Finite Group Databasebeta

← Group #173869

Character table — Group #173869

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444444444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-11-1-1-111-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111-1-111-1-1-1-11-1-1-111-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-111-1-1-1-1-1-1111-1-1-111-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-111-1-1-1-1-1-1111-1-1-111-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1-1-111111-1-11-1-1-1-1111111111-1-1-1-1-1-1
χ811111111111111111111-1-1-1-1-1-111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111
χ911111111-1-1-1-11-1-1111111111-1-111-1-1-1-1-111-11-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-11-1-1111111111-1-111-1-1-1-1-111-11-1-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-11-1-11111111-1-1-1-1-1-111-111-11-1-11111-1-1-1-11111-1-1-11
χ1211111111-1-1-1-11-1-11111111-1-1-1-1-1-111-111-11-1-111-1-11111-1-1-1-1111-1
χ1311111111-1-1-1-11-1-111111-1-11111-1-111-1-1-1-1-111-1111-1-1-1-111-1-1111-1
χ1411111111-1-1-1-11-1-111111-1-11111-1-111-1-1-1-1-111-11-1-11111-1-111-1-1-11
χ1511111111-1-1-1-11-1-111111-1-1-1-11111-1-1-1111-11-11-111-1-111-1-1-1-111-11
χ1611111111-1-1-1-11-1-111111-1-1-1-11111-1-1-1111-11-11-1-1-111-1-11111-1-11-1
χ172222222222222-2-2-2-2-2-220000002222-200-20000-200000000000000
χ182222222222222-2-2-2-2-2-22000000-2-2-2-2-20020000200000000000000
χ192222222222-2-2-22222-2-2-22200220000-2000-2-200000000000000000
χ202222222222-2-2-22222-2-2-2-2-200-2-20000-20002200000000000000000
χ212222222222-2-2-2-2-2-2-222-200220000002-2-2000-22000000000000000
χ222222222222-2-2-2-2-2-2-222-200-2-20000002220002-2000000000000000
χ2322222222-2-222-222-2-222-20022000000-222000-2-2000000000000000
χ2422222222-2-222-222-2-222-200-2-2000000-2-2-200022000000000000000
χ2522222222-2-222-2-2-222-2-2-22200-2-200002000-2200000000000000000
χ2622222222-2-222-2-2-222-2-2-2-2-20022000020002-200000000000000000
χ2722222222-2-2-2-2222-2-2-2-2200000022-2-2200-20000200000000000000
χ2822222222-2-2-2-2222-2-2-2-22000000-2-22220020000-200000000000000
χ292-22-22-2-22002i−2i02i−2i002-20002i−2i00000002-20000000000i2−i22−22−2i2−i200
χ302-22-22-2-22002i−2i02i−2i002-20002i−2i00000002-20000000000−i2i2−22−22−i2i200
χ312-22-22-2-22002i−2i02i−2i002-2000−2i2i0000000-220000000000i2−i22−2−22−i2i200
χ322-22-22-2-22002i−2i02i−2i002-2000−2i2i0000000-220000000000−i2i2−222−2i2−i200
χ332-22-22-2-2200−2i2i0−2i2i002-20002i−2i0000000-220000000000i2−i2−222−2−i2i200
χ342-22-22-2-2200−2i2i0−2i2i002-20002i−2i0000000-220000000000−i2i22−2−22i2−i200
χ352-22-22-2-2200−2i2i0−2i2i002-2000−2i2i00000002-20000000000i2−i2−22−22i2−i200
χ362-22-22-2-2200−2i2i0−2i2i002-2000−2i2i00000002-20000000000−i2i22−22−2−i2i200
χ37444-4-44-4-400000004-400000004-4000000000000000000000000000
χ38444-4-44-4-400000004-40000000-44000000000000000000000000000
χ39444-4-44-4-40000000-440004-40000000000000000000000000000000
χ40444-4-44-4-40000000-44000-440000000000000000000000000000000
χ414-44-44-4-44004i−4i0−4i4i00-440000000000000000000000000000000000
χ424-44-44-4-4400−4i4i04i−4i00-440000000000000000000000000000000000
χ434-4-4444-4-44i−4i000000000000000000000000000002-22i−2i0000000000
χ444-4-4444-4-44i−4i00000000000000000000000000000-22−2i2i0000000000
χ454-4-4444-4-4−4i4i000000000000000000000000000002-2−2i2i0000000000
χ464-4-4444-4-4−4i4i00000000000000000000000000000-222i−2i0000000000
χ474-4-4-4-444400004000000-4000000004i−4i00000000000000000000000
χ484-4-4-4-444400004000000-400000000−4i4i00000000000000000000000
χ494-4-4-4-44440000-400000040000004-40000000000000000000000000
χ504-4-4-4-44440000-40000004000000-440000000000000000000000000
χ5188-88-8-8-88000000000000000000000000000000000000000000000
χ5288-8-88-88-8000000000000000000000000000000000000000000000
χ538-888-8-88-8000000000000000000000000000000000000000000000

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