Finite Group Databasebeta

← Group #173690

Character table — Group #173690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444224444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-11-1-1-1-111-1-111-1-1-11-111111-1-1-1-11111-1-1
χ811111111111111111111-1-11-1-1-1-111-1-111-1-1-11-11-1-1-1-11111-1-1-1-111
χ911111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-111-1-1111-1-111-1-111-1-11-1
χ1011111111-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-111-1-11-1-111-1-111-1-111-11
χ1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-111111-111-1-111-1-111-1-1-1-111-11
χ1211111111-1-111-1-1-1-1111111-1-1-1-1-1-1-111111-111-1-1-1-111-1-11111-1-11-1
χ1311111111-1-111-1-1-1-11111-1-1-11111-1-1-1-111-11-111-111-1-1-1-111-1-1111-1
χ1411111111-1-111-1-1-1-11111-1-1-11111-1-1-1-111-11-111-1-1-11111-1-111-1-1-11
χ1511111111-1-111-1-1-1-11111-1-1-111-1-11111-1-11-1-1-11111-1-1-1-11111-1-1-11
χ1611111111-1-111-1-1-1-11111-1-1-111-1-11111-1-11-1-1-111-1-11111-1-1-1-1111-1
χ1722222222222-2-2-2-2-2-2-22-200200002200-2-200020-200000000000000
χ1822222222222-2-2-2-2-2-2-22-20020000-2-20022000-20200000000000000
χ192222222222-2222-2-2-2-2-2222-2220000000000-20-2000000000000000
χ202222222222-2222-2-2-2-2-22-2-2-2-2-20000000000202000000000000000
χ212222222222-2-2-2-22222-2-200-20022002200-2-2000000000000000000
χ222222222222-2-2-2-22222-2-200-200-2-200-2-20022000000000000000000
χ2322222222-2-22-22222-2-22-200-20000220022000-20-200000000000000
χ2422222222-2-22-22222-2-22-200-20000-2-200-2-200020200000000000000
χ2522222222-2-2-22-2-222-2-2-22222-2-20000000000-202000000000000000
χ2622222222-2-2-22-2-222-2-2-22-2-2222000000000020-2000000000000000
χ2722222222-2-2-2-222-2-222-2-2002002200-2-2002-2000000000000000000
χ2822222222-2-2-2-222-2-222-2-200200-2-2002200-22000000000000000000
χ2922-2-222-2-22-20-22-20000022-202-200000000000000i2−i2i2−i2i2−i2i2−i2000000
χ3022-2-222-2-22-20-22-20000022-202-200000000000000−i2i2−i2i2−i2i2−i2i2000000
χ3122-2-222-2-22-20-22-2000002-220-2200000000000000i2−i2i2−i2−i2i2−i2i2000000
χ3222-2-222-2-22-20-22-2000002-220-2200000000000000−i2i2−i2i2i2−i2i2−i2000000
χ3322-2-222-2-2-220-2-220000022-20-2200000000000000i2−i2−i2i2i2−i2−i2i2000000
χ3422-2-222-2-2-220-2-220000022-20-2200000000000000−i2i2i2−i2−i2i2i2−i2000000
χ3522-2-222-2-2-220-2-22000002-2202-200000000000000i2−i2−i2i2−i2i2i2−i2000000
χ3622-2-222-2-2-220-2-22000002-2202-200000000000000−i2i2i2−i2i2−i2−i2i2000000
χ3744-44-4-44-40040000000-4000000004-4000000000000000000000000
χ3844-44-4-44-40040000000-400000000-44000000000000000000000000
χ3944-44-4-44-400-4000000040000000000004i−4i00000000000000000000
χ4044-44-4-44-400-400000004000000000000−4i4i00000000000000000000
χ4144-4-444-4-44-404-4400000-4000000000000000000000000000000000
χ4244-4-444-4-4-44044-400000-4000000000000000000000000000000000
χ434-44-44-44-40000004i−4i00000000000000000000000000000002-22i−2i00
χ444-44-44-44-40000004i−4i0000000000000000000000000000000-22−2i2i00
χ454-44-44-44-4000000−4i4i00000000000000000000000000000002-2−2i2i00
χ464-44-44-44-4000000−4i4i0000000000000000000000000000000-222i−2i00
χ474-4-4-4-4444000000004-4000000000004-40000000000000000000000
χ484-4-4-4-4444000000004-400000000000-440000000000000000000000
χ494-4-4-4-444400000000-4400000004-400000000000000000000000000
χ504-4-4-4-444400000000-440000000-4400000000000000000000000000
χ51888-8-8-8-88000000000000000000000000000000000000000000000
χ528-888-88-8-8000000000000000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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