Finite Group Databasebeta

← Group #173876

Character table — Group #173876

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444224444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-1-1-111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1111-1-111-1-111-1-1-1-1-1-111111111-1-1
χ911111111-1-11-1-1-1-11111111-1-11111-1-1-1-1-11-11-1-1111-1-111-1-111-1-11-1
χ1011111111-1-11-1-1-1-11111111-1-11111-1-1-1-1-11-11-1-11-1-111-1-111-1-111-11
χ1111111111-1-11-1-1-1-11111111-1-1-1-1-1-1-11111-11-11-1111-1-1-1-11111-1-1-11
χ1211111111-1-11-1-1-1-11111111-1-1-1-1-1-1-11111-11-11-11-1-11111-1-1-1-1111-1
χ1311111111-1-11-1-1-1-111111-1-11111-1-1-1-1-1111-1-111-111-1-111-1-1-1-111-11
χ1411111111-1-11-1-1-1-111111-1-11111-1-1-1-1-1111-1-111-1-1-111-1-11111-1-11-1
χ1511111111-1-11-1-1-1-111111-1-111-1-111-111-1-1-111-11-111-1-1-1-111-1-1111-1
χ1611111111-1-11-1-1-1-111111-1-111-1-111-111-1-1-111-11-1-1-11111-1-111-1-1-11
χ1722222222222-2-222-2-2-2-2200002200-22200-2-2000000000000000000
χ1822222222222-2-222-2-2-2-220000-2-200-2-2-20022000000000000000000
χ192222222222-222-2-222-2-2-222220000-200000000-2-200000000000000
χ202222222222-222-2-222-2-2-2-2-2-2-20000-2000000002200000000000000
χ212222222222-2-2-2-2-2-2-222-200000022200-2-200-220000000000000000
χ222222222222-2-2-2-2-2-2-222-2000000-2-220022002-20000000000000000
χ2322222222-2-2222-2-2-2-2-2-22000022002-2-200-22000000000000000000
χ2422222222-2-2222-2-2-2-2-2-220000-2-200222002-2000000000000000000
χ2522222222-2-2-22222-2-222-200000022-2002200-2-20000000000000000
χ2622222222-2-2-22222-2-222-2000000-2-2-200-2-200220000000000000000
χ2722222222-2-2-2-2-22222-2-2-222-2-200002000000002-200000000000000
χ2822222222-2-2-2-2-22222-2-2-2-2-2220000200000000-2200000000000000
χ2922-22-2-2-220002i−2i2i−2i002-200000002i−2i0002-20000000000i2−i22−22−2i2−i200
χ3022-22-2-2-220002i−2i2i−2i002-200000002i−2i0002-20000000000−i2i2−22−22−i2i200
χ3122-22-2-2-220002i−2i2i−2i002-20000000−2i2i000-220000000000i2−i22−2−22−i2i200
χ3222-22-2-2-220002i−2i2i−2i002-20000000−2i2i000-220000000000−i2i2−222−2i2−i200
χ3322-22-2-2-22000−2i2i−2i2i002-200000002i−2i000-220000000000i2−i2−222−2−i2i200
χ3422-22-2-2-22000−2i2i−2i2i002-200000002i−2i000-220000000000−i2i22−2−22i2−i200
χ3522-22-2-2-22000−2i2i−2i2i002-20000000−2i2i0002-20000000000i2−i2−22−22i2−i200
χ3622-22-2-2-22000−2i2i−2i2i002-20000000−2i2i0002-20000000000−i2i22−22−2−i2i200
χ37444-44-4-4-400000004-4000004-400000000000000000000000000000
χ38444-44-4-4-400000004-400000-4400000000000000000000000000000
χ39444-44-4-4-40000000-440004-40000000000000000000000000000000
χ40444-44-4-4-40000000-44000-440000000000000000000000000000000
χ4144-44-4-4-440004i−4i−4i4i00-440000000000000000000000000000000000
χ4244-44-4-4-44000−4i4i4i−4i00-440000000000000000000000000000000000
χ434-4-444-44-44i−4i000000000000000000000000000002-22i−2i0000000000
χ444-4-444-44-44i−4i00000000000000000000000000000-22−2i2i0000000000
χ454-4-444-44-4−4i4i000000000000000000000000000002-2−2i2i0000000000
χ464-4-444-44-4−4i4i00000000000000000000000000000-222i−2i0000000000
χ474-4-4-444-4400400000000-400004i−4i000000000000000000000000000
χ484-4-4-444-4400400000000-40000−4i4i000000000000000000000000000
χ494-4-4-444-4400-40000000040000000004-40000000000000000000000
χ504-4-4-444-4400-4000000004000000000-440000000000000000000000
χ5188-8-8-888-8000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-88-8-8-888000000000000000000000000000000000000000000000

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