Finite Group Databasebeta

← Group #166754

Character table — Group #166754

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
χ3111111111111111111111111-1-1111-1-111111111-11-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111111111-1-1-1-1
χ51111111111111111111111-1-1111-1-11111111111-1-1-11-1-11-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11-1-1-1-1111111111-11-11-1-11-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111111-1-1-1-11111
χ911111111-1-1-1-1-1-111-1-111111111-1-1-1-1-11111-1-1-1-1111-1-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-11-1-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-11-111-1-11-1-111-1-11111-1-1
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-11111-11-111-1-1111-1-111-1-1-1-111
χ1311111111-1-1-1-1-1-111-1-11111-1-111-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-111-1-11111-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1-1-11-111-11-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1-1-111111-111-11-1-111-1-1-1-11111-1-1
χ17222222222222222-2-2-2-2-22-20022-200-2-200000000000200-20000000000000
χ18222222222222222-2-2-2-2-22-200-2-2-2002200000000000-20020000000000000
χ19222222222222-2-2-22-2-2-2-2-220000200000000000020-20200-2000000000000
χ20222222222222-2-2-22-2-2-2-2-2200002000000000000-2020-2002000000000000
χ21222222222222-2-2-2-22222-2-22200-22200000000000-2000-200000000000000
χ22222222222222-2-2-2-22222-2-2-2-200-2-2-2000000000002000200000000000000
χ2322222222-2-2-2-222-2222-2-2-220000-200000000000020-20-2002000000000000
χ2422222222-2-2-2-222-2222-2-2-220000-2000000000000-2020200-2000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-222002-2-200000000000-2000200000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-200222000000000002000-200000000000000
χ2722222222-2-2-2-2-2-22-222-2-22-200222002200000000000-200-20000000000000
χ2822222222-2-2-2-2-2-22-222-2-22-200-2-2200-2-20000000000020020000000000000
χ29222-2-2-22-22i2i−2i−2i00002i−2i2-2002-20002i−2i00i2i2−i2−i222−2−20000000000000000i2−i22−2
χ30222-2-2-22-22i2i−2i−2i00002i−2i2-2002-20002i−2i00−i2−i2i2i2−2−2220000000000000000−i2i2−22
χ31222-2-2-22-22i2i−2i−2i00002i−2i2-200-22000−2i2i00i2i2−i2−i222−2−20000000000000000−i2i2−22
χ32222-2-2-22-22i2i−2i−2i00002i−2i2-200-22000−2i2i00−i2−i2i2i2−2−2220000000000000000i2−i22−2
χ33222-2-2-22-2−2i−2i2i2i0000−2i2i2-2002-2000−2i2i00i2i2−i2−i2−2−2220000000000000000i2−i2−22
χ34222-2-2-22-2−2i−2i2i2i0000−2i2i2-2002-2000−2i2i00−i2−i2i2i222−2−20000000000000000−i2i22−2
χ35222-2-2-22-2−2i−2i2i2i0000−2i2i2-200-220002i−2i00i2i2−i2−i2−2−2220000000000000000−i2i22−2
χ36222-2-2-22-2−2i−2i2i2i0000−2i2i2-200-220002i−2i00−i2−i2i2i222−2−20000000000000000i2−i2−22
χ37444-4-4-44-44i4i−4i−4i0000−4i4i-44000000000000000000000000000000000000000
χ38444-4-4-44-4−4i−4i4i4i00004i−4i-44000000000000000000000000000000000000000
χ3944-444-4-4-4000000400000-40004-4000000000000000000000000000000000
χ4044-444-4-4-4000000400000-4000-44000000000000000000000000000000000
χ4144-444-4-4-4000000-4000004000000004i−4i0000000000000000000000000000
χ4244-444-4-4-4000000-400000400000000−4i4i0000000000000000000000000000
χ434-444-4-4-444i−4i4i−4i0000000000000000000000000000000000000002-22i−2i0000
χ444-444-4-4-444i−4i4i−4i000000000000000000000000000000000000000-22−2i2i0000
χ454-444-4-4-44−4i4i−4i4i0000000000000000000000000000000000000002-2−2i2i0000
χ464-444-4-4-44−4i4i−4i4i000000000000000000000000000000000000000-222i−2i0000
χ474-44-444-4-44-4-44000000000000000000000000000000000002i−2i2i−2i00000000
χ484-44-444-4-44-4-4400000000000000000000000000000000000−2i2i−2i2i00000000
χ494-44-444-4-4-444-4000000000000000000000000000000000002i−2i−2i2i00000000
χ504-44-444-4-4-444-400000000000000000000000000000000000−2i2i2i−2i00000000
χ514-4-44-444-40000000400000-40000000002i2−2i22i2−2i2000000000000000000000000
χ524-4-44-444-40000000400000-4000000000−2i22i2−2i22i2000000000000000000000000
χ534-4-44-444-40000000-4000004000000000000022−2222−2200000000000000000000
χ544-4-44-444-40000000-40000040000000000000−2222−222200000000000000000000
χ554-4-4-44-44400004-4000000000000000002-2-222-2-2200000000000000000000
χ564-4-4-44-44400004-400000000000000000-222-2-222-200000000000000000000
χ574-4-4-44-4440000-44000000000000000002-2-22-222-200000000000000000000
χ584-4-4-44-4440000-4400000000000000000-222-22-2-2200000000000000000000
χ5988-8-8-88-88000000000000000000000000000000000000000000000000000

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