Finite Group Databasebeta

← Group #173598

Character table — Group #173598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444444444444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111-1-1-111-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-111111111-1-1
χ911111111-1-111-1-1-1-11111-111-1-111-1-111-1-111-11-1-111-1-111-1-111-1-11-1
χ1011111111-1-111-1-1-1-11111-111-1-111-1-111-1-111-11-1-1-1-111-1-111-1-111-11
χ1111111111-1-111-1-1-1-11111-111-1-1-1-111-1-111-11-1-11111-1-111-1-1-1-111-11
χ1211111111-1-111-1-1-1-11111-111-1-1-1-111-1-111-11-1-111-1-111-1-11111-1-11-1
χ1311111111-1-111-1-1-1-11111-1-1-11111-1-1-1-1111-11-11-111-1-1-1-11111-1-1-11
χ1411111111-1-111-1-1-1-11111-1-1-11111-1-1-1-1111-11-11-1-1-11111-1-1-1-1111-1
χ1511111111-1-111-1-1-1-11111-1-1-111-1-11111-1-1-1-111-1111-1-1-1-111-1-1111-1
χ1611111111-1-111-1-1-1-11111-1-1-111-1-11111-1-1-1-111-11-1-11111-1-111-1-1-11
χ1722222222222-222-2-2-22-2-2-2000022220000-20000-200000000000000
χ1822222222222-222-2-2-22-2-2-20000-2-2-2-2000020000200000000000000
χ192222222222-22-2-222-2-22-2-22222000000000-2-200000000000000000
χ202222222222-22-2-222-2-22-2-2-2-2-2-20000000002200000000000000000
χ212222222222-2-2-2-2-2-22-2-2220000000022-2-2000-22000000000000000
χ222222222222-2-2-2-2-2-22-2-22200000000-2-2220002-2000000000000000
χ2322222222-2-22-2-2-222-22-2-22000022-2-20000-20000200000000000000
χ2422222222-2-22-2-2-222-22-2-220000-2-222000020000-200000000000000
χ2522222222-2-2-2222-2-2-2-22-2222-2-2000000000-2200000000000000000
χ2622222222-2-2-2222-2-2-2-22-22-2-2220000000002-200000000000000000
χ2722222222-2-2-2-222222-2-22-2000000002222000-2-2000000000000000
χ2822222222-2-2-2-222222-2-22-200000000-2-2-2-200022000000000000000
χ292-2-222-2-2200002-22-2200-20000000002i−2i2i−2i00000000002−22−2i2−i2i2−i200
χ302-2-222-2-2200002-22-2200-20000000002i−2i2i−2i0000000000−22−22−i2i2−i2i200
χ312-2-222-2-2200002-22-2200-2000000000−2i2i−2i2i00000000002−22−2−i2i2−i2i200
χ322-2-222-2-2200002-22-2200-2000000000−2i2i−2i2i0000000000−22−22i2−i2i2−i200
χ332-2-222-2-220000-22-22200-20000000002i−2i−2i2i00000000002−2−22i2−i2−i2i200
χ342-2-222-2-220000-22-22200-20000000002i−2i−2i2i0000000000−222−2−i2i2i2−i200
χ352-2-222-2-220000-22-22200-2000000000−2i2i2i−2i00000000002−2−22−i2i2i2−i200
χ362-2-222-2-220000-22-22200-2000000000−2i2i2i−2i0000000000−222−2i2−i2−i2i200
χ37444-4-4-4-444-4000000000000000000000000000002i−2i2i−2i0000000000
χ38444-4-4-4-444-400000000000000000000000000000−2i2i−2i2i0000000000
χ39444-4-4-4-44-44000000000000000000000000000002i−2i−2i2i0000000000
χ40444-4-4-4-44-4400000000000000000000000000000−2i2i2i−2i0000000000
χ4144-44-44-4-40004000000-400004-40000000000000000000000000000
χ4244-44-44-4-40004000000-40000-440000000000000000000000000000
χ4344-44-44-4-4000-40000004004i−4i000000000000000000000000000000
χ4444-44-44-4-4000-4000000400−4i4i000000000000000000000000000000
χ4544-4-44-44-4004000000-40000000004-4000000000000000000000000
χ4644-4-44-44-4004000000-4000000000-44000000000000000000000000
χ4744-4-44-44-400-4000000400000004i−4i00000000000000000000000000
χ4844-4-44-44-400-400000040000000−4i4i00000000000000000000000000
χ494-4-444-4-4400004-4-44-4004000000000000000000000000000000000
χ504-4-444-4-440000-444-4-4004000000000000000000000000000000000
χ518-888-8-88-8000000000000000000000000000000000000000000000
χ528-88-888-8-8000000000000000000000000000000000000000000000
χ538-8-8-8-8888000000000000000000000000000000000000000000000

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