Finite Group Databasebeta

← Group #166753

Character table — Group #166753

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444442222444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1111-1-111111111-111-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1111-1-11111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-11-111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111111-1-1-1-11111
χ911111111-1-1-1-1-1-111-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-111-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-11-111-1-1111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-11-111-1-11-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-111-1-11111-1-111-111-1-11111-1-1-1-1-1-11-111-11-1-111-1-11111-1-1
χ1411111111-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-1-1-11111-1-11-111-1111-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1-1-11-111-1-11-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1-1-111111-111-1-11-111-1-1-1-11111-1-1
χ17222222222222222-2-2-2-2-22-22200-2-2-200000000000-2200000000000000000
χ18222222222222222-2-2-2-2-22-2-2-200-222000000000002-200000000000000000
χ19222222222222-2-2-22-2-2-2-2-22000020000000000002000-20-22000000000000
χ20222222222222-2-2-22-2-2-2-2-2200002000000000000-2000202-2000000000000
χ21222222222222-2-2-2-22222-2-20022-2002200000000000-20-200000000000000
χ22222222222222-2-2-2-22222-2-200-2-2-200-2-20000000000020200000000000000
χ2322222222-2-2-2-222-2222-2-2-220000-2000000000000200020-2-2000000000000
χ2422222222-2-2-2-222-2222-2-2-220000-2000000000000-2000-2022000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-20022200-2-20000000000020-200000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-200-2-22002200000000000-20200000000000000
χ2722222222-2-2-2-2-2-22-222-2-22-2220022200000000000-2-200000000000000000
χ2822222222-2-2-2-2-2-22-222-2-22-2-2-2002-2-2000000000002200000000000000000
χ29222-2-22-2-22i2i−2i−2i00002i−2i2-200002-20002i−2ii2i2−i2−i222−2−20000000000000000i2−i22−2
χ30222-2-22-2-22i2i−2i−2i00002i−2i2-200002-20002i−2i−i2−i2i2i2−2−2220000000000000000−i2i2−22
χ31222-2-22-2-22i2i−2i−2i00002i−2i2-20000-22000−2i2ii2i2−i2−i222−2−20000000000000000−i2i2−22
χ32222-2-22-2-22i2i−2i−2i00002i−2i2-20000-22000−2i2i−i2−i2i2i2−2−2220000000000000000i2−i22−2
χ33222-2-22-2-2−2i−2i2i2i0000−2i2i2-200002-2000−2i2ii2i2−i2−i2−2−2220000000000000000i2−i2−22
χ34222-2-22-2-2−2i−2i2i2i0000−2i2i2-200002-2000−2i2i−i2−i2i2i222−2−20000000000000000−i2i22−2
χ35222-2-22-2-2−2i−2i2i2i0000−2i2i2-20000-220002i−2ii2i2−i2−i2−2−2220000000000000000−i2i22−2
χ36222-2-22-2-2−2i−2i2i2i0000−2i2i2-20000-220002i−2i−i2−i2i2i222−2−20000000000000000i2−i2−22
χ37444-4-44-4-44i4i−4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ38444-4-44-4-4−4i−4i4i4i00004i−4i-44000000000000000000000000000000000000000
χ3944-44-4-44-44-44-4000000000000000000000000000000000002i−2i2i−2i00000000
χ4044-44-4-44-44-44-400000000000000000000000000000000000−2i2i−2i2i00000000
χ4144-44-4-44-4-44-44000000000000000000000000000000000002i−2i−2i2i00000000
χ4244-44-4-44-4-44-4400000000000000000000000000000000000−2i2i2i−2i00000000
χ4344-4-44-4-444i−4i−4i4i0000000000000000000000000000000000000002-22i−2i0000
χ4444-4-44-4-444i−4i−4i4i000000000000000000000000000000000000000-22−2i2i0000
χ4544-4-44-4-44−4i4i4i−4i0000000000000000000000000000000000000002-2−2i2i0000
χ4644-4-44-4-44−4i4i4i−4i000000000000000000000000000000000000000-222i−2i0000
χ474-4444-4-4-400004-4000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ484-4444-4-4-400004-400000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ494-4444-4-4-40000-44000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ504-4444-4-4-40000-4400000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ514-44-4-4-4440000000400000-400000000000002i2−2i2−2i22i200000000000000000000
χ524-44-4-4-4440000000400000-40000000000000−2i22i22i2−2i200000000000000000000
χ534-44-4-4-4440000000-400000400000000022−22−2222000000000000000000000000
χ544-44-4-4-4440000000-4000004000000000−222222−22000000000000000000000000
χ554-4-44-44-44000000400000-40000004i−4i000000000000000000000000000000
χ564-4-44-44-44000000400000-4000000−4i4i000000000000000000000000000000
χ574-4-44-44-44000000-400000404-400000000000000000000000000000000000
χ584-4-44-44-44000000-40000040-4400000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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