Finite Group Databasebeta

← Group #173519

Character table — Group #173519

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444222222444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-11-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-111-1-11-1-111-1-1-111-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1111-1-1-1-111-1-1-111-11111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-111
χ911111111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-11-1
χ1011111111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111-11
χ1111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-11111-1-111-1111-1-111-1-1-1-111-11
χ1211111111-1-11-1-1-1-11111111-1-1-1-1-1-1-11111-1-111-11-1-111-1-11111-1-11-1
χ1311111111-1-11-1-1-1-111111-1-111-1-1-111-1-11111-11-1-111-1-1-1-111-1-1111-1
χ1411111111-1-11-1-1-1-111111-1-111-1-1-111-1-11111-11-1-1-1-11111-1-111-1-1-11
χ1511111111-1-11-1-1-1-111111-1-1-1-111-11111-1-11-11-11-111-1-1-1-11111-1-1-11
χ1611111111-1-11-1-1-1-111111-1-1-1-111-11111-1-11-11-11-1-1-11111-1-1-1-1111-1
χ172222222222222-2-2-2-2-22-2000022-2000022000-2-2000000000000000
χ182222222222222-2-2-2-2-22-20000-2-2-20000-2-200022000000000000000
χ192222222222-2-2-222-222-2-2002200-20022000-2-200000000000000000
χ202222222222-2-2-222-222-2-200-2-200-200-2-20002200000000000000000
χ212222222222-2-2-2-2-22-2-2-222200002-2-2000020000-200000000000000
χ222222222222-2-2-2-2-22-2-2-22-2-200002220000-20000200000000000000
χ2322222222-2-22-2-222-2-2-22-200002220000-2-20002-2000000000000000
χ2422222222-2-22-2-222-2-2-22-20000-2-22000022000-22000000000000000
χ2522222222-2-2-222222-2-2-22220000-2220000-20000-200000000000000
χ2622222222-2-2-222222-2-2-22-2-20000-2-2-2000020000200000000000000
χ2722222222-2-2-222-2-2-222-2-2002200200-2-2000-2200000000000000000
χ2822222222-2-2-222-2-2-222-2-200-2-200200220002-200000000000000000
χ292-222-2-2-222-222-200000-2000002-2000002-2000000i2−i2i2−i20000i2−i2i2−i200
χ302-222-2-2-222-222-200000-2000002-2000002-2000000−i2i2−i2i20000−i2i2−i2i200
χ312-222-2-2-222-222-200000-200000-2200000-22000000i2−i2i2−i20000−i2i2−i2i200
χ322-222-2-2-222-222-200000-200000-2200000-22000000−i2i2−i2i20000i2−i2i2−i200
χ332-222-2-2-22-222-2200000-2000002-200000-22000000i2−i2−i2i20000i2−i2−i2i200
χ342-222-2-2-22-222-2200000-2000002-200000-22000000−i2i2i2−i20000−i2i2i2−i200
χ352-222-2-2-22-222-2200000-200000-22000002-2000000i2−i2−i2i20000−i2i2i2−i200
χ362-222-2-2-22-222-2200000-200000-22000002-2000000−i2i2i2−i20000i2−i2−i2i200
χ3744-44-44-4-4000004i−4i00000000000000000000000000002-22i−2i000000
χ3844-44-44-4-4000004i−4i0000000000000000000000000000-22−2i2i000000
χ3944-44-44-4-400000−4i4i00000000000000000000000000002-2−2i2i000000
χ4044-44-44-4-400000−4i4i0000000000000000000000000000-222i−2i000000
χ414-444-4-4-444-4-4-440000040000000000000000000000000000000000
χ424-444-4-4-44-44-44-40000040000000000000000000000000000000000
χ434-44-4-444-400000004000-400000004i−4i000000000000000000000000
χ444-44-4-444-400000004000-40000000−4i4i000000000000000000000000
χ454-44-4-444-40000000-400044-40000000000000000000000000000000
χ464-44-4-444-40000000-40004-440000000000000000000000000000000
χ474-4-4-444-44000000004-4000000000004-40000000000000000000000
χ484-4-4-444-44000000004-400000000000-440000000000000000000000
χ494-4-4-444-4400000000-4400004-400000000000000000000000000000
χ504-4-4-444-4400000000-440000-4400000000000000000000000000000
χ51888-88-8-8-8000000000000000000000000000000000000000000000
χ5288-8-8-8-888000000000000000000000000000000000000000000000
χ538-8-888-88-8000000000000000000000000000000000000000000000

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