Finite Group Databasebeta

← Group #506415

Character table — Group #506415

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11222222222444888888888888161616161616161616161616161616161616161616161616
order122224444888884444888816161616222244444444488888161616161616
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111
χ31111111111111111111111-1-1-1-1111-11-1-1-1111-1-1111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-11-11111-1-1111-1-111-1-1-1-1-1-1
χ51111111111111111-1-111-1-11111111-1111-1-1-1-111-1-1-1-1-111-1-1-1-1
χ61111111111111111-1-111-1-11111-1-1-11-1-1-11-111-1-1-1111111-1-1-1-1
χ71111111111111111-1-111-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1-11111
χ81111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-1-11111
χ911111111111111-1-111-1-111111111-11-1111-111-1-1-1-1-1-1-1-1-111-1-1
χ1011111111111111-1-111-1-1111111-1-11-11-1-1-1-1-1-111-11111-1-111-1-1
χ1111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-11111-1-111
χ1211111111111111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ1311111111111111-1-1-1-1-1-1-1-1111111-1-1-111-11-1-1-1-111111-1-1-1-111
χ1411111111111111-1-1-1-1-1-1-1-11111-1-1111-1-11111111-1-1-1-1-1-1-1-111
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111111-1-11111-1-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1111-1-11-1-1111111-1-1
χ17222222222-2-2-2-2-22222-2-2-2-2000000000000-2000020000000000
χ18222222222-2-2-2-2-222-2-2-2-22200000000000020000-20000000000
χ19222222222-2-2-2-2-2-2-22222-2-200000000000020000-20000000000
χ20222222222-2-2-2-2-2-2-2-2-22222000000000000-2000020000000000
χ2122-22-22-22-2222-2-2002-2002-20000000202-2-20000000000000000
χ2222-22-22-22-2222-2-2002-2002-20000000-20-2220000000000000000
χ2322-22-22-22-2222-2-200-2200-22000000020-22-20000000000000000
χ2422-22-22-22-2222-2-200-2200-220000000-202-220000000000000000
χ2522-22-22-22-2-2-2-222002-200-220000000000000002i−2i0002i−2i000000
χ2622-22-22-22-2-2-2-222002-200-22000000000000000−2i2i000−2i2i000000
χ2722-22-22-22-2-2-2-22200-22002-20000000000000002i−2i000−2i2i000000
χ2822-22-22-22-2-2-2-22200-22002-2000000000000000−2i2i0002i−2i000000
χ2922-2-222-2-2222-22-22-2002-20000002-220-20000000000000000000
χ3022-2-222-2-2222-22-22-2002-2000000-22-2020000000000000000000
χ3122-2-222-2-2222-22-2-2200-220000002-2-2020000000000000000000
χ3222-2-222-2-2222-22-2-2200-22000000-2220-20000000000000000000
χ3322-2-222-2-22-2-22-222-200-220000000000000002i−2i0002i−2i00000000
χ3422-2-222-2-22-2-22-222-200-22000000000000000−2i2i000−2i2i00000000
χ3522-2-222-2-22-2-22-22-22002-20000000000000002i−2i000−2i2i00000000
χ3622-2-222-2-22-2-22-22-22002-2000000000000000−2i2i0002i−2i00000000
χ3744444-4-4-4-400000000000002222−22−22000000000000000000000000
χ3844444-4-4-4-40000000000000−22−222222000000000000000000000000
χ39444-4-444-4-444-4-44000000000000000000000000000000000000
χ40444-4-444-4-4-4-444-4000000000000000000000000000000000000
χ41444-4-4-4-44400000000000000000000000000000000000000022−22
χ42444-4-4-4-444000000000000000000000000000000000000000−2222
χ4344-44-4-44-44000000000000000000000000000000000000022−2200
χ4444-44-4-44-440000000000000000000000000000000000000−222200
χ4544-4-44-444-40000000000000000000000000000000000022−220000
χ4644-4-44-444-400000000000000000000000000000000000−22220000
χ478-8000000042−42000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ488-8000000042−4200000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ498-80000000−4242000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ508-80000000−424200000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000

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