Finite Group Databasebeta

← Group #171944

Character table — Group #171944

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11111
χ5111111111111111111111111-1-111-1-1-1-1-1-11111111111-11-1-11-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-11-1-111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ911111111-1-1-1-11-1-11-1-11-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1111-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11-1-11-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11-1-11-1-111111-1-1-1-111-1-1111111-1-1-1-1-11-11-11-1-11111-1-1-1-111
χ1211111111-1-1-1-11-1-11-1-11-1-111111-1-1-1-111-1-111-1-1-1-11111-11-11-1111-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-11-1-11-1-1111-1-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-11-1-11-1-1111-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-11-1-11-1-1111-1-1-1-111-1-111111111-1-1-1-1111-1-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-11-1-11-1-11-1-1111-1-1-1-111-1-11111-1-1-1-11111111-1-1-1-1-11111-1-111-1-1
χ17222222222222222-2-2-2-2-2-22-2-222002200000000000000-200-200000000000000
χ18222222222222222-2-2-2-2-2-22-2-2-2-200-2-200000000000000200200000000000000
χ19222222222222-2-2-2222-2-2-2-22-200000022-2-2000000000000200-2000000000000
χ20222222222222-2-2-2222-2-2-2-22-2000000-2-222000000000000-2002000000000000
χ21222222222222-2-2-2-2-2-2222-2-22002200000022000000000-200-20000000000000
χ22222222222222-2-2-2-2-2-2222-2-2200-2-2000000-2-200000000020020000000000000
χ2322222222-2-2-2-22-2-2-222-2222-2-22200-2-200000000000000200-200000000000000
χ2422222222-2-2-2-22-2-2-222-2222-2-2-2-2002200000000000000-200200000000000000
χ2522222222-2-2-2-2-2222-2-2-222-22-20000002222000000000000-200-2000000000000
χ2622222222-2-2-2-2-2222-2-2-222-22-2000000-2-2-2-20000000000002002000000000000
χ2722222222-2-2-2-2-222-2222-2-2-2-220022000000-2-2000000000200-20000000000000
χ2822222222-2-2-2-2-222-2222-2-2-2-2200-2-200000022000000000-20020000000000000
χ29222-22-2-2-222-2-222-2000000-2002-2002-200000022−2−222−2−200000000002−22−20000
χ30222-22-2-2-222-2-222-2000000-2002-2002-2000000−2−222−2−2220000000000−22−220000
χ31222-22-2-2-222-2-222-2000000-200-2200-2200000022−2−222−2−20000000000−22−220000
χ32222-22-2-2-222-2-222-2000000-200-2200-22000000−2−222−2−22200000000002−22−20000
χ33222-22-2-2-2-2-2222-22000000-2002-200-2200000022−2−2−2−22200000000002−2−220000
χ34222-22-2-2-2-2-2222-22000000-2002-200-22000000−2−22222−2−20000000000−222−20000
χ35222-22-2-2-2-2-2222-22000000-200-22002-200000022−2−2−2−2220000000000−222−20000
χ36222-22-2-2-2-2-2222-22000000-200-22002-2000000−2−22222−2−200000000002−2−220000
χ3722-22-2-2-222-22-2000000-22-2002002-20000002-2i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i2
χ3822-22-2-2-222-22-2000000-22-2002002-20000002-2−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i2
χ3922-22-2-2-222-22-2000000-22-200200-22000000-22i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i2
χ4022-22-2-2-222-22-2000000-22-200200-22000000-22−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i2
χ4122-22-2-2-22-22-22000000-2-22002002-2000000-22i2−i2i2−i2−i2i2−i2i200000000000000i2−i2−i2i2
χ4222-22-2-2-22-22-22000000-2-22002002-2000000-22−i2i2−i2i2i2−i2i2−i200000000000000−i2i2i2−i2
χ4322-22-2-2-22-22-22000000-2-2200200-220000002-2i2−i2i2−i2−i2i2−i2i200000000000000−i2i2i2−i2
χ4422-22-2-2-22-22-22000000-2-2200200-220000002-2−i2i2−i2i2i2−i2i2−i200000000000000i2−i2−i2i2
χ45444-44-4-4-444-4-4-4-4400000040000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444-44-400000040000000000000000000000000000000000000000
χ4744-44-4-4-444-44-40000004-4400-400000000000000000000000000000000000000
χ4844-44-4-4-44-44-4400000044-400-400000000000000000000000000000000000000
χ4944-4-4-444-44-4-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ5044-4-4-444-44-4-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ5144-4-4-444-4-444-40000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ5244-4-4-444-4-444-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ534-444-4-44-400000004000000-40000000004-40000000000000000000000000000
χ544-444-4-44-400000004000000-4000000000-440000000000000000000000000000
χ554-444-4-44-40000000-4000000400000004i−4i000000000000000000000000000000
χ564-444-4-44-40000000-400000040000000−4i4i000000000000000000000000000000
χ574-4-4-44-444000000004-4000000000000000000000000000000002-22-200000000
χ584-4-4-44-444000000004-400000000000000000000000000000000-22-2200000000
χ594-4-4-44-44400000000-44000000000000000000000000000000002-2-2200000000
χ604-4-4-44-44400000000-4400000000000000000000000000000000-222-200000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-8888-8-8000000000000000000000000000000000000000000000000000000

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