Finite Group Databasebeta

← Group #510385

Character table — Group #510385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size112222222224448888888888888888888816161616161616161616161632323232
order1222244448888824444488161616161616161616161616222244448816168888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11-11
χ51111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-11-1-11
χ61111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ911111111111111-1-111-1-1-1-11111-1-1-1-11111111111-1-11-1-1-1-1-1-11
χ1011111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1111-1
χ1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-111-11-1-1
χ1211111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1111-111
χ1311111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1111
χ1411111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-11111-1-1-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1111111111111-1-111-11-1-1-1-11-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-11
χ17222222222-2-2-2-2-2222222-2-200000000000000000000-2-2000000
χ18222222222-2-2-2-2-222-2-2-2-2-2-20000000000000000000022000000
χ19222222222-2-2-2-2-2-2-222-2-22200000000000000000000-22000000
χ20222222222-2-2-2-2-2-2-2-2-22222000000000000000000002-2000000
χ21222-2-2-222-2000002-22i−2i2i−2i00i2i2−i2−i2i2i2−i2−i222−2−200000000002−20000
χ22222-2-2-222-2000002-22i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2−2−2220000000000−220000
χ23222-2-2-222-2000002-2−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2−2−2220000000000−220000
χ24222-2-2-222-2000002-2−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i222−2−200000000002−20000
χ25222-2-2-222-200000-222i−2i−2i2i00i2i2−i2−i2−i2−i2i2i222−2−20000000000−220000
χ26222-2-2-222-200000-222i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−2−22200000000002−20000
χ27222-2-2-222-200000-22−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−2−22200000000002−20000
χ28222-2-2-222-200000-22−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i222−2−20000000000−220000
χ2922-22-222-2-2-2-22-220000000000002i−2i2i−2i00002-200002i−2i00000000
χ3022-22-222-2-2-2-22-220000000000002i−2i2i−2i0000-220000−2i2i00000000
χ3122-22-222-2-2-2-22-22000000000000−2i2i−2i2i00002-20000−2i2i00000000
χ3222-22-222-2-2-2-22-22000000000000−2i2i−2i2i0000-2200002i−2i00000000
χ3322-2-222-22-2-2-2-222000000002i−2i2i−2i00000000002-22i−2i0000000000
χ3422-2-222-22-2-2-2-222000000002i−2i2i−2i0000000000-22−2i2i0000000000
χ3522-2-222-22-2-2-2-22200000000−2i2i−2i2i00000000002-2−2i2i0000000000
χ3622-2-222-22-2-2-2-22200000000−2i2i−2i2i0000000000-222i−2i0000000000
χ3744444-4-4-4-4000000000004i−4i0000000000000000000000000000
χ3844444-4-4-4-400000000000−4i4i0000000000000000000000000000
χ39444-4-44-4-4444-4-44000000000000000000000000000000000000
χ40444-4-44-4-44-4-444-4000000000000000000000000000000000000
χ4144-44-444-4-444-44-4000000000000000000000000000000000000
χ4244-44-4-4-444000000000000022−22−2222000000000000000000000000
χ4344-44-4-4-4440000000000000−222222−22000000000000000000000000
χ4444-4-444-44-4444-4-4000000000000000000000000000000000000
χ4544-4-44-44-440000000000000000022−22−222200000000000000000000
χ4644-4-44-44-4400000000000000000−222222−2200000000000000000000
χ478-8000000042−4200000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000
χ488-8000000042−420000000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000
χ498-80000000−424200000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000
χ508-80000000−42420000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.