Finite Group Databasebeta

← Group #326598

Character table — Group #326598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12224444224444448888444488888888884444444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111-1-1-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ17222222222222-2-2-2-222220000220000-2-2-2-200002-20000000000000000
χ18222222222222-2-2-2-222220000-2-2000022-2-20000-220000000000000000
χ19222222222222-2-2-2-2-2-2-2-20000220000-2-2220000-220000000000000000
χ20222222222222-2-2-2-2-2-2-2-20000-2-20000222200002-20000000000000000
χ212222-2-2-2-222-2-22-22-2000000002i−2i2i2i−2i−2i2i−2i000000002-200000000000000
χ222222-2-2-2-222-2-22-22-2000000002i−2i−2i−2i2i2i2i−2i00000000-2200000000000000
χ232222-2-2-2-222-2-22-22-200000000−2i2i2i2i−2i−2i−2i2i00000000-2200000000000000
χ242222-2-2-2-222-2-22-22-200000000−2i2i−2i−2i2i2i−2i2i000000002-200000000000000
χ252222-2-2-2-222-2-2-22-22000022-2-22i−2i0000−2i2i0000000000002i−2i0000000000
χ262222-2-2-2-222-2-2-22-22000022-2-2−2i2i00002i−2i000000000000−2i2i0000000000
χ272222-2-2-2-222-2-2-22-220000-2-2222i−2i0000−2i2i000000000000−2i2i0000000000
χ282222-2-2-2-222-2-2-22-220000-2-222−2i2i00002i−2i0000000000002i−2i0000000000
χ292222-2-2-2-2-2-22222-2-222-2-20000000000002-22-22-2000000000000000000
χ302222-2-2-2-2-2-22222-2-222-2-20000000000002-2-22-22000000000000000000
χ312222-2-2-2-2-2-22222-2-2-2-222000000000000-222-2-22000000000000000000
χ322222-2-2-2-2-2-22222-2-2-2-222000000000000-22-222-2000000000000000000
χ332222-2-2-2-2-2-222-2-22222-2-2000000000000-22000000002i−2i002i−2i00000000
χ342222-2-2-2-2-2-222-2-22222-2-2000000000000-2200000000−2i2i00−2i2i00000000
χ352222-2-2-2-2-2-222-2-222-2-2220000000000002-2000000002i−2i00−2i2i00000000
χ362222-2-2-2-2-2-222-2-222-2-2220000000000002-200000000−2i2i002i−2i00000000
χ3744444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ3844444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ3944-4-444-4-44-44-40000000000000000000000000000000000000022−220000
χ4044-4-444-4-44-44-400000000000000000000000000000000000000−22220000
χ4144-4-444-4-4-44-44000000000000000000000000000000000000000022−2200
χ4244-4-444-4-4-44-440000000000000000000000000000000000000000−222200
χ4344-4-4-4-4444-4-440000000000000000000000000000000000000000002i2−2i2
χ4444-4-4-4-4444-4-44000000000000000000000000000000000000000000−2i22i2
χ4544-4-4-4-444-444-40000000000000000000000000000000000002i2−2i2000000
χ4644-4-4-4-444-444-4000000000000000000000000000000000000−2i22i2000000
χ474-44-44i−4i4i−4i000000002i2−2i222−222-22i−2i002ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ484-44-44i−4i4i−4i000000002i2−2i222−22-22−2i2i00−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ494-44-44i−4i4i−4i00000000−2i22i2−22222-22i−2i00−2ζ2ζ−2ζ32ζ300000000000000000000000000
χ504-44-44i−4i4i−4i00000000−2i22i2−2222-22−2i2i002ζ−2ζ2ζ3−2ζ300000000000000000000000000
χ514-44-4−4i4i−4i4i000000002i2−2i2−22222-2−2i2i002ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ524-44-4−4i4i−4i4i000000002i2−2i2−2222-222i−2i00−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ534-44-4−4i4i−4i4i00000000−2i22i222−222-2−2i2i00−2ζ32ζ3−2ζ2ζ00000000000000000000000000
χ544-44-4−4i4i−4i4i00000000−2i22i222−22-222i−2i002ζ3−2ζ32ζ−2ζ00000000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

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