Finite Group Databasebeta

← Group #509296

Character table — Group #509296

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11222222222444444488888888888888161616161616161616161616161632323232
order1222244448888816161616224444881616161616164444888888161616162488
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111-11-1-1-11111111111-1-1-1-111-1-1-1-1-1-11-1-11
χ41111111111111111111-11-1-1-111111111-1-111-1-1-1-111-1-1-1-1-111-1
χ5111111111111111111-11-11-1-1-1-111-1-1-1-111-1-11-1-1-1-1-111-1-1111-1
χ6111111111111111111-11-11-1-1-1-111-1-1-1-1-1-1111-1111111-1-1-1-1-11
χ7111111111111111111-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-1111-1-1-1
χ8111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1111
χ911111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-11-1
χ1111111111111111-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111
χ1211111111111111-1-1-1-11-11-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1
χ1311111111111111-1-1-1-1-11-11-1-1-1-1-1-1111111-1-11-11111-1-111-11-1-1
χ1411111111111111-1-1-1-1-11-11-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1111-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1111-1-111-1-1-1-11-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111-1-111-11
χ17222222222-2-2-2-2-200002222-2-2-2-20000000000-22000000000000
χ18222222222-2-2-2-2-200002-22-222-2-200000000002-2000000000000
χ19222222222-2-2-2-2-20000-22-2222220000000000-2-2000000000000
χ20222222222-2-2-2-2-20000-2-2-2-2-2-222000000000022000000000000
χ21222-2-222-2-222-2-22222200000000-2-20000002i−2i00002i−2i00000000
χ22222-2-222-2-222-2-22222200000000-2-2000000−2i2i0000−2i2i00000000
χ23222-2-222-2-222-2-22-2-2-2-200000000220000002i−2i0000−2i2i00000000
χ24222-2-222-2-222-2-22-2-2-2-20000000022000000−2i2i00002i−2i00000000
χ2522-22-22-22-20000022−2−2020-22i−2i2i−2i2−2i2i2−i2−i200000000002−2i2−i20000
χ2622-22-22-22-20000022−2−2020-2−2i2i−2i2i2−2−i2−i2i2i200000000002−2−i2i20000
χ2722-22-22-22-20000022−2−20-2022i−2i−2i2i2−2−i2−i2i2i20000000000−22i2−i20000
χ2822-22-22-22-20000022−2−20-202−2i2i2i−2i2−2i2i2−i2−i20000000000−22−i2i20000
χ2922-22-22-22-200000−2−222020-22i−2i2i−2i−22−i2−i2i2i20000000000−22−i2i20000
χ3022-22-22-22-200000−2−222020-2−2i2i−2i2i−22i2i2−i2−i20000000000−22i2−i20000
χ3122-22-22-22-200000−2−2220-2022i−2i−2i2i−22i2i2−i2−i200000000002−2−i2i20000
χ3222-22-22-22-200000−2−2220-202−2i2i2i−2i−22−i2−i2i2i200000000002−2i2−i20000
χ3322-22-2-22-22-2-2-222000000000000002-22-22-200002-20000000000
χ3422-22-2-22-22-2-2-222000000000000002-22-2-220000-220000000000
χ3522-22-2-22-22-2-2-22200000000000000-22-222-20000-220000000000
χ3622-22-2-22-22-2-2-22200000000000000-22-22-2200002-20000000000
χ3744444-4-4-4-400000000000000000002i2−2i2−2i22i2000000000000000000
χ3844444-4-4-4-40000000000000000000−2i22i22i2−2i2000000000000000000
χ39444-4-444-4-4-4-444-4000000000000000000000000000000000000
χ40444-4-4-4-44400000000040-400000000000000000000000000000
χ41444-4-4-4-444000000000-40400000000000000000000000000000
χ4244-44-4-44-44444-4-4000000000000000000000000000000000000
χ4344-4-444-4-44000002222−22−2200000000−22220000000000000000000000
χ4444-4-444-4-4400000−22−2222220000000022−220000000000000000000000
χ4544-4-44-444-444-44-4000000000000000000000000000000000000
χ4644-4-44-444-4-4-44-44000000000000000000000000000000000000
χ478-8000000042−420002ζ+2ζ3+2ζ5+2ζ7−2ζ−2ζ3−2ζ5−2ζ72ζ−2ζ3−2ζ5+2ζ7−2ζ+2ζ3+2ζ5−2ζ700000000000000000000000000000000
χ488-8000000042−42000−2ζ−2ζ3−2ζ5−2ζ72ζ+2ζ3+2ζ5+2ζ7−2ζ+2ζ3+2ζ5−2ζ72ζ−2ζ3−2ζ5+2ζ700000000000000000000000000000000
χ498-80000000−42420002ζ−2ζ3−2ζ5+2ζ7−2ζ+2ζ3+2ζ5−2ζ7−2ζ−2ζ3−2ζ5−2ζ72ζ+2ζ3+2ζ5+2ζ700000000000000000000000000000000
χ508-80000000−4242000−2ζ+2ζ3+2ζ5−2ζ72ζ−2ζ3−2ζ5+2ζ72ζ+2ζ3+2ζ5+2ζ7−2ζ−2ζ3−2ζ5−2ζ700000000000000000000000000000000

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