Finite Group Databasebeta

← Group #10513

Character table — Group #10513

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34
size111122222244448888888888881616161616161616
order1222224444444444448888888822448888
χ11111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ4111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111-1-1-1-1-1-1-1-111111-11-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111-11-1111-1-1
χ92222222222-2-2-2-2000022-2-2000000000000
χ102222222222-2-2-2-20000-2-222000000000000
χ11222222-2-2-2-222-2-2000000002i2i−2i−2i00000000
χ12222222-2-2-2-222-2-200000000−2i−2i2i2i00000000
χ13222222-2-2-2-2-2-22222-2-20000000000000000
χ14222222-2-2-2-2-2-222-2-2220000000000000000
χ152222-2-222-2-22-22-20000000000000000002i−2i
χ162222-2-222-2-22-22-2000000000000000000−2i2i
χ172222-2-222-2-2-22-2200000000000000002i−2i00
χ182222-2-222-2-2-22-220000000000000000−2i2i00
χ192222-2-2-2-2222-2-2200000000000020-200000
χ202222-2-2-2-2222-2-22000000000000-20200000
χ212222-2-2-2-222-222-2000000000000020-20000
χ222222-2-2-2-222-222-20000000000000-2020000
χ2344-4-400004-400002i−2i2i−2i0000000000000000
χ2444-4-400004-40000−2i2i−2i2i0000000000000000
χ2544-4-40000-4400002i−2i−2i2i0000000000000000
χ2644-4-40000-440000−2i2i2i−2i0000000000000000
χ274-44-4004i−4i000000000000002ζ−2ζ2ζ3−2ζ300000000
χ284-44-4004i−4i00000000000000−2ζ2ζ−2ζ32ζ300000000
χ294-44-400−4i4i000000000000002ζ3−2ζ32ζ−2ζ00000000
χ304-44-400−4i4i00000000000000−2ζ32ζ3−2ζ2ζ00000000
χ314-4-444-40000000000000022−22000000000000
χ324-4-444-400000000000000−2222000000000000
χ334-4-44-4400000000000022−2200000000000000
χ344-4-44-44000000000000−222200000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.