Finite Group Databasebeta

← Group #173536

Character table — Group #173536

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222444444444444224444444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-11111-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-11-1-1-1-1-1-11111-11-1-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-11-1-1-1-1-1-11111-11-1-1-11-1-1-1-111111111-1-1
χ911111111-1-111-1-1-1-1111111-1-1-111-1-111-1-11-1-11-1111-1-111-1-111-1-11-1
χ1011111111-1-111-1-1-1-1111111-1-1-111-1-111-1-11-1-11-11-1-111-1-111-1-111-11
χ1111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1111-1-111-1-111-1-1-1-111-11
χ1211111111-1-111-1-1-1-1111111-1-1-1-1-111-1-111-1111-1-1-1-111-1-11111-1-11-1
χ1311111111-1-111-1-1-1-11111-1-1-11111-1-1-1-11111-1-11-111-1-1-1-11111-1-1-11
χ1411111111-1-111-1-1-1-11111-1-1-11111-1-1-1-11111-1-11-1-1-11111-1-1-1-1111-1
χ1511111111-1-111-1-1-1-11111-1-1-111-1-11111-1-1-1-11-11111-1-1-1-111-1-1111-1
χ1611111111-1-111-1-1-1-11111-1-1-111-1-11111-1-1-1-11-111-1-11111-1-111-1-1-11
χ1722222222222-222-2-2-22-2-200-20022220000-20-200000000000000000
χ1822222222222-222-2-2-22-2-200-200-2-2-2-2000020200000000000000000
χ192222222222-22-2-2-2-2-2-22-200200000022-2-202000-200000000000000
χ202222222222-22-2-2-2-2-2-22-2002000000-2-2220-2000200000000000000
χ212222222222-2-2-2-2222-2-2222-22200000000000-2-2000000000000000
χ222222222222-2-2-2-2222-2-22-2-2-2-2-20000000000022000000000000000
χ2322222222-2-22-2-2-222-22-2-20020022-2-20000-20200000000000000000
χ2422222222-2-22-2-2-222-22-2-200200-2-222000020-200000000000000000
χ2522222222-2-2-222222-2-22-200-200000022220-2000-200000000000000
χ2622222222-2-2-222222-2-22-200-2000000-2-2-2-202000200000000000000
χ2722222222-2-2-2-222-2-22-2-22222-2-200000000000-22000000000000000
χ2822222222-2-2-2-222-2-22-2-22-2-2222000000000002-2000000000000000
χ292-2-2-2222-200022-22-200-200000000002-22-20000000000i2−i2i2−i2i2−i2i2−i200
χ302-2-2-2222-200022-22-200-200000000002-22-20000000000−i2i2−i2i2−i2i2−i2i200
χ312-2-2-2222-200022-22-200-20000000000-22-220000000000i2−i2i2−i2−i2i2−i2i200
χ322-2-2-2222-200022-22-200-20000000000-22-220000000000−i2i2−i2i2i2−i2i2−i200
χ332-2-2-2222-20002-22-2200-200000000002-2-220000000000i2−i2−i2i2i2−i2−i2i200
χ342-2-2-2222-20002-22-2200-200000000002-2-220000000000−i2i2i2−i2−i2i2i2−i200
χ352-2-2-2222-20002-22-2200-20000000000-222-20000000000i2−i2−i2i2−i2i2i2−i200
χ362-2-2-2222-20002-22-2200-20000000000-222-20000000000−i2i2i2−i2i2−i2−i2i200
χ37444-44-4-4-44-4000000000000000000000000000002-22-20000000000
χ38444-44-4-4-44-400000000000000000000000000000-22-220000000000
χ39444-44-4-4-4-44000000000000000000000000000002-2-220000000000
χ40444-44-4-4-4-4400000000000000000000000000000-222-20000000000
χ4144-44-44-4-4004000000-40000000004-4000000000000000000000000
χ4244-44-44-4-4004000000-4000000000-44000000000000000000000000
χ4344-44-44-4-400-4000000400000004i−4i00000000000000000000000000
χ4444-44-44-4-400-400000040000000−4i4i00000000000000000000000000
χ4544-4-4-4-44400000000400-40004i−4i0000000000000000000000000000
χ4644-4-4-4-44400000000400-4000−4i4i0000000000000000000000000000
χ4744-4-4-4-44400000000-40044-40000000000000000000000000000000
χ4844-4-4-4-44400000000-4004-440000000000000000000000000000000
χ494-4-4-4444-4000-44-4-440040000000000000000000000000000000000
χ504-4-4-4444-4000-4-444-40040000000000000000000000000000000000
χ518-888-8-88-8000000000000000000000000000000000000000000000
χ528-88-8-88-88000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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