Finite Group Databasebeta

← Group #167213

Character table — Group #167213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ61111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-111-1-11111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11-11-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11-11-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-111-1-11-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-11-111-1-1111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-22-2-20022220000000000000000000000-2-20000000000
χ1822222222222222222-2-2-2-2-22-2-200-2-2-2-20000000000000000000000220000000000
χ19222222222222-2-2-2-2-2222-2-2-22-2220000220000000000000000-2-200000000000000
χ20222222222222-2-2-2-2-2222-2-2-22-2-2-20000-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-22000000000000000000000000002-200-2200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2200000000000000000000000000-22002-200000000
χ2322222222-2-2-2-22222-22-2-2-2-2-222220000-2-20000000000000000-2200000000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-222-2-200002200000000000000002-200000000000000
χ2522222222-2-2-2-22222-2-22222-2-2-2000000000000000000000000002200-2-200000000
χ2622222222-2-2-2-22222-2-22222-2-2-200000000000000000000000000-2-2002200000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-220022-2-20000000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-2200-2-22200000000000000000000002-20000000000
χ29222-2-2-22-222-2-222-2-2-200000200002i−2i2i−2i0022−2−222−2−200000000000000000000i2−i2i2−i2
χ30222-2-2-22-222-2-222-2-2-200000200002i−2i2i−2i00−2−222−2−22200000000000000000000−i2i2−i2i2
χ31222-2-2-22-222-2-222-2-2-20000020000−2i2i−2i2i0022−2−222−2−200000000000000000000−i2i2−i2i2
χ32222-2-2-22-222-2-222-2-2-20000020000−2i2i−2i2i00−2−222−2−22200000000000000000000i2−i2i2−i2
χ33222-2-2-22-2-2-222-2-222-200000200002i−2i−2i2i0022−2−2−2−22200000000000000000000i2−i2−i2i2
χ34222-2-2-22-2-2-222-2-222-200000200002i−2i−2i2i00−2−22222−2−200000000000000000000−i2i2i2−i2
χ35222-2-2-22-2-2-222-2-222-20000020000−2i2i2i−2i0022−2−2−2−22200000000000000000000−i2i2i2−i2
χ36222-2-2-22-2-2-222-2-222-20000020000−2i2i2i−2i00−2−22222−2−200000000000000000000i2−i2−i2i2
χ3722-2-22-2-222-22-20000022-2000-202i−2i00002i−2i2−22−22−22−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822-2-22-2-222-22-20000022-2000-202i−2i00002i−2i−22−22−22−22−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922-2-22-2-222-22-20000022-2000-20−2i2i0000−2i2i2−22−22−22−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022-2-22-2-222-22-20000022-2000-20−2i2i0000−2i2i−22−22−22−22i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122-2-22-2-22-22-22000002-22000-202i−2i0000−2i2i2−22−2−22−22i2i2−i2−i2−i2−i2i2i20000000000000000
χ4222-2-22-2-22-22-22000002-22000-202i−2i0000−2i2i−22−222−22−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4322-2-22-2-22-22-22000002-22000-20−2i2i00002i−2i2−22−2−22−22−i2−i2i2i2i2i2−i2−i20000000000000000
χ4422-2-22-2-22-22-22000002-22000-20−2i2i00002i−2i−22−222−22−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ45444-4-4-44-444-4-4-4-444400000-4000000000000000000000000000000000000000000
χ46444-4-4-44-4-4-44444-4-4400000-4000000000000000000000000000000000000000000
χ4744-44-44-4-44-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ4844-44-44-4-44-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ4944-44-44-4-4-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ5044-44-44-4-4-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ5144-4-44-4-444-44-400000-4-44000400000000000000000000000000000000000000000
χ5244-4-44-4-44-44-4400000-44-4000400000000000000000000000000000000000000000
χ534-4444-4-4-40000000000004-4000000000000000000022−2222−2200000000000000000000
χ544-4444-4-4-40000000000004-40000000000000000000−2222−222200000000000000000000
χ554-4444-4-4-4000000000000-440000000000000000000000022−2222−220000000000000000
χ564-4444-4-4-4000000000000-4400000000000000000000000−2222−22220000000000000000
χ574-4-44-4-44400004-44-4000000000000000000000000000000000000000002-22-20000
χ584-4-44-4-44400004-44-400000000000000000000000000000000000000000-22-220000
χ594-4-44-4-4440000-44-44000000000000000000000000000000000000000002-2-220000
χ604-4-44-4-4440000-44-4400000000000000000000000000000000000000000-222-20000
χ614-4-4-4444-400004-4-4400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ624-4-4-4444-400004-4-440000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ634-4-4-4444-40000-444-400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ644-4-4-4444-40000-444-40000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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