Finite Group Databasebeta

← Group #173770

Character table — Group #173770

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444224444444444444444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111-1-1111-1-1-11-11-1-11111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111-1-1111-1-1-11-11-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-111-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-11-1111-1-111-1-111-1-11-1
χ1011111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-11-11-1-111-1-111-1-111-11
χ1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-11-111-1-111-1-1-1-111-11
χ1211111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-11-1-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1111-111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1111-1-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1-1-1111111-1-111-1-111-111-1-1-111-1-1111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1-1-1111111-1-111-1-111-111-1-1-111-1-11-1-11111-1-111-1-1-11
χ17222222222222-2-222-2-2-2-222220000-20000-20-200000000000000000
χ18222222222222-2-222-2-2-2-2-2-2-2-20000-2000020200000000000000000
χ192222222222-2-222-2-222-2-200002200-222000-20-20000000000000000
χ202222222222-2-222-2-222-2-20000-2-200-2-2-20002020000000000000000
χ212222222222-2-2-2-2-2-2-2-22200000022200-2-200002-200000000000000
χ222222222222-2-2-2-2-2-2-2-222000000-2-2200220000-2200000000000000
χ2322222222-2-22222-2-2-2-22200000022-200220000-2-200000000000000
χ2422222222-2-22222-2-2-2-222000000-2-2-200-2-200002200000000000000
χ2522222222-2-222-2-2-2-222-2-2000022002-2-200020-20000000000000000
χ2622222222-2-222-2-2-2-222-2-20000-2-200222000-2020000000000000000
χ2722222222-2-2-2-22222-2-2-2-222-2-2000020000-20200000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-22200002000020-200000000000000000
χ2922-22-2-2-22002i−2i2i−2i00002-20000002i−2i0002-200000000002−2i2−i2i2−i22−200
χ3022-22-2-2-22002i−2i2i−2i00002-20000002i−2i0002-20000000000−22−i2i2−i2i2−2200
χ3122-22-2-2-22002i−2i2i−2i00002-2000000−2i2i000-2200000000002−2i2−i2−i2i2−2200
χ3222-22-2-2-22002i−2i2i−2i00002-2000000−2i2i000-220000000000−22−i2i2i2−i22−200
χ3322-22-2-2-2200−2i2i−2i2i00002-20000002i−2i000-2200000000002−2−i2i2i2−i2−2200
χ3422-22-2-2-2200−2i2i−2i2i00002-20000002i−2i000-220000000000−22i2−i2−i2i22−200
χ3522-22-2-2-2200−2i2i−2i2i00002-2000000−2i2i0002-200000000002−2−i2i2−i2i22−200
χ3622-22-2-2-2200−2i2i−2i2i00002-2000000−2i2i0002-20000000000−22i2−i2i2−i2−2200
χ37444-44-4-4-40000004-40000004-400000000000000000000000000000
χ38444-44-4-4-40000004-4000000-4400000000000000000000000000000
χ39444-44-4-4-4000000-4400004-40000000000000000000000000000000
χ40444-44-4-4-4000000-440000-440000000000000000000000000000000
χ4144-44-4-4-44004i−4i−4i4i0000-44000000000000000000000000000000000
χ4244-44-4-4-4400−4i4i4i−4i0000-44000000000000000000000000000000000
χ434-4-4444-4-4000000004-4000000000004i−4i0000000000000000000000
χ444-4-4444-4-4000000004-400000000000−4i4i0000000000000000000000
χ454-4-4444-4-400000000-440000004i−4i000000000000000000000000000
χ464-4-4444-4-400000000-44000000−4i4i000000000000000000000000000
χ474-4-4-44-4444-4000000000000000000000000000002-22-20000000000
χ484-4-4-44-4444-400000000000000000000000000000-22-220000000000
χ494-4-4-44-444-44000000000000000000000000000002-2-220000000000
χ504-4-4-44-444-4400000000000000000000000000000-222-20000000000
χ5188-8-8-888-8000000000000000000000000000000000000000000000
χ528-888-8-88-8000000000000000000000000000000000000000000000
χ538-88-8-88-88000000000000000000000000000000000000000000000

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