Finite Group Databasebeta

← Group #171910

Character table — Group #171910

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444422444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-111-111-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111-1-111-1-1111111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11-1-11111111-1-11111-1-1-1-11111-1-1-1-1-11-1111-11-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-11-1-11111111-1-11111-1-1-1-1-1-1-1-11111-11-11-1-1-1111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-11-1-111111-1-11111-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-11111-1-11111-1-1-1-11-11-1-1-1-1111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-11-1-111111-1-111-1-11111-1-1-1-1-1-111111-11-111-11-1-111-1-1-1-111
χ1722222222222222-2-22-2-2-2-2-2-2200002200220000000000-200-200000000000000
χ1822222222222222-2-22-2-2-2-2-2-220000-2-200-2-20000000000200200000000000000
χ19222222222222-2-222-2-2-2-2-222-222-2-200000000000000000-22000000000000000
χ20222222222222-2-222-2-2-2-2-222-2-2-222000000000000000002-2000000000000000
χ21222222222222-2-2-2-2-22222-2-2-200000022002200000000000000-2-20000000000
χ22222222222222-2-2-2-2-22222-2-2-2000000-2-200-2-200000000000000220000000000
χ2322222222-2-2-2-22222-2-2-222-2-2-20000002200-2-2000000000000002-20000000000
χ2422222222-2-2-2-22222-2-2-222-2-2-2000000-2-2002200000000000000-220000000000
χ2522222222-2-2-2-222-2-2-222-2-222-2222200000000000000000-2-2000000000000000
χ2622222222-2-2-2-222-2-2-222-2-222-2-2-2-2-20000000000000000022000000000000000
χ2722222222-2-2-2-2-2-222222-2-2-2-2200002200-2-20000000000200-200000000000000
χ2822222222-2-2-2-2-2-222222-2-2-2-220000-2-200220000000000-200200000000000000
χ29222-2-2-2-222i2i−2i−2i000002i−2i2-20000000002i−2i002-2i2i2−i2−i222−2−2000000000000002−2i2−i2
χ30222-2-2-2-222i2i−2i−2i000002i−2i2-20000000002i−2i002-2−i2−i2i2i2−2−22200000000000000−22−i2i2
χ31222-2-2-2-222i2i−2i−2i000002i−2i2-2000000000−2i2i00-22i2i2−i2−i222−2−200000000000000−22−i2i2
χ32222-2-2-2-222i2i−2i−2i000002i−2i2-2000000000−2i2i00-22−i2−i2i2i2−2−222000000000000002−2i2−i2
χ33222-2-2-2-22−2i−2i2i2i00000−2i2i2-20000000002i−2i00-22i2i2−i2−i2−2−222000000000000002−2−i2i2
χ34222-2-2-2-22−2i−2i2i2i00000−2i2i2-20000000002i−2i00-22−i2−i2i2i222−2−200000000000000−22i2−i2
χ35222-2-2-2-22−2i−2i2i2i00000−2i2i2-2000000000−2i2i002-2i2i2−i2−i2−2−22200000000000000−22i2−i2
χ36222-2-2-2-22−2i−2i2i2i00000−2i2i2-2000000000−2i2i002-2−i2−i2i2i222−2−2000000000000002−2−i2i2
χ3722-222-2-2-22-22-22-200-2000000200002i−2i002i−2i00i2−i2i2−i2i2−i2i2−i200000000002−22−20000
χ3822-222-2-2-22-22-22-200-2000000200002i−2i002i−2i00−i2i2−i2i2−i2i2−i2i20000000000−22−220000
χ3922-222-2-2-22-22-22-200-200000020000−2i2i00−2i2i00i2−i2i2−i2i2−i2i2−i20000000000−22−220000
χ4022-222-2-2-22-22-22-200-200000020000−2i2i00−2i2i00−i2i2−i2i2−i2i2−i2i200000000002−22−20000
χ4122-222-2-2-2-22-22-2200-2000000200002i−2i00−2i2i00i2−i2i2−i2−i2i2−i2i200000000002−2−220000
χ4222-222-2-2-2-22-22-2200-2000000200002i−2i00−2i2i00−i2i2−i2i2i2−i2i2−i20000000000−222−20000
χ4322-222-2-2-2-22-22-2200-200000020000−2i2i002i−2i00i2−i2i2−i2−i2i2−i2i20000000000−222−20000
χ4422-222-2-2-2-22-22-2200-200000020000−2i2i002i−2i00−i2i2−i2i2i2−i2i2−i200000000002−2−220000
χ45444-4-4-4-444i4i−4i−4i00000−4i4i-4400000000000000000000000000000000000000000
χ46444-4-4-4-44−4i−4i4i4i000004i−4i-4400000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4-44004000000-400000000000000000000000000000000000000
χ4844-444-4-4-4-44-444-4004000000-400000000000000000000000000000000000000
χ4944-4-4-444-44i−4i−4i4i0000000000000000000000002-2-22−2i2i2i−2i000000000000000000
χ5044-4-4-444-44i−4i−4i4i000000000000000000000000-222-22i−2i−2i2i000000000000000000
χ5144-4-4-444-4−4i4i4i−4i0000000000000000000000002-2-222i−2i−2i2i000000000000000000
χ5244-4-4-444-4−4i4i4i−4i000000000000000000000000-222-2−2i2i2i−2i000000000000000000
χ534-444-4-44-40000004-4000000000000000000000000000000002i−2i002i−2i00000000
χ544-444-4-44-40000004-400000000000000000000000000000000−2i2i00−2i2i00000000
χ554-444-4-44-4000000-44000000000000000000000000000000002i−2i00−2i2i00000000
χ564-444-4-44-4000000-4400000000000000000000000000000000−2i2i002i−2i00000000
χ574-4-4-44-44400000000000004-40004-40000000000000000000000000000000000
χ584-4-4-44-44400000000000004-4000-440000000000000000000000000000000000
χ594-4-4-44-4440000000000000-4404-4000000000000000000000000000000000000
χ604-4-4-44-4440000000000000-440-44000000000000000000000000000000000000
χ618-88-888-8-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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