Finite Group Databasebeta

← Group #173520

Character table — Group #173520

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111111144444444444488888888888881616161616161616161616161616161616163232
order12222222224444444444222222444444424444488888888888844
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1111-1-1-1-11-1-1-11-111111111-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1111-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-11-1-111-1-1-11-11-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-111-1-11-1-111-1-1-11-11-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1111-1-1-1-111-1-11-1-111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-1111-1-1-1-111-1-11-1-11-1-1-1-11111-1-1-1-111
χ911111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-111-1-111-1-111-1-11-1
χ1011111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-11-1-1-111-1-111-1-111-11
χ1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-111111-1-111-1-1-1-111-11
χ1211111111-1-111-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1111-1-111-1-11111-1-11-1
χ1311111111-1-111-1-1-1-11111-1-111-1-1-111-1-11111-1-1-1111-1-1-1-111-1-1111-1
χ1411111111-1-111-1-1-1-11111-1-111-1-1-111-1-11111-1-1-11-1-11111-1-111-1-1-11
χ1511111111-1-111-1-1-1-11111-1-1-1-111-11111-1-11-111-1-111-1-1-1-11111-1-1-11
χ1611111111-1-111-1-1-1-11111-1-1-1-111-11111-1-11-111-1-1-1-11111-1-1-1-1111-1
χ1722222222222-2-2-2-2-2-2-22-22200002-2-200002000-2000000000000000
χ1822222222222-2-2-2-2-2-2-22-2-2-200002220000-20002000000000000000
χ192222222222-2222-2-2-2-2-22000022-200002200-200-200000000000000
χ202222222222-2222-2-2-2-2-220000-2-2-20000-2-200200200000000000000
χ212222222222-2-2-2-22222-2-2002200-20022000-20-20000000000000000
χ222222222222-2-2-2-22222-2-200-2-200-200-2-20002020000000000000000
χ2322222222-2-22-22222-2-22-2220000-2220000-2000-2000000000000000
χ2422222222-2-22-22222-2-22-2-2-20000-2-2-2000020002000000000000000
χ2522222222-2-2-22-2-222-2-2-2200002220000-2-200-200200000000000000
χ2622222222-2-2-22-2-222-2-2-220000-2-2200002200200-200000000000000
χ2722222222-2-2-2-222-2-222-2-2002200200-2-2000-2020000000000000000
χ2822222222-2-2-2-222-2-222-2-200-2-2002002200020-20000000000000000
χ2922-2-22-22-22-2022-200000-200002-2000002-2000000i2−i2i2−i20000i2−i2i2−i200
χ3022-2-22-22-22-2022-200000-200002-2000002-2000000−i2i2−i2i20000−i2i2−i2i200
χ3122-2-22-22-22-2022-200000-20000-2200000-22000000i2−i2i2−i20000−i2i2−i2i200
χ3222-2-22-22-22-2022-200000-20000-2200000-22000000−i2i2−i2i20000i2−i2i2−i200
χ3322-2-22-22-2-2202-2200000-200002-200000-22000000i2−i2−i2i20000i2−i2−i2i200
χ3422-2-22-22-2-2202-2200000-200002-200000-22000000−i2i2i2−i20000−i2i2i2−i200
χ3522-2-22-22-2-2202-2200000-20000-22000002-2000000i2−i2−i2i20000−i2i2i2−i200
χ3622-2-22-22-2-2202-2200000-20000-22000002-2000000−i2i2i2−i20000i2−i2−i2i200
χ374444-4-4-4-40040000000-404-40000000000000000000000000000000
χ384444-4-4-4-40040000000-40-440000000000000000000000000000000
χ394444-4-4-4-400-400000004000000004i−4i000000000000000000000000
χ404444-4-4-4-400-40000000400000000−4i4i000000000000000000000000
χ4144-4-44-44-44-40-4-44000004000000000000000000000000000000000
χ4244-4-44-44-4-440-44-4000004000000000000000000000000000000000
χ434-44-444-4-40000004i−4i0000000000000000000000000002-22i−2i000000
χ444-44-444-4-40000004i−4i000000000000000000000000000-22−2i2i000000
χ454-44-444-4-4000000−4i4i0000000000000000000000000002-2−2i2i000000
χ464-44-444-4-4000000−4i4i000000000000000000000000000-222i−2i000000
χ474-44-4-4-444000000004-4000000000004-40000000000000000000000
χ484-44-4-4-444000000004-400000000000-440000000000000000000000
χ494-44-4-4-44400000000-4400004-400000000000000000000000000000
χ504-44-4-4-44400000000-440000-4400000000000000000000000000000
χ5188-8-8-88-88000000000000000000000000000000000000000000000
χ528-8-888-8-88000000000000000000000000000000000000000000000
χ538-8-88-888-8000000000000000000000000000000000000000000000

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