Finite Group Databasebeta

← Group #168489

Character table — Group #168489

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422448888888888888888224444444444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11-1-1111111-1-1-1-1
χ911111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-11111-1-1-1-1-11-111-11-11-111-1-111-1-1
χ1011111111-1-1-1-11-1-1-1-11-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-11-111-11-11-1-111-1-111
χ1111111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-11111-11-111-11-11-1-1-111-1-111
χ1211111111-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-11-111-11-1111-1-111-1-1
χ1311111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-111-1-1111-1-1-1-111
χ1411111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1-111-1-1-11111-1-1
χ1511111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1-111-1-11-1-11111-1-1
χ1611111111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1-1-111111111-1-1-1-11-111-1-1-111-111-1-1-1-111
χ172222222222222-2-2-2-2-222-2-22-20000000000000000000000020200-2-200000000
χ182222222222222-2-2-2-2-222-2-22-200000000000000000000000-20-2002200000000
χ19222222222222-222-2-22-2-2-2-2-2200000000000000000000022000-2-20000000000
χ20222222222222-222-2-22-2-2-2-2-22000000000000000000000-2-2000220000000000
χ21222222222222-2-2-222-2-2-222-2-222220000000000000000-2000-20000000000000
χ22222222222222-2-2-222-2-2-222-2-2-2-2-2-20000000000000000200020000000000000
χ2322222222-2-2-2-222222-2-2-2-2-22-20000000000000000000000020-200-2200000000
χ2422222222-2-2-2-222222-2-2-2-2-22-200000000000000000000000-202002-200000000
χ2522222222-2-2-2-2-222-2-2-22222-2-222-2-200000000000000002000-20000000000000
χ2622222222-2-2-2-2-222-2-2-22222-2-2-2-2220000000000000000-200020000000000000
χ2722222222-2-2-2-2-2-2-222222-2-2-220000000000000000000002-2000-220000000000
χ2822222222-2-2-2-2-2-2-222222-2-2-22000000000000000000000-220002-20000000000
χ2922-22-2-22-22i2i−2i−2i0002i−2i0002-2002-22i−2ii2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000000000
χ3022-22-2-22-22i2i−2i−2i0002i−2i0002-2002-22i−2i−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000000000
χ3122-22-2-22-22i2i−2i−2i0002i−2i0002-200-22−2i2ii2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000000000
χ3222-22-2-22-22i2i−2i−2i0002i−2i0002-200-22−2i2i−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000000000
χ3322-22-2-22-2−2i−2i2i2i000−2i2i0002-2002-2−2i2ii2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000000000
χ3422-22-2-22-2−2i−2i2i2i000−2i2i0002-2002-2−2i2i−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000000000
χ3522-22-2-22-2−2i−2i2i2i000−2i2i0002-200-222i−2ii2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000000000
χ3622-22-2-22-2−2i−2i2i2i000−2i2i0002-200-222i−2i−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000000000
χ37444-44-4-4-4000004-40000000000000000000002-22-22-22-2000000000000000000
χ38444-44-4-4-4000004-4000000000000000000000-22-22-22-22000000000000000000
χ39444-44-4-4-400000-440000000000000000000002-22-2-22-22000000000000000000
χ40444-44-4-4-400000-44000000000000000000000-22-222-22-2000000000000000000
χ4144-44-4-44-44i4i−4i−4i000−4i4i000-440000000000000000000000000000000000000000
χ4244-44-4-44-4−4i−4i4i4i0004i−4i000-440000000000000000000000000000000000000000
χ4344-4-4-44-44000000000400000-40000000000002i2−2i2−2i22i20000000000000000000000
χ4444-4-4-44-44000000000400000-4000000000000−2i22i22i2−2i20000000000000000000000
χ4544-4-4-44-44000000000-4000004000000000000000022−22−2222000000000000000000
χ4644-4-4-44-44000000000-40000040000000000000000−222222−22000000000000000000
χ474-444-4-4-444i−4i4i−4i0000000000000000000000000000000000000000002-22i−2i0000
χ484-444-4-4-444i−4i4i−4i000000000000000000000000000000000000000000-22−2i2i0000
χ494-444-4-4-44−4i4i−4i4i0000000000000000000000000000000000000000002-2−2i2i0000
χ504-444-4-4-44−4i4i−4i4i000000000000000000000000000000000000000000-222i−2i0000
χ514-44-4-444-400004000000000-4000002i2−2i22i2−2i2000000000000000000000000000000
χ524-44-4-444-400004000000000-400000−2i22i2−2i22i2000000000000000000000000000000
χ534-44-4-444-40000-4000000000400000000022−2222−2200000000000000000000000000
χ544-44-4-444-40000-40000000004000000000−2222−222200000000000000000000000000
χ554-4-4444-4-44-4-4400000000000000000000000000000000000000000000002i−2i2i−2i
χ564-4-4444-4-44-4-440000000000000000000000000000000000000000000000−2i2i−2i2i
χ574-4-4444-4-4-444-400000000000000000000000000000000000000000000002i−2i−2i2i
χ584-4-4444-4-4-444-40000000000000000000000000000000000000000000000−2i2i2i−2i
χ594-4-4-44-44400000000004-4000000002-2-222-2-2200000000000000000000000000
χ604-4-4-44-44400000000004-400000000-222-2-222-200000000000000000000000000
χ614-4-4-44-4440000000000-44000000002-2-22-222-200000000000000000000000000
χ624-4-4-44-4440000000000-4400000000-222-22-2-2200000000000000000000000000

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