Finite Group Databasebeta

← Group #173796

Character table — Group #173796

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444444444444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111-11-11-1-111111111-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1111-11-11-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-111-1-11-1-11-1-1-11-11111-1-1-1-11111-1-1
χ611111111111111111111-1-111-1-111-1-11-1-11-1-1-11-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1111-1-1-1-11-1-111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1111-1-1-1-11-1-11-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-111-1-111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-11-111-1-1-1-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-11111-1-1-1111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-11111-1-1-11-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-111-111-11-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-111-111-11-1-1-11111-1-111-1-1-11
χ17222222222222-2-222-2-2-2-20022002200-200-2000-2000000000000000
χ18222222222222-2-222-2-2-2-200-2-200-2-200-20020002000000000000000
χ192222222222-2-222-2-222-2-22200000000-2220-20-20000000000000000
χ202222222222-2-222-2-222-2-2-2-200000000-2-2-202020000000000000000
χ212222222222-2-2-2-2-2-2-2-22200002200-2-220000200-200000000000000
χ222222222222-2-2-2-2-2-2-2-2220000-2-2002220000-200200000000000000
χ2322222222-2-22222-2-2-2-2220000220022-20000-200-200000000000000
χ2422222222-2-22222-2-2-2-2220000-2-200-2-2-20000200200000000000000
χ2522222222-2-222-2-2-2-222-2-222000000002-2-2020-20000000000000000
χ2622222222-2-222-2-2-2-222-2-2-2-2000000002220-2020000000000000000
χ2722222222-2-2-2-22222-2-2-2-2002200-2-200200-20002000000000000000
χ2822222222-2-2-2-22222-2-2-2-200-2-20022002002000-2000000000000000
χ292-222-2-2-22002i−2i2i−2i00002-200002-2002i−2i0000000000000i2−i22−22−2i2−i200
χ302-222-2-2-22002i−2i2i−2i00002-200002-2002i−2i0000000000000−i2i2−22−22−i2i200
χ312-222-2-2-22002i−2i2i−2i00002-20000-2200−2i2i0000000000000i2−i22−2−22−i2i200
χ322-222-2-2-22002i−2i2i−2i00002-20000-2200−2i2i0000000000000−i2i2−222−2i2−i200
χ332-222-2-2-2200−2i2i−2i2i00002-200002-200−2i2i0000000000000i2−i2−22−22i2−i200
χ342-222-2-2-2200−2i2i−2i2i00002-200002-200−2i2i0000000000000−i2i22−22−2−i2i200
χ352-222-2-2-2200−2i2i−2i2i00002-20000-22002i−2i0000000000000i2−i2−222−2−i2i200
χ362-222-2-2-2200−2i2i−2i2i00002-20000-22002i−2i0000000000000−i2i22−2−22i2−i200
χ3744-4-44-4-444-4000000000000000000000000000002i−2i2i−2i0000000000
χ3844-4-44-4-444-400000000000000000000000000000−2i2i−2i2i0000000000
χ3944-4-44-4-44-44000000000000000000000000000002i−2i−2i2i0000000000
χ4044-4-44-4-44-4400000000000000000000000000000−2i2i2i−2i0000000000
χ414-444-4-4-44004i−4i−4i4i0000-44000000000000000000000000000000000
χ424-444-4-4-4400−4i4i4i−4i0000-44000000000000000000000000000000000
χ434-44-444-4-40000004-400000000004i−4i0000000000000000000000000
χ444-44-444-4-40000004-40000000000−4i4i0000000000000000000000000
χ454-44-444-4-4000000-440000004i−4i00000000000000000000000000000
χ464-44-444-4-4000000-44000000−4i4i00000000000000000000000000000
χ474-4-444-44-4000000004-400000000000004i−4i00000000000000000000
χ484-4-444-44-4000000004-40000000000000−4i4i00000000000000000000
χ494-4-444-44-400000000-44004i−4i0000000000000000000000000000000
χ504-4-444-44-400000000-4400−4i4i0000000000000000000000000000000
χ51888-8-8-88-8000000000000000000000000000000000000000000000
χ5288-88-88-8-8000000000000000000000000000000000000000000000
χ538-8-8-8-8888000000000000000000000000000000000000000000000

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