Finite Group Databasebeta

← Group #171792

Character table — Group #171792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222222244444444444422444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-11-1-1-11-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-111-1-1111111111-11-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-111-1-11111111111-1-1-111-11111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ911111111-1-1-1-11-1-11-1-11-1-111111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11-1-11-1-111111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11-1-11-1-11-1-111111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-1-11111-1-1
χ1311111111-1-1-1-11-1-11-1-11-1-1111-1-11111-1-1-1-1111111-1-1-1-11-1-11-11-1-111-1-11111-1-1
χ1411111111-1-1-1-11-1-11-1-11-1-1111-1-11111-1-1-1-111-1-1-1-111111-1-11-1111-1-111-1-1-1-111
χ1511111111-1-1-1-11-1-11-1-11-1-1111-1-111-1-11111-1-11111-1-1-1-1-1-11-11111-1-1-1-111-1-111
χ1611111111-1-1-1-11-1-11-1-11-1-1111-1-111-1-11111-1-1-1-1-1-11111-1-11-111-1-11111-1-111-1-1
χ17222222222222222-2-2-2-2-2-22-2-20000002200-2-2000000000002-20000000000000
χ18222222222222222-2-2-2-2-2-22-2-2000000-2-2002200000000000-220000000000000
χ19222222222222-2-2-2222-2-2-2-22-2222200000000000000000-2000-2000000000000
χ20222222222222-2-2-2222-2-2-2-22-2-2-2-2-20000000000000000020002000000000000
χ21222222222222-2-2-2-2-2-2222-2-2200002200220000000000-20-2000000000000000
χ22222222222222-2-2-2-2-2-2222-2-220000-2-200-2-20000000000202000000000000000
χ2322222222-2-2-2-22-2-2-222-2222-2-200000022002200000000000-2-20000000000000
χ2422222222-2-2-2-22-2-2-222-2222-2-2000000-2-200-2-200000000000220000000000000
χ2522222222-2-2-2-2-2222-2-2-222-22-222-2-200000000000000000-20002000000000000
χ2622222222-2-2-2-2-2222-2-2-222-22-2-2-222000000000000000002000-2000000000000
χ2722222222-2-2-2-2-222-2222-2-2-2-2200002200-2-20000000000-202000000000000000
χ2822222222-2-2-2-2-222-2222-2-2-2-220000-2-20022000000000020-2000000000000000
χ292-22-22-2-2222-2-200000022-200-200002i−2i002i−2i00i2i2−i2−i2i2i2−i2−i2000000000000002−22−2
χ302-22-22-2-2222-2-200000022-200-200002i−2i002i−2i00−i2−i2i2i2−i2−i2i2i200000000000000−22−22
χ312-22-22-2-2222-2-200000022-200-20000−2i2i00−2i2i00i2i2−i2−i2i2i2−i2−i200000000000000−22−22
χ322-22-22-2-2222-2-200000022-200-20000−2i2i00−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000002−22−2
χ332-22-22-2-22-2-2220000002-2200-200002i−2i00−2i2i00i2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ342-22-22-2-22-2-2220000002-2200-200002i−2i00−2i2i00−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ352-22-22-2-22-2-2220000002-2200-20000−2i2i002i−2i00i2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ362-22-22-2-22-2-2220000002-2200-20000−2i2i002i−2i00−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ372-2-2-2222-22-22-200022-20000-202-22-200000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-2-2222-22-22-200022-20000-202-22-200000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-2-2222-22-22-200022-20000-20-22-2200000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-2-2222-22-22-200022-20000-20-22-2200000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-2-2222-2-22-220002-220000-202-2-2200000000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i20000
χ422-2-2-2222-2-22-220002-220000-202-2-2200000000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i20000
χ432-2-2-2222-2-22-220002-220000-20-222-200000000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i20000
χ442-2-2-2222-2-22-220002-220000-20-222-200000000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i20000
χ4544-444-4-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ4644-444-4-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ4744-444-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ4844-444-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ494-444-44-4-40000400000000-4000000004-4000000000000000000000000000000
χ504-444-44-4-40000400000000-400000000-44000000000000000000000000000000
χ514-444-44-4-40000-40000000040000000000004i−4i00000000000000000000000000
χ524-444-44-4-40000-4000000004000000000000−4i4i00000000000000000000000000
χ534-44-44-4-4444-4-4000000-4-4400400000000000000000000000000000000000000
χ544-44-44-4-44-4-444000000-44-400400000000000000000000000000000000000000
χ554-4-44-4-444000004-4000000000000000000000000000000000002-22-200000000
χ564-4-44-4-444000004-400000000000000000000000000000000000-22-2200000000
χ574-4-44-4-44400000-44000000000000000000000000000000000002-2-2200000000
χ584-4-44-4-44400000-4400000000000000000000000000000000000-222-200000000
χ594-4-4-4444-44-44-4000-4-4400004000000000000000000000000000000000000000
χ604-4-4-4444-4-44-44000-44-400004000000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-8-88-88000000000000000000000000000000000000000000000000000000

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