Finite Group Databasebeta

← Group #167409

Character table — Group #167409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444488888888888888882222444444448888
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
χ311111111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
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
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
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
χ911111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-111-1-11-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-11111-11-111-1-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11-11-11-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-11-11-1111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1-111-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-22-2-2000022220000000000000000-2-200000000000000
χ1822222222222222222-2-2-2-2-22-2-20000-2-2-2-200000000000000002200000000000000
χ19222222222222-2-2-2-2-2222-2-2-22-22222000000000000000000000000-2-20000000000
χ20222222222222-2-2-2-2-2222-2-2-22-2-2-2-2-2000000000000000000000000220000000000
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
χ2322222222-2-2-2-22222-22-2-2-2-2-22222-2-2000000000000000000000000-220000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-222-2-2220000000000000000000000002-20000000000
χ2522222222-2-2-2-22222-2-22222-2-2-2000000000000000000000000002200-2-200000000
χ2622222222-2-2-2-22222-2-22222-2-2-200000000000000000000000000-2-2002200000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-22000022-2-20000000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-220000-2-22200000000000000002-200000000000000
χ29222-2-2-2-2222-2-222-2-2200000-20000002i−2i2i−2i22−2−222−2−200000000000000000000i2−i2i2−i2
χ30222-2-2-2-2222-2-222-2-2200000-20000002i−2i2i−2i−2−222−2−22200000000000000000000−i2i2−i2i2
χ31222-2-2-2-2222-2-222-2-2200000-2000000−2i2i−2i2i22−2−222−2−200000000000000000000−i2i2−i2i2
χ32222-2-2-2-2222-2-222-2-2200000-2000000−2i2i−2i2i−2−222−2−22200000000000000000000i2−i2i2−i2
χ33222-2-2-2-22-2-222-2-222200000-20000002i−2i−2i2i22−2−2−2−22200000000000000000000i2−i2−i2i2
χ34222-2-2-2-22-2-222-2-222200000-20000002i−2i−2i2i−2−22222−2−200000000000000000000−i2i2i2−i2
χ35222-2-2-2-22-2-222-2-222200000-2000000−2i2i2i−2i22−2−2−2−22200000000000000000000−i2i2i2−i2
χ36222-2-2-2-22-2-222-2-222200000-2000000−2i2i2i−2i−2−22222−2−200000000000000000000i2−i2−i2i2
χ372-2-2-22-2222-22-200000-22-2000202-22-200002−22−22−22−222−2−222−2−20000000000000000
χ382-2-2-22-2222-22-200000-22-2000202-22-20000−22−22−22−22−2−222−2−2220000000000000000
χ392-2-2-22-2222-22-200000-22-200020-22-2200002−22−22−22−2−2−222−2−2220000000000000000
χ402-2-2-22-2222-22-200000-22-200020-22-220000−22−22−22−2222−2−222−2−20000000000000000
χ412-2-2-22-222-22-2200000-2-22000202-2-2200002−22−2−22−2222−2−2−2−2220000000000000000
χ422-2-2-22-222-22-2200000-2-22000202-2-220000−22−222−22−2−2−22222−2−20000000000000000
χ432-2-2-22-222-22-2200000-2-2200020-222-200002−22−2−22−22−2−22222−2−20000000000000000
χ442-2-2-22-222-22-2200000-2-2200020-222-20000−22−222−22−222−2−2−2−2220000000000000000
χ45444-4-4-4-4444-4-4-4-444-4000004000000000000000000000000000000000000000000
χ46444-4-4-4-44-4-44444-4-4-4000004000000000000000000000000000000000000000000
χ4744-4-4-444-40000000000004-400000000000000000002i2−2i22i2−2i200000000000000000000
χ4844-4-4-444-40000000000004-40000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-4-4-444-4000000000000-44000000000000000000000002i2−2i22i2−2i20000000000000000
χ5044-4-4-444-4000000000000-4400000000000000000000000−2i22i2−2i22i20000000000000000
χ514-444-4-44-400004-44-400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ524-444-4-44-400004-44-40000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ534-444-4-44-40000-44-4400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ544-444-4-44-40000-44-440000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ554-44-444-4-400004-4-44000000000000000000000000000000000000000002i−2i2i−2i0000
χ564-44-444-4-400004-4-4400000000000000000000000000000000000000000−2i2i−2i2i0000
χ574-44-444-4-40000-444-4000000000000000000000000000000000000000002i−2i−2i2i0000
χ584-44-444-4-40000-444-400000000000000000000000000000000000000000−2i2i2i−2i0000
χ594-4-44-44-444-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ604-4-44-44-444-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ614-4-44-44-44-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ624-4-44-44-44-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ634-4-4-44-4444-44-4000004-44000-400000000000000000000000000000000000000000
χ644-4-4-44-444-44-440000044-4000-400000000000000000000000000000000000000000
χ6588-888-8-8-8000000000000000000000000000000000000000000000000000000000

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