000000000000
χ504-4-4-44-4440000000000-44-440000000000000000000000000000000
χ5188-88-8-88-8000000000000000000000000000000000000000000000
χ5288-8-8-88-88000000000000000000000000000000000000000000000
χ538-88-8-888-8000000000000000000000000000000000000000000000

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