Finite Group Databasebeta

← Group #166552

Character table — Group #166552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444444444444448888888844444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11111111111-1-11-1-1-1-11-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-11111-1-11111111111-1-1-111-111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-111-1-1-1-11111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-111111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-111111-11111-1-1-1-1-1-1-1-11111-1-111-111-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-111111-111-1-111-1-11111-1-1-1-1-1-11-1111-1-11-1111-1-1-1-111
χ1211111111-1-1-1-1-1-11-1-111111-111-1-111-1-1-1-1-1-11111111-11-1-1-1-11-11-1-11111-1-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-111-1-11-1-111-1-11-1-111-1-111
χ1411111111-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1111-1-111-1-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-1-1-1-11-1111-111-1-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-1111111-11-1-1-11-111-111-1-1-1-111
χ17222222222222222-2-2-2-2-2-22-2220000220000000000-20000-2000000000000
χ18222222222222222-2-2-2-2-2-22-2-2-20000-2-20000000000200002000000000000
χ19222222222222-2-2-22222-2-2-2-20022-2-2000000000000000000-220000000000
χ20222222222222-2-2-22222-2-2-2-200-2-2220000000000000000002-20000000000
χ21222222222222-2-2-2-2-2-2-222-2200000000000000000002-200000-2200000000
χ22222222222222-2-2-2-2-2-2-222-220000000000000000000-22000002-200000000
χ2322222222-2-2-2-222-222-2-222-2-200000000000000000002200000-2-200000000
χ2422222222-2-2-2-222-222-2-222-2-20000000000000000000-2-2000002200000000
χ2522222222-2-2-2-222-2-2-222-2-2-22002222000000000000000000-2-20000000000
χ2622222222-2-2-2-222-2-2-222-2-2-2200-2-2-2-2000000000000000000220000000000
χ2722222222-2-2-2-2-2-2222-2-2-2-222220000-2-20000000000-200002000000000000
χ2822222222-2-2-2-2-2-2222-2-2-2-222-2-2000022000000000020000-2000000000000
χ292-222-22-2-222-2-22-2-2000000202-200002-2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i20000
χ302-222-22-2-222-2-22-2-2000000202-200002-2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i20000
χ312-222-22-2-222-2-22-2-200000020-220000-22i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i20000
χ322-222-22-2-222-2-22-2-200000020-220000-22−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i20000
χ332-222-22-2-2-2-222-22-2000000202-20000-22i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i20000
χ342-222-22-2-2-2-222-22-2000000202-20000-22−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i20000
χ352-222-22-2-2-2-222-22-200000020-2200002-2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i20000
χ362-222-22-2-2-2-222-22-200000020-2200002-2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i20000
χ37444-4-4-44-4000000000004-40000000000000022−2222−2200000000000000000000
χ38444-4-4-44-4000000000004-400000000000000−2222−222200000000000000000000
χ39444-4-4-44-400000000000-44000000000022−2222−22000000000000000000000000
χ40444-4-4-44-400000000000-440000000000−2222−2222000000000000000000000000
χ4144-444-4-4-40000000004-4000000004-4000000000000000000000000000000
χ4244-444-4-4-40000000004-400000000-44000000000000000000000000000000
χ4344-444-4-4-4000000000-440000004-400000000000000000000000000000000
χ4444-444-4-4-4000000000-44000000-4400000000000000000000000000000000
χ4544-4-4-44-444i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i
χ4644-4-4-44-444i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i
χ4744-4-4-44-44−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i
χ4844-4-4-44-44−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i
χ494-444-44-4-444-4-4-444000000-40000000000000000000000000000000000000
χ504-444-44-4-4-4-4444-44000000-40000000000000000000000000000000000000
χ514-44-44-4-4400000004-4000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ524-44-44-4-4400000004-400000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ534-44-44-4-440000000-44000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ544-44-44-4-440000000-4400000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ554-4-4-4444-44i−4i−4i4i0000000000000000000000000002i−2i0002-20000000000000
χ564-4-4-4444-44i−4i−4i4i000000000000000000000000000−2i2i000-220000000000000
χ574-4-4-4444-4−4i4i4i−4i0000000000000000000000000002i−2i000-220000000000000
χ584-4-4-4444-4−4i4i4i−4i000000000000000000000000000−2i2i0002-20000000000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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