Finite Group Databasebeta

← Group #167331

Character table — Group #167331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888884444444444448888
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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ51111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11-111-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11-111-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-1-111-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-1-111-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-11-11-1-11-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-11-1-1111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1111-1-11-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1111-1-11-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-22-2-2000022220000000000000000-2-200000000000000
χ1822222222222222222-2-2-2-2-22-2-20000-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-2-2222-2-2-22-222220000000000000000000000-200-20000000000
χ20222222222222-2-2-2-2-2222-2-2-22-2-2-2-2-2000000000000000000000020020000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-220000000000000000000000000002-20-2200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-22000000000000000000000000000-2202-200000000
χ2322222222-2-2-2-22222-22-2-2-2-2-22222-2-20000000000000000000000200-20000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-222-2-2220000000000000000000000-20020000000000
χ2522222222-2-2-2-22222-2-22222-2-2-2000000000000000000000000000220-2-200000000
χ2622222222-2-2-2-22222-2-22222-2-2-2000000000000000000000000000-2-202200000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-22000022-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-220000-2-22200000000000000002-200000000000000
χ29222-22-2-2-222-2-222-2-2200000-20000002-22-222−2−222−2−2000000000000000000002−22−2
χ30222-22-2-2-222-2-222-2-2200000-20000002-22-2−2−222−2−22200000000000000000000−22−22
χ31222-22-2-2-222-2-222-2-2200000-2000000-22-2222−2−222−2−200000000000000000000−22−22
χ32222-22-2-2-222-2-222-2-2200000-2000000-22-22−2−222−2−222000000000000000000002−22−2
χ33222-22-2-2-2-2-222-2-222200000-20000002-2-2222−2−2−2−222000000000000000000002−2−22
χ34222-22-2-2-2-2-222-2-222200000-20000002-2-22−2−22222−2−200000000000000000000−222−2
χ35222-22-2-2-2-2-222-2-222200000-2000000-222-222−2−2−2−22200000000000000000000−222−2
χ36222-22-2-2-2-2-222-2-222200000-2000000-222-2−2−22222−2−2000000000000000000002−2−22
χ3722-2-2-2-2222-22-20000022-2000-202i−2i2i−2i00002−22−22−22−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3822-2-2-2-2222-22-20000022-2000-202i−2i2i−2i0000−22−22−22−22−i2−i2i2i2−i2−i2i2i20000000000000000
χ3922-2-2-2-2222-22-20000022-2000-20−2i2i−2i2i00002−22−22−22−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ4022-2-2-2-2222-22-20000022-2000-20−2i2i−2i2i0000−22−22−22−22i2i2−i2−i2i2i2−i2−i20000000000000000
χ4122-2-2-2-222-22-22000002-22000-202i−2i−2i2i00002−22−2−22−22i2i2−i2−i2−i2−i2i2i20000000000000000
χ4222-2-2-2-222-22-22000002-22000-202i−2i−2i2i0000−22−222−22−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ4322-2-2-2-222-22-22000002-22000-20−2i2i2i−2i00002−22−2−22−22−i2−i2i2i2i2i2−i2−i20000000000000000
χ4422-2-2-2-222-22-22000002-22000-20−2i2i2i−2i0000−22−222−22−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ45444-44-4-4-444-4-4-4-444-4000004000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44444-4-4-4000004000000000000000000000000000000000000000000
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
χ5144-4-4-4-4444-44-400000-4-44000400000000000000000000000000000000000000000
χ5244-4-4-4-444-44-4400000-44-4000400000000000000000000000000000000000000000
χ534-444-4-4-440000000000004-4000000000000000000000002i2−2i22i2−2i20000000000000000
χ544-444-4-4-440000000000004-400000000000000000000000−2i22i2−2i22i20000000000000000
χ554-444-4-4-44000000000000-4400000000000000000002i2−2i22i2−2i200000000000000000000
χ564-444-4-4-44000000000000-440000000000000000000−2i22i2−2i22i200000000000000000000
χ574-4-444-44-400004-44-4000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-4-444-44-400004-44-400000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-4-444-44-40000-44-44000000000000000000000000000000000000000002i−2i−2i2i0000
χ604-4-444-44-40000-44-4400000000000000000000000000000000000000000−2i2i2i−2i0000
χ614-4-4-444-4400004-4-4400000000000000000000000002-2-222-2-220000000000000000
χ624-4-4-444-4400004-4-440000000000000000000000000-222-2-222-20000000000000000
χ634-4-4-444-440000-444-400000000000000000000000002-2-22-222-20000000000000000
χ644-4-4-444-440000-444-40000000000000000000000000-222-22-2-220000000000000000
χ658-88-8-888-8000000000000000000000000000000000000000000000000000000000

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