Finite Group Databasebeta

← Group #166807

Character table — Group #166807

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444422444444444444444448888888822224444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-1111111111-111-1-1-11-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111111111
χ51111111111111111111111-1-1111-1-11111111111-1-1-1-11-1-1-11-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-11-1111111-1-1-1-1
χ71111111111111111111111-1-11-1-1-1-1-1-111111111-11-1-1-111-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111-1-1-1-11111
χ911111111-1-1-1-1-1-11-1-11111111-111-1-1-1-11111-1-1-1-11111-11-1-11-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-11111111-111-1-1-1-1-1-1-1-1111111-1-1-11-1-11-111-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-11-1111-11-1-11-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-111111-1-1-11-11-1-111111-1-111-1-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ1411111111-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-11-1-111111-1-1-1-1-111111111-1-1-1-1-11-1-111-11-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-11-1-111111-1-1-1-1-11111-1-1-1-11111-111111-11-1-1-1-1-1-11111-1-1
χ1722222222222222-2-2-22-2-2-2222-200-2-20000000000-20000002000000000000
χ1822222222222222-2-2-22-2-2-22-2-2-2002200000000002000000-2000000000000
χ19222222222222-2-22-2-2-2-2-22-20020000000000000002000-2200-20000000000
χ20222222222222-2-22-2-2-2-2-22-2002000000000000000-20002-20020000000000
χ21222222222222-2-2-222-222-2-200-2220022000000000000-2000-200000000000
χ22222222222222-2-2-222-222-2-200-2-2-200-2-20000000000002000200000000000
χ2322222222-2-2-2-222222-2-2-22-200-20000000000000002000-2-20020000000000
χ2422222222-2-2-2-222222-2-2-22-200-2000000000000000-20002200-20000000000
χ2522222222-2-2-2-222-2-2-2-222-2-20022200-2-20000000000002000-200000000000
χ2622222222-2-2-2-222-2-2-2-222-2-2002-2-20022000000000000-2000200000000000
χ2722222222-2-2-2-2-2-2-2222-2-2-2222200220000000000-2000000-2000000000000
χ2822222222-2-2-2-2-2-2-2222-2-2-22-2-2200-2-2000000000020000002000000000000
χ292-2222-2-2-22i2i−2i−2i0002i−2i02-2000002-2002i−2i22−2−2i2i2−i2−i200000000000000002−2i2−i2
χ302-2222-2-2-22i2i−2i−2i0002i−2i02-2000002-2002i−2i−2−222−i2−i2i2i20000000000000000−22−i2i2
χ312-2222-2-2-22i2i−2i−2i0002i−2i02-200000-2200−2i2i22−2−2i2i2−i2−i20000000000000000−22−i2i2
χ322-2222-2-2-22i2i−2i−2i0002i−2i02-200000-2200−2i2i−2−222−i2−i2i2i200000000000000002−2i2−i2
χ332-2222-2-2-2−2i−2i2i2i000−2i2i02-2000002-200−2i2i22−2−2−i2−i2i2i200000000000000002−2−i2i2
χ342-2222-2-2-2−2i−2i2i2i000−2i2i02-2000002-200−2i2i−2−222i2i2−i2−i20000000000000000−22i2−i2
χ352-2222-2-2-2−2i−2i2i2i000−2i2i02-200000-22002i−2i22−2−2−i2−i2i2i20000000000000000−22i2−i2
χ362-2222-2-2-2−2i−2i2i2i000−2i2i02-200000-22002i−2i−2−222i2i2−i2−i200000000000000002−2−i2i2
χ37444-4-44-4-4000000400000-4000000000022−2222−22000000000000000000000000
χ38444-4-44-4-4000000400000-40000000000−2222−2222000000000000000000000000
χ39444-4-44-4-4000000-4000004000000000000002i2−2i22i2−2i200000000000000000000
χ40444-4-44-4-4000000-400000400000000000000−2i22i2−2i22i200000000000000000000
χ4144-44-4-44-44i−4i4i−4i0000000000000000000000000000000000000002-22i−2i0000
χ4244-44-4-44-44i−4i4i−4i000000000000000000000000000000000000000-22−2i2i0000
χ4344-44-4-44-4−4i4i−4i4i0000000000000000000000000000000000000002-2−2i2i0000
χ4444-44-4-44-4−4i4i−4i4i000000000000000000000000000000000000000-222i−2i0000
χ4544-4-44-4-440000000004000-44i−4i00000000000000000000000000000000000
χ4644-4-44-4-440000000004000-4−4i4i00000000000000000000000000000000000
χ4744-4-44-4-44000000000-40004000004-4000000000000000000000000000000
χ4844-4-44-4-44000000000-4000400000-44000000000000000000000000000000
χ494-4444-4-4-44i4i−4i−4i000−4i4i0-44000000000000000000000000000000000000000
χ504-4444-4-4-4−4i−4i4i4i0004i−4i0-44000000000000000000000000000000000000000
χ514-44-4-4-44400004-4000000000000000002-2-222-2-2200000000000000000000
χ524-44-4-4-44400004-400000000000000000-222-2-222-200000000000000000000
χ534-44-4-4-4440000-44000000000000000002-2-22-222-200000000000000000000
χ544-44-4-4-4440000-4400000000000000000-222-22-2-2200000000000000000000
χ554-4-44-44-444-4-44000000000000000000000000000002-20000002-200000000
χ564-4-44-44-444-4-4400000000000000000000000000000-22000000-2200000000
χ574-4-44-44-44-444-4000000000000000000000000000002-2000000-2200000000
χ584-4-44-44-44-444-400000000000000000000000000000-220000002-200000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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