Finite Group Databasebeta

← Group #166237

Character table — Group #166237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444444444444224444444444442224444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11-1-111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11-1-11-1-1-1-11111-111-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1-11-1-1111-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1111-11-1-1-1111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-11-1111-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1111111-1-1-111-111-1-1-1-111111-11-1-1-1-11-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1111111-1-1-111-111-1-1-1-1111-1-1-11-111-1111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1-111-111-1-11-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-1-1-111111-111-1-111-1-1-1-111
χ172222222222222222-2-2-2-200-200-20000222200000000-2-2000000000000
χ182222222222222222-2-2-2-200-200-20000-2-2-2-20000000022000000000000
χ19222222222222-2-2-2-222-2-200200-222220000-20000-20000000000000000
χ20222222222222-2-2-2-222-2-200200-2-2-2-2-200002000020000000000000000
χ21222222222222-2-2-2-2-2-22222-222200000000000-2-200000000000000000
χ22222222222222-2-2-2-2-2-222-2-2-2-2-22000000000002200000000000000000
χ2322222222-2-2-2-222-2-222-2-200-200222-2-20000-2000020000000000000000
χ2422222222-2-2-2-222-2-222-2-200-2002-2-222000020000-20000000000000000
χ2522222222-2-2-2-222-2-2-2-222222-2-2-200000000000-2200000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2222-2000000000002-200000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2002002000022-2-200000000-22000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-20020020000-2-222000000002-2000000000000
χ29222-2-2-22-22i2i−2i−2i2i−2i2-2000000000000002-22i−2i00000000002−2i2−i22−2i2−i20000
χ30222-2-2-22-22i2i−2i−2i2i−2i2-2000000000000002-22i−2i0000000000−22−i2i2−22−i2i20000
χ31222-2-2-22-22i2i−2i−2i2i−2i2-200000000000000-22−2i2i00000000002−2i2−i2−22−i2i20000
χ32222-2-2-22-22i2i−2i−2i2i−2i2-200000000000000-22−2i2i0000000000−22−i2i22−2i2−i20000
χ33222-2-2-22-2−2i−2i2i2i−2i2i2-2000000000000002-2−2i2i00000000002−2−i2i22−2−i2i20000
χ34222-2-2-22-2−2i−2i2i2i−2i2i2-2000000000000002-2−2i2i0000000000−22i2−i2−22i2−i20000
χ35222-2-2-22-2−2i−2i2i2i−2i2i2-200000000000000-222i−2i00000000002−2−i2i2−22i2−i20000
χ36222-2-2-22-2−2i−2i2i2i−2i2i2-200000000000000-222i−2i0000000000−22i2−i22−2−i2i20000
χ37444-4-4-44-44i4i−4i−4i−4i4i-440000000000000000000000000000000000000000
χ38444-4-4-44-4−4i−4i4i4i4i−4i-440000000000000000000000000000000000000000
χ3944-44-4-4-444i−4i4i−4i000000000000000000000002-20002i−2i00000000000000
χ4044-44-4-4-444i−4i4i−4i00000000000000000000000-22000−2i2i00000000000000
χ4144-44-4-4-44−4i4i−4i4i000000000000000000000002-2000−2i2i00000000000000
χ4244-44-4-4-44−4i4i−4i4i00000000000000000000000-220002i−2i00000000000000
χ4344-4-444-4-44-4-4400000000000000000000000000000000000000002i−2i2i−2i
χ4444-4-444-4-44-4-440000000000000000000000000000000000000000−2i2i−2i2i
χ4544-4-444-4-4-444-400000000000000000000000000000000000000002i−2i−2i2i
χ4644-4-444-4-4-444-40000000000000000000000000000000000000000−2i2i2i−2i
χ474-4444-4-4-4000000004-400000000004i−4i00000000000000000000000000
χ484-4444-4-4-4000000004-40000000000−4i4i00000000000000000000000000
χ494-4444-4-4-400000000-44000000004i−4i0000000000000000000000000000
χ504-4444-4-4-400000000-4400000000−4i4i0000000000000000000000000000
χ514-4-4-44-44400000000004-40004-40000000000000000000000000000000
χ524-4-4-44-44400000000004-4000-440000000000000000000000000000000
χ534-4-4-44-4440000000000-444-40000000000000000000000000000000000
χ544-4-4-44-4440000000000-44-440000000000000000000000000000000000
χ558-88-8-88-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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