Finite Group Databasebeta

← Group #166256

Character table — Group #166256

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-1-1-1111-11-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-111-1-1111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-111-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-1-1-1111-1-111-1-111-11-1111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-1-1-1111-1-111-1-1-1-1-11-11-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-11-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-1-11-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-111-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-111-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1111-11111-1-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1111-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-111-111-1-1-11111-1-11-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-111-111-1-1-11-1-11-1-111111-1-111-1-1-1-111
χ172222222222222222-2-2-2-200-2000022-2002200000-20-200000000000000
χ182222222222222222-2-2-2-200-20000-2-2-200-2-20000020200000000000000
χ19222222222222-2-2-2-222-2-2222220000-200000000-20-2000000000000000
χ20222222222222-2-2-2-222-2-2-2-22-2-20000-200000000202000000000000000
χ21222222222222-2-2-2-2-2-22200-200220022200-2-200000000000000000000
χ22222222222222-2-2-2-2-2-22200-200-2-2002-2-2002200000000000000000000
χ2322222222-2-2-2-222-2-222-2-222-2-2-2000020000000020-2000000000000000
χ2422222222-2-2-2-222-2-222-2-2-2-2-2220000200000000-202000000000000000
χ2522222222-2-2-2-222-2-2-2-222002002200-2-2-200-2200000000000000000000
χ2622222222-2-2-2-222-2-2-2-22200200-2-200-222002-200000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2002000022200-2-20000020-200000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-20020000-2-22002200000-20200000000000000
χ29222-2-2-2-222i2i−2i−2i2i−2i2-2000000000002i−2i0002-20000000000i2−i22−22−2i2−i20000
χ30222-2-2-2-222i2i−2i−2i2i−2i2-2000000000002i−2i0002-20000000000−i2i2−22−22−i2i20000
χ31222-2-2-2-222i2i−2i−2i2i−2i2-200000000000−2i2i000-220000000000i2−i22−2−22−i2i20000
χ32222-2-2-2-222i2i−2i−2i2i−2i2-200000000000−2i2i000-220000000000−i2i2−222−2i2−i20000
χ33222-2-2-2-22−2i−2i2i2i−2i2i2-2000000000002i−2i000-220000000000i2−i2−222−2−i2i20000
χ34222-2-2-2-22−2i−2i2i2i−2i2i2-2000000000002i−2i000-220000000000−i2i22−2−22i2−i20000
χ35222-2-2-2-22−2i−2i2i2i−2i2i2-200000000000−2i2i0002-20000000000i2−i2−22−22i2−i20000
χ36222-2-2-2-22−2i−2i2i2i−2i2i2-200000000000−2i2i0002-20000000000−i2i22−22−2−i2i20000
χ37444-4-4-4-444i4i−4i−4i−4i4i-440000000000000000000000000000000000000000
χ38444-4-4-4-44−4i−4i4i4i4i−4i-440000000000000000000000000000000000000000
χ3944-44-44-4-4000000004-4000004-40000000000000000000000000000000
χ4044-44-44-4-4000000004-400000-440000000000000000000000000000000
χ4144-44-44-4-400000000-44004-40000000000000000000000000000000000
χ4244-44-44-4-400000000-4400-440000000000000000000000000000000000
χ434-4444-4-4-44-44-400000000000000000000000000000000000000002-22-2
χ444-4444-4-4-44-44-40000000000000000000000000000000000000000-22-22
χ454-4444-4-4-4-44-4400000000000000000000000000000000000000002-2-22
χ464-4444-4-4-4-44-440000000000000000000000000000000000000000-222-2
χ474-44-4-444-44i−4i−4i4i0000000000000000000000002-200002i−2i000000000000
χ484-44-4-444-44i−4i−4i4i000000000000000000000000-220000−2i2i000000000000
χ494-44-4-444-4−4i4i4i−4i0000000000000000000000002-20000−2i2i000000000000
χ504-44-4-444-4−4i4i4i−4i000000000000000000000000-2200002i−2i000000000000
χ514-4-44-4-44400000000004-400000000004-4000000000000000000000000
χ524-4-44-4-44400000000004-40000000000-44000000000000000000000000
χ534-4-44-4-4440000000000-44000004-400000000000000000000000000000
χ544-4-44-4-4440000000000-4400000-4400000000000000000000000000000
χ5588-8-88-88-8000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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