Finite Group Databasebeta

← Group #169804

Character table — Group #169804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888822444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-11-1-1-1-11-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-11111-1-1
χ911111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-111-1-11-1
χ1011111111-1-1-1-11-1-11-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-111111-1111-1-1-1-1-111-11
χ1111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-11
χ1211111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-111-111-1-11-1
χ1311111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-11
χ1411111111-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1111-1-1111-1
χ1511111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-111-1-11-1-1111-1
χ1611111111-1-1-1-11-1-11-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-11-111-1-1111-1-1-11
χ172222222222222-2-2-2-2-222-2-22-222220000000000000000000000-20000-2000000
χ182222222222222-2-2-2-2-222-2-22-2-2-2-2-20000000000000000000000200002000000
χ19222222222222-222-2-2-2-2-222-2-20000000000000000000000000002-22-20000000
χ20222222222222-222-2-2-2-2-222-2-2000000000000000000000000000-22-220000000
χ21222222222222-2-2-2222-2-2-2-2-22000022220000000000000000-2-2000000000000
χ22222222222222-2-2-2222-2-2-2-2-220000-2-2-2-2000000000000000022000000000000
χ2322222222-2-2-2-2222-222-2-2-2-22-222-2-20000000000000000000000-200002000000
χ2422222222-2-2-2-2222-222-2-2-2-22-2-2-222000000000000000000000020000-2000000
χ2522222222-2-2-2-2-2222-2-222-2-2-22000022-2-20000000000000000-22000000000000
χ2622222222-2-2-2-2-2222-2-222-2-2-220000-2-22200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000002-2-220000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000-222-20000000
χ29222-2-2-2-2222-2-22000002-200-202i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000
χ30222-2-2-2-2222-2-22000002-200-202i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000
χ31222-2-2-2-2222-2-22000002-200-20−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000
χ32222-2-2-2-2222-2-22000002-200-20−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000
χ33222-2-2-2-22-2-222200000-2200-202i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000
χ34222-2-2-2-22-2-222200000-2200-202i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000
χ35222-2-2-2-22-2-222200000-2200-20−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000
χ36222-2-2-2-22-2-222200000-2200-20−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000
χ3722-2-2-222-22-22-2000-22-200000200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000000000002−22−200
χ3822-2-2-222-22-22-2000-22-200000200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000000000000−22−2200
χ3922-2-2-222-22-22-2000-22-20000020000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000−22−2200
χ4022-2-2-222-22-22-2000-22-20000020000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000000000002−22−200
χ4122-2-2-222-2-22-22000-2-2200000200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200000000000000002−2−2200
χ4222-2-2-222-2-22-22000-2-2200000200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000−222−200
χ4322-2-2-222-2-22-22000-2-220000020000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000−222−200
χ4422-2-2-222-2-22-22000-2-220000020000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200000000000000002−2−2200
χ45444-4-4-4-4444-4-4-400000-44004000000000000000000000000000000000000000
χ46444-4-4-4-44-4-444-4000004-4004000000000000000000000000000000000000000
χ4744-444-4-4-44-4-44000000000000000000002-2-222-2-220000000000000000000000
χ4844-444-4-4-44-4-4400000000000000000000-222-2-222-20000000000000000000000
χ4944-444-4-4-4-444-4000000000000000000002-2-22-222-20000000000000000000000
χ5044-444-4-4-4-444-400000000000000000000-222-22-2-220000000000000000000000
χ5144-4-4-444-44-44-40004-4400000-400000000000000000000000000000000000000
χ5244-4-4-444-4-44-4400044-400000-400000000000000000000000000000000000000
χ534-4-44-44-440000000000004-4000000000000000000000022−2222−2200000000000000
χ544-4-44-44-440000000000004-40000000000000000000000−2222−222200000000000000
χ554-4-44-44-44000000000000-4400000000000000000022−2222−22000000000000000000
χ564-4-44-44-44000000000000-44000000000000000000−2222−2222000000000000000000
χ574-4-4-44-444000004-400000000000000000000000002-2-222-2-2200000000000000
χ584-4-4-44-444000004-40000000000000000000000000-222-2-222-200000000000000
χ594-4-4-44-44400000-4400000000000000000000000002-2-22-222-200000000000000
χ604-4-4-44-44400000-440000000000000000000000000-222-22-2-2200000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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