Finite Group Databasebeta

← Group #167265

Character table — Group #167265

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422224444488888888888888884444444444448888
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
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-11-11-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11-11-1111-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-11111-1-1-1-11111-1-1-1-11-11-1-11-11-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-1111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-11-111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-11111-1-1
χ1722222222222222222-2-2-2-2-22-2222200-20000000000000000000-2-20000000000000
χ1822222222222222222-2-2-2-2-22-2-2-2-2-200-20000000000000000000220000000000000
χ19222222222222-2-2-2-2-2222-2-2-22000022-2220000000000000000-200-2000000000000
χ20222222222222-2-2-2-2-2222-2-2-220000-2-2-2-2-200000000000000002002000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2000000200000000000000000000002-2-2200000000
χ22222222222222-2-2-2-2-2-2-2-222-2-200000020000000000000000000000-222-200000000
χ2322222222-2-2-2-22222-22-2-2-2-2-220000222-2-20000000000000000-2002000000000000
χ2422222222-2-2-2-22222-22-2-2-2-2-220000-2-22220000000000000000200-2000000000000
χ2522222222-2-2-2-22222-2-22222-2-2000000-2000000000000000000000022-2-200000000
χ2622222222-2-2-2-22222-2-22222-2-2000000-20000000000000000000000-2-22200000000
χ2722222222-2-2-2-2-2-2-2-22-222-2-22-222-2-20020000000000000000000-220000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-2-22-2-2-22200200000000000000000002-20000000000000
χ29222-2-2-22-222-2-222-2-2-200000202-22-200000i2i2−i2−i2i2i2−i2−i200000000000000000000i2−i2i2−i2
χ30222-2-2-22-222-2-222-2-2-200000202-22-200000−i2−i2i2i2−i2−i2i2i200000000000000000000−i2i2−i2i2
χ31222-2-2-22-222-2-222-2-2-20000020-22-2200000i2i2−i2−i2i2i2−i2−i200000000000000000000−i2i2−i2i2
χ32222-2-2-22-222-2-222-2-2-20000020-22-2200000−i2−i2i2i2−i2−i2i2i200000000000000000000i2−i2i2−i2
χ33222-2-2-22-2-2-222-2-222-200000202-2-2200000i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2
χ34222-2-2-22-2-2-222-2-222-200000202-2-2200000−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2
χ35222-2-2-22-2-2-222-2-222-20000020-222-200000i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2
χ36222-2-2-22-2-2-222-2-222-20000020-222-200000−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2
χ372-2-222-22-22-22-20000022-2000-200002i−2i02i−2ii2−i2i2−i2i2−i2i2−i222−2−222−2−20000000000000000
χ382-2-222-22-22-22-20000022-2000-200002i−2i02i−2i−i2i2−i2i2−i2i2−i2i2−2−222−2−2220000000000000000
χ392-2-222-22-22-22-20000022-2000-20000−2i2i0−2i2ii2−i2i2−i2i2−i2i2−i2−2−222−2−2220000000000000000
χ402-2-222-22-22-22-20000022-2000-20000−2i2i0−2i2i−i2i2−i2i2−i2i2−i2i222−2−222−2−20000000000000000
χ412-2-222-22-2-22-22000002-22000-200002i−2i0−2i2ii2−i2i2−i2−i2i2−i2i222−2−2−2−2220000000000000000
χ422-2-222-22-2-22-22000002-22000-200002i−2i0−2i2i−i2i2−i2i2i2−i2i2−i2−2−22222−2−20000000000000000
χ432-2-222-22-2-22-22000002-22000-20000−2i2i02i−2ii2−i2i2−i2−i2i2−i2i2−2−22222−2−20000000000000000
χ442-2-222-22-2-22-22000002-22000-20000−2i2i02i−2i−i2i2−i2i2i2−i2i2−i222−2−2−2−2220000000000000000
χ45444-4-4-44-444-4-4-4-444400000-4000000000000000000000000000000000000000000
χ46444-4-4-44-4-4-44444-4-4400000-4000000000000000000000000000000000000000000
χ4744-4-44-4-440000000000004-400000000000000000002i2−2i22i2−2i200000000000000000000
χ4844-4-44-4-440000000000004-40000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-4-44-4-44000000000000-44000000000000000000000002i2−2i22i2−2i20000000000000000
χ5044-4-44-4-44000000000000-4400000000000000000000000−2i22i2−2i22i20000000000000000
χ514-444-4-4-4400004-44-4000000000000000000000000000000000000000002i−2i2i−2i0000
χ524-444-4-4-4400004-44-400000000000000000000000000000000000000000−2i2i−2i2i0000
χ534-444-4-4-440000-44-44000000000000000000000000000000000000000002i−2i−2i2i0000
χ544-444-4-4-440000-44-4400000000000000000000000000000000000000000−2i2i2i−2i0000
χ554-44-444-4-400004-4-4400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ564-44-444-4-400004-4-440000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ574-44-444-4-40000-444-400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ584-44-444-4-40000-444-40000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ594-4-444-44-44-44-400000-4-44000400000000000000000000000000000000000000000
χ604-4-444-44-4-44-4400000-44-4000400000000000000000000000000000000000000000
χ614-4-4-4-44444-4-440000000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-4-44444-4-44000000000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-4-4444-444-40000000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-4-4444-444-4000000000000000000000-222-22-2-22000000000000000000000000
χ6588-88-88-8-8000000000000000000000000000000000000000000000000000000000

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