Finite Group Databasebeta

← Group #173526

Character table — Group #173526

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444224444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111111111-1-1
χ511111111111111111111-1-1-1-1111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-11-1-111-1-111-1-1-11-111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-11-1-111-1-111-1-1-11-11-1-1-1-11111-1-1-1-111
χ911111111-1-11-1-11-1-1111111-1-1-11111-1-1-1-11-11-1-1111-1-111-1-111-1-11-1
χ1011111111-1-11-1-11-1-1111111-1-1-11111-1-1-1-11-11-1-11-1-111-1-111-1-111-11
χ1111111111-1-11-1-11-1-1111111-1-1-1-1-1-1-11111-1111-1-111-1-1-1-111-1-1111-1
χ1211111111-1-11-1-11-1-1111111-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-111-1-1-11
χ1311111111-1-11-1-11-1-11111-1-111-111-1-1-1-1111-1-111-111-1-111-1-1-1-111-11
χ1411111111-1-11-1-11-1-11111-1-111-111-1-1-1-1111-1-111-1-1-111-1-11111-1-11-1
χ1511111111-1-11-1-11-1-11111-1-111-1-1-11111-1-1-11-1-11111-1-1-1-11111-1-1-11
χ1611111111-1-11-1-11-1-11111-1-111-1-1-11111-1-1-11-1-111-1-11111-1-1-1-1111-1
χ1722222222222-2-2-2-2-2-2-22-200002002200-2-200020-200000000000000
χ1822222222222-2-2-2-2-2-2-22-20000200-2-20022000-20200000000000000
χ192222222222-222-2-2-222-2-22222-20000000000-20-2000000000000000
χ202222222222-222-2-2-222-2-2-2-2-2-2-20000000000202000000000000000
χ212222222222-2-2-2222-2-2-220000-222002200-2-2000000000000000000
χ222222222222-2-2-2222-2-2-220000-2-2-200-2-20022000000000000000000
χ2322222222-2-2222-222-2-22-20000-200220022000-20-200000000000000
χ2422222222-2-2222-222-2-22-20000-200-2-200-2-200020200000000000000
χ2522222222-2-2-2222-2-2-2-2-22000022200-2-200-22000000000000000000
χ2622222222-2-2-2222-2-2-2-2-2200002-2-20022002-2000000000000000000
χ2722222222-2-2-2-2-2-22222-2-222-2-220000000000-202000000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-2222000000000020-2000000000000000
χ292-22-2-2-2222-200022-2000-2000002-2002-200000000i2−i2i2−i2i2−i2i2−i2000000
χ302-22-2-2-2222-200022-2000-2000002-2002-200000000−i2i2−i2i2−i2i2−i2i2000000
χ312-22-2-2-2222-200022-2000-200000-2200-2200000000i2−i2i2−i2−i2i2−i2i2000000
χ322-22-2-2-2222-200022-2000-200000-2200-2200000000−i2i2−i2i2i2−i2i2−i2000000
χ332-22-2-2-222-220002-22000-2000002-200-2200000000i2−i2−i2i2i2−i2−i2i2000000
χ342-22-2-2-222-220002-22000-2000002-200-2200000000−i2i2i2−i2−i2i2i2−i2000000
χ352-22-2-2-222-220002-22000-200000-22002-200000000i2−i2−i2i2−i2i2i2−i2000000
χ362-22-2-2-222-220002-22000-200000-22002-200000000−i2i2i2−i2i2−i2−i2i2000000
χ37444-44-4-4-4000000004-400004-400000000000000000000000000000
χ38444-44-4-4-4000000004-40000-4400000000000000000000000000000
χ39444-44-4-4-400000000-44004-40000000000000000000000000000000
χ40444-44-4-4-400000000-4400-440000000000000000000000000000000
χ4144-44-4-44-40040000000-4000000004-4000000000000000000000000
χ4244-44-4-44-40040000000-400000000-44000000000000000000000000
χ4344-44-4-44-400-4000000040000000000004i−4i00000000000000000000
χ4444-44-4-44-400-400000004000000000000−4i4i00000000000000000000
χ4544-4-4-44-440004i−4i00000000000000000000000000000000002i−2i2-200
χ4644-4-4-44-440004i−4i0000000000000000000000000000000000−2i2i-2200
χ4744-4-4-44-44000−4i4i00000000000000000000000000000000002i−2i-2200
χ4844-4-4-44-44000−4i4i0000000000000000000000000000000000−2i2i2-200
χ494-44-4-4-4444-4000-4-440004000000000000000000000000000000000
χ504-44-4-4-444-44000-44-40004000000000000000000000000000000000
χ518-888-88-8-8000000000000000000000000000000000000000000000
χ528-8-888-8-88000000000000000000000000000000000000000000000
χ538-8-8-8888-8000000000000000000000000000000000000000000000

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