Finite Group Databasebeta

← Group #166990

Character table — Group #166990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444444444444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1111111111-1-1-1-1-1111-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-1-1-111111111
χ511111111111111111111111-1-111-1-11111111111-1-1-11-1-1-1-1-11-1-1-1-1-1-11111
χ611111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-11111111-1-1-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-11111
χ911111111-1-1-1-1-1-11-1-111111-11111-1-1-1-11111-1-1-1-1-11-1-11-11111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-111111-11111-1-1-1-1-1-1-1-11111-11-1-11-1-1-11111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-111111-111-1-1-1-1111111-1-1-1-1-1-111-11111-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-11-1-111111-111-1-1-1-111-1-1-1-11111-1-111-11-1-11-11111-1-111-1-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-11-11-1-11-1-1-1111-1-11111-1-1
χ1411111111-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-111111-11-1-1111-11-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-1111111-111-111-1-1-1-1-1-11111-1-1
χ1722222222222222-2-2-222-2-2-2-20022002200000000000-200000-20000000000
χ1822222222222222-2-2-222-2-2-2-200-2-200-2-20000000000020000020000000000
χ19222222222222-2-22-2-2-2-2-2-222000000000000000002-20-2200000000000000
χ20222222222222-2-22-2-2-2-2-2-22200000000000000000-2202-200000000000000
χ21222222222222-2-2-222-2-222-2-22200-2-2000000000020000000-200000000000
χ22222222222222-2-2-222-2-222-2-2-2-200220000000000-20000000200000000000
χ2322222222-2-2-2-222222-2-2-2-22-200000000000000000220-2-200000000000000
χ2422222222-2-2-2-222222-2-2-2-22-200000000000000000-2-202200000000000000
χ2522222222-2-2-2-222-2-2-2-2-222-222200220000000000-20000000-200000000000
χ2622222222-2-2-2-222-2-2-2-2-222-22-2-200-2-2000000000020000000200000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-22002200-2-200000000000200000-20000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2200-2-2002200000000000-20000020000000000
χ292-22-22-22-22i2i−2i−2i2i−2i0002-20000002-2002i−2ii2i2−i2−i222−2−20000000000000000i2−i22−2
χ302-22-22-22-22i2i−2i−2i2i−2i0002-20000002-2002i−2i−i2−i2i2i2−2−2220000000000000000−i2i2−22
χ312-22-22-22-22i2i−2i−2i2i−2i0002-2000000-2200−2i2ii2i2−i2−i222−2−20000000000000000−i2i2−22
χ322-22-22-22-22i2i−2i−2i2i−2i0002-2000000-2200−2i2i−i2−i2i2i2−2−2220000000000000000i2−i22−2
χ332-22-22-22-2−2i−2i2i2i−2i2i0002-20000002-200−2i2ii2i2−i2−i2−2−2220000000000000000i2−i2−22
χ342-22-22-22-2−2i−2i2i2i−2i2i0002-20000002-200−2i2i−i2−i2i2i222−2−20000000000000000−i2i22−2
χ352-22-22-22-2−2i−2i2i2i−2i2i0002-2000000-22002i−2ii2i2−i2−i2−2−2220000000000000000−i2i22−2
χ362-22-22-22-2−2i−2i2i2i−2i2i0002-2000000-22002i−2i−i2−i2i2i222−2−20000000000000000i2−i2−22
χ37444-4-44-4-44-44-40000000000000000000000000000000000000002-22-20000
χ38444-4-44-4-44-44-4000000000000000000000000000000000000000-22-220000
χ39444-4-44-4-4-44-440000000000000000000000000000000000000002-2-220000
χ40444-4-44-4-4-44-44000000000000000000000000000000000000000-222-20000
χ4144-44-4-44-40000004000000-4000000000000022−2222−2200000000000000000000
χ4244-44-4-44-40000004000000-40000000000000−2222−222200000000000000000000
χ4344-44-4-44-4000000-400000040000000002i2−2i22i2−2i2000000000000000000000000
χ4444-44-4-44-4000000-40000004000000000−2i22i2−2i22i2000000000000000000000000
χ4544-4-44-4-44000000000004-40000004i−4i000000000000000000000000000000
χ4644-4-44-4-44000000000004-4000000−4i4i000000000000000000000000000000
χ4744-4-44-4-4400000000000-44004i−4i0000000000000000000000000000000000
χ4844-4-44-4-4400000000000-4400−4i4i0000000000000000000000000000000000
χ494-444-4-4-444i−4i−4i4i0000000000000000000000000000000002i−2i002-200000000
χ504-444-4-4-444i−4i−4i4i000000000000000000000000000000000−2i2i00-2200000000
χ514-444-4-4-44−4i4i4i−4i0000000000000000000000000000000002i−2i00-2200000000
χ524-444-4-4-44−4i4i4i−4i000000000000000000000000000000000−2i2i002-200000000
χ534-44-44-44-44i4i−4i−4i−4i4i000-440000000000000000000000000000000000000000
χ544-44-44-44-4−4i−4i4i4i4i−4i000-440000000000000000000000000000000000000000
χ554-4-4-4-444400000004-4000000000000002-2-222-2-2200000000000000000000
χ564-4-4-4-444400000004-400000000000000-222-2-222-200000000000000000000
χ574-4-4-4-44440000000-44000000000000002-2-22-222-200000000000000000000
χ584-4-4-4-44440000000-4400000000000000-222-22-2-2200000000000000000000
χ598-8-8888-8-8000000000000000000000000000000000000000000000000000

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