Finite Group Databasebeta

← Group #506307

Character table — Group #506307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11222222222444888888888888161616161616161616161616161616161616161616161616
order122224444888884444888816161616224444444444488888161616161616
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1111111
χ31111111111111111111111-1-1-1-11-1111-1-1-1111-1-1111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-11-1-1-11111-1-1111-1-111-1-1-1-1-1-1
χ51111111111111111-1-111-1-11111111-1-11-1-1-111-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-111-1-11111-1-1-111-111-1-1-111-111-1-111-1-1-1-1
χ71111111111111111-1-111-1-1-1-1-1-11-11-1-1-111-11111-1-1-1-1-1-1-11111
χ81111111111111111-1-111-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-11111-1-11111
χ911111111111111-1-111-1-11111111-11-1-1-1-1-1-1-1-111-11111-1-1-1-111
χ1011111111111111-1-111-1-1111111-11-111111-111-1-1-1-1-1-1-1-1-1-1-111
χ1111111111111111-1-111-1-111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-11111-1-1
χ1211111111111111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1111111-1-1
χ1311111111111111-1-1-1-1-1-1-1-111111-1111-1111-1-1-1-11-1-111-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-11111-11-1-1-11-1-111111111-1-1-1-111-1-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-111-1-111
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111111-1-111
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
χ21222-2-222-2-2222-2-22i−2i002i−2i00000020-20000002i−2i0000000000000
χ22222-2-222-2-2222-2-22i−2i002i−2i000000-202000000−2i2i0000000000000
χ23222-2-222-2-2222-2-2−2i2i00−2i2i00000020-2000000−2i2i0000000000000
χ24222-2-222-2-2222-2-2−2i2i00−2i2i000000-2020000002i−2i0000000000000
χ25222-2-222-2-2-2-2-2222i−2i00−2i2i0000000002-20000000002i−2i00000000
χ26222-2-222-2-2-2-2-2222i−2i00−2i2i000000000-22000000000−2i2i00000000
χ27222-2-222-2-2-2-2-222−2i2i002i−2i0000000002-2000000000−2i2i00000000
χ28222-2-222-2-2-2-2-222−2i2i002i−2i000000000-220000000002i−2i00000000
χ2922-22-22-22-222-2-22002-2002-2000002000-22-20000000000000000
χ3022-22-22-22-222-2-22002-2002-200000-20002-220000000000000000
χ3122-22-22-22-222-2-2200-2200-22000002000-2-220000000000000000
χ3222-22-22-22-222-2-2200-2200-2200000-200022-20000000000000000
χ3322-22-22-22-2-2-222-2002-200-220000000000000002i−2i0002i−2i000000
χ3422-22-22-22-2-2-222-2002-200-22000000000000000−2i2i000−2i2i000000
χ3522-22-22-22-2-2-222-200-22002-20000000000000002i−2i000−2i2i000000
χ3622-22-22-22-2-2-222-200-22002-2000000000000000−2i2i0002i−2i000000
χ3744444-4-4-4-400000000000000000000000000000000000000022−22
χ3844444-4-4-4-4000000000000000000000000000000000000000−2222
χ39444-4-4-4-444000000000000000000000000000000000000022−2200
χ40444-4-4-4-4440000000000000000000000000000000000000−222200
χ4144-44-4-44-4400000000000002222−22−22000000000000000000000000
χ4244-44-4-44-440000000000000−22−222222000000000000000000000000
χ4344-4-444-4-4444-44-4000000000000000000000000000000000000
χ4444-4-444-4-44-4-44-44000000000000000000000000000000000000
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.