Finite Group Databasebeta

← Group #166809

Character table — Group #166809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444442224444448888888822244444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-11-1-11-111-1-1-1-1-11111
χ511111111111111111111111-1-111-1-11111111111-1111-11-1-1-111-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11-11-1-11-1-1-1-11111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-11111-1-1-1-1111-111-1-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-1-1-1-111-11-1-111111-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-1111111-111-1-1-1-111-1-1-1-11111-11111-11-1-1-1-11-1-11111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-11111-1-1-1-1-111-1-1111-1-1-11-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-111111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111111-1-1-1-11-1-11-1-1-11111-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-111-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2002200-2-20000000000020-200000000000000
χ1822222222222222-2-2-2-2-2-222-200-2-2002200000000000-20200000000000000
χ19222222222222-2-22222-2-2-2-2-222002200000000000000-200-2000000000000
χ20222222222222-2-22222-2-2-2-2-2-2-200-2-2000000000000002002000000000000
χ21222222222222-2-2-2-2-2-222-2-220000000000000000200000-20-200200000000
χ22222222222222-2-2-2-2-2-222-2-220000000000000000-20000020200-200000000
χ2322222222-2-2-2-22222-2-222-2-2-2000000000000000020000020-200-200000000
χ2422222222-2-2-2-22222-2-222-2-2-20000000000000000-200000-20200200000000
χ2522222222-2-2-2-222-2-222-2-2-2-222200-2-200000000000000-2002000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-22-2-2002200000000000000200-2000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-22220022002200000000000-20-200000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-222200-2-200-2-20000000000020200000000000000
χ2922-22-22-2-22i2i−2i−2i002i−2i2-2000002-2002i−2i0022−2−2i2i2−i2−i20000000000002−2i2−i20000
χ3022-22-22-2-22i2i−2i−2i002i−2i2-2000002-2002i−2i00−2−222−i2−i2i2i2000000000000−22−i2i20000
χ3122-22-22-2-22i2i−2i−2i002i−2i2-200000-2200−2i2i0022−2−2i2i2−i2−i2000000000000−22−i2i20000
χ3222-22-22-2-22i2i−2i−2i002i−2i2-200000-2200−2i2i00−2−222−i2−i2i2i20000000000002−2i2−i20000
χ3322-22-22-2-2−2i−2i2i2i00−2i2i2-2000002-200−2i2i0022−2−2−i2−i2i2i20000000000002−2−i2i20000
χ3422-22-22-2-2−2i−2i2i2i00−2i2i2-2000002-200−2i2i00−2−222i2i2−i2−i2000000000000−22i2−i20000
χ3522-22-22-2-2−2i−2i2i2i00−2i2i2-200000-22002i−2i0022−2−2−i2−i2i2i2000000000000−22i2−i20000
χ3622-22-22-2-2−2i−2i2i2i00−2i2i2-200000-22002i−2i00−2−222i2i2−i2−i20000000000002−2−i2i20000
χ37444-4-4-4-4400004i−4i000000000000000002i−2i2i−2i2-22-200000000000000000000
χ38444-4-4-4-4400004i−4i00000000000000000−2i2i−2i2i-22-2200000000000000000000
χ39444-4-4-4-440000−4i4i000000000000000002i−2i2i−2i-22-2200000000000000000000
χ40444-4-4-4-440000−4i4i00000000000000000−2i2i−2i2i2-22-200000000000000000000
χ4144-44-44-4-44i4i−4i−4i00−4i4i-4400000000000000000000000000000000000000000
χ4244-44-44-4-4−4i−4i4i4i004i−4i-4400000000000000000000000000000000000000000
χ4344-4-44-44-400000000004-40000000000000002i2−2i2−2i22i200000000000000000000
χ4444-4-44-44-400000000004-4000000000000000−2i22i22i2−2i200000000000000000000
χ4544-4-44-44-40000000000-44000000000002i2−2i2−2i22i2000000000000000000000000
χ4644-4-44-44-40000000000-4400000000000−2i22i22i2−2i2000000000000000000000000
χ474-4444-4-4-44i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i
χ484-4444-4-4-44i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i
χ494-4444-4-4-4−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i
χ504-4444-4-4-4−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i
χ514-4-44-4-4444-4-4400000000000000000000000000002-20000002-2000000000
χ524-4-44-4-4444-4-440000000000000000000000000000-22000000-22000000000
χ534-4-44-4-444-444-400000000000000000000000000002-2000000-22000000000
χ544-4-44-4-444-444-40000000000000000000000000000-220000002-2000000000
χ554-4-4-444-440000000000004-400000004-40000000000000000000000000000
χ564-4-4-444-440000000000004-40000000-440000000000000000000000000000
χ574-4-4-444-44000000000000-440004-400000000000000000000000000000000
χ584-4-4-444-44000000000000-44000-4400000000000000000000000000000000
χ598-88-8-888-8000000000000000000000000000000000000000000000000000

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