Finite Group Databasebeta

← Group #168739

Character table — Group #168739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444444444444888888884444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ71111111111111111111111-1-11-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-1-1-111-1-1111111-111-1-111-1-1-1-11111-1-1-1-11-11-11-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111-1-1111111-111-1-111-1-1-1-1-1-1-1-111111-11-11-1-1-111-1-111-11
χ1111111111-1-1-1-1-1-111-1-1111111-1-1-111-1-111-1-11111-1-1-1-11-1-11-1111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111-1-1111111-1-1-111-1-111-1-1-1-1-1-111111-1-11-11-1-11111-1-11-1
χ1311111111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-111111111-1-1-1-1-111-1-11-1-11111-1-1-11
χ1411111111-1-1-1-1-1-111-1-11111-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1111111-1-1-1-1-11-111-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-111-1-1-1-11111-11-111-111-1-111-1-1-11
χ1722222222222222-2-2-2-22-2-2222-2000000002200000000-2-200000000000000
χ1822222222222222-2-2-2-22-2-22-2-2-200000000-2-2000000002200000000000000
χ19222222222222-2-22-2-2-2-22-2-20020000222200000000000000-2-20000000000
χ20222222222222-2-22-2-2-2-22-2-20020000-2-2-2-200000000000000220000000000
χ21222222222222-2-2-2222-2-22-200-222220000000000000000-2-2000000000000
χ22222222222222-2-2-2222-2-22-200-2-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-2222-222-22-2-200-2000022-2-200000000000000-220000000000
χ2422222222-2-2-2-2222-222-22-2-200-20000-2-222000000000000002-20000000000
χ2522222222-2-2-2-222-22-2-2-2-22-200222-2-20000000000000000-22000000000000
χ2622222222-2-2-2-222-22-2-2-2-22-2002-2-22200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-2222200000000-2-200000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-22-2-220000000022000000002-200000000000000
χ29222-2-2-2-2222-2-22-20000-20022-20000000002-2i2i2−i2−i2i2i2−i2−i2000000i2−i2i2−i2000000
χ30222-2-2-2-2222-2-22-20000-20022-20000000002-2−i2−i2i2i2−i2−i2i2i2000000−i2i2−i2i2000000
χ31222-2-2-2-2222-2-22-20000-2002-22000000000-22i2i2−i2−i2i2i2−i2−i2000000−i2i2−i2i2000000
χ32222-2-2-2-2222-2-22-20000-2002-22000000000-22−i2−i2i2i2−i2−i2i2i2000000i2−i2i2−i2000000
χ33222-2-2-2-22-2-222-220000-20022-2000000000-22i2i2−i2−i2−i2−i2i2i2000000i2−i2−i2i2000000
χ34222-2-2-2-22-2-222-220000-20022-2000000000-22−i2−i2i2i2i2i2−i2−i2000000−i2i2i2−i2000000
χ35222-2-2-2-22-2-222-220000-2002-220000000002-2i2i2−i2−i2−i2−i2i2i2000000−i2i2i2−i2000000
χ36222-2-2-2-22-2-222-220000-2002-220000000002-2−i2−i2i2i2i2i2−i2−i2000000i2−i2−i2i2000000
χ3722-2-2-222-22-22-2000-22-200200002i−2i2i−2i000000i2−i2i2−i2i2−i2i2−i200000000002−22−200
χ3822-2-2-222-22-22-2000-22-200200002i−2i2i−2i000000−i2i2−i2i2−i2i2−i2i20000000000−22−2200
χ3922-2-2-222-22-22-2000-22-20020000−2i2i−2i2i000000i2−i2i2−i2i2−i2i2−i20000000000−22−2200
χ4022-2-2-222-22-22-2000-22-20020000−2i2i−2i2i000000−i2i2−i2i2−i2i2−i2i200000000002−22−200
χ4122-2-2-222-2-22-22000-2-2200200002i−2i−2i2i000000i2−i2i2−i2−i2i2−i2i200000000002−2−2200
χ4222-2-2-222-2-22-22000-2-2200200002i−2i−2i2i000000−i2i2−i2i2i2−i2i2−i20000000000−222−200
χ4322-2-2-222-2-22-22000-2-220020000−2i2i2i−2i000000i2−i2i2−i2−i2i2−i2i20000000000−222−200
χ4422-2-2-222-2-22-22000-2-220020000−2i2i2i−2i000000−i2i2−i2i2i2−i2i2−i200000000002−2−2200
χ45444-4-4-4-4444-4-4-440000400-40000000000000000000000000000000000000
χ46444-4-4-4-44-4-4444-40000400-40000000000000000000000000000000000000
χ4744-444-4-4-44-4-44000000000000000000000002-2-222-2-220000000000000000
χ4844-444-4-4-44-4-4400000000000000000000000-222-2-222-20000000000000000
χ4944-444-4-4-4-444-4000000000000000000000002-2-22-222-20000000000000000
χ5044-444-4-4-4-444-400000000000000000000000-222-22-2-220000000000000000
χ5144-4-4-444-44-44-40004-4400-400000000000000000000000000000000000000
χ5244-4-4-444-4-44-4400044-400-400000000000000000000000000000000000000
χ534-444-44-4-400000040000-40000000004-40000000000000000000000000000
χ544-444-44-4-400000040000-4000000000-440000000000000000000000000000
χ554-444-44-4-4000000-400004000000000004i−4i00000000000000000000000000
χ564-444-44-4-4000000-40000400000000000−4i4i00000000000000000000000000
χ578-88-88-88-8000000000000000000000000000000000000000000000000000
χ588-8-88-8-888000000000000000000000000000000000000000000000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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