Finite Group Databasebeta

← Group #265281

Character table — Group #265281

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444488888888888888888888881616161616161616161632323232
order12222222224444448888244444444444888888888824444444884444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-11-11
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-111-1-11-11-1
χ131111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1
χ141111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-111-1
χ172222222222-2-2-2-2-2-200002222-2-2-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-2-2-2000022-2-2-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-20000-2-22222-2-2-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-20000-2-2-2-2222222-2-2000000000000000000000000
χ2122222-2-2-2-222-2-222-222-2-200000000000000002-200002-22-20000000000
χ2222222-2-2-2-222-2-222-222-2-200000000000000002-20000-22-220000000000
χ2322222-2-2-2-222-2-222-2-2-2220000000000000000-2200002-2-220000000000
χ2422222-2-2-2-222-2-222-2-2-2220000000000000000-220000-222-20000000000
χ252222-222-2-2-22222-2-222222-2002-20000000000-2-20000000000002-20000
χ262222-222-2-2-22222-2-22222-2200-220000000000-2-2000000000000-220000
χ272222-222-2-2-22222-2-2-2-2-2-22-2002-2000000000022000000000000-220000
χ282222-222-2-2-22222-2-2-2-2-2-2-2200-220000000000220000000000002-20000
χ292222-222-2-2-2-2-2-2-22200002-200-220000002i2i−2i−2i002i2i−2i−2i00000000000000
χ302222-222-2-2-2-2-2-2-22200002-200-22000000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ312222-222-2-2-2-2-2-2-2220000-22002-20000002i2i−2i−2i00−2i−2i2i2i00000000000000
χ322222-222-2-2-2-2-2-2-2220000-22002-2000000−2i−2i2i2i002i2i−2i−2i00000000000000
χ332222-2-2-222-22-2-22-2222-2-20000000000000000-22000000002-22-2000000
χ342222-2-2-222-22-2-22-2222-2-20000000000000000-2200000000-22-22000000
χ352222-2-2-222-22-2-22-22-2-22200000000000000002-2000000002-2-22000000
χ362222-2-2-222-22-2-22-22-2-22200000000000000002-200000000-222-2000000
χ3744444-4-4-4-44-444-4-440000000000000000000000000000000000000000
χ384444-4-4-444-4-444-44-40000000000000000000000000000000000000000
χ3944-4-444-44-4-4000000000000000000000022−2222−2200000000000000000000
χ4044-4-444-44-4-40000000000000000000000−2222−222200000000000000000000
χ4144-4-44-44-44-40000000000000000004-400000000000000000000000000
χ4244-4-44-44-44-4000000000000000000-4400000000000000000000000000
χ4344-4-4-44-4-44400000000000000000000002i2−2i2−2i22i200000000000000000000
χ4444-4-4-44-4-4440000000000000000000000−2i22i22i2−2i200000000000000000000
χ4544-4-4-4-444-44000000000000000000004i−4i000000000000000000000000
χ4644-4-4-4-444-4400000000000000000000−4i4i000000000000000000000000
χ474-44-400000004i−4i0002i2−2i222−22002i−2i002-200000000002ζ−2ζ2ζ3−2ζ300000000000000
χ484-44-400000004i−4i0002i2−2i222−2200−2i2i00-220000000000−2ζ2ζ−2ζ32ζ300000000000000
χ494-44-400000004i−4i000−2i22i2−2222002i−2i002-20000000000−2ζ2ζ−2ζ32ζ300000000000000
χ504-44-400000004i−4i000−2i22i2−222200−2i2i00-2200000000002ζ−2ζ2ζ3−2ζ300000000000000
χ514-44-40000000−4i4i0002i2−2i2−2222002i−2i00-220000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ524-44-40000000−4i4i0002i2−2i2−222200−2i2i002-200000000002ζ3−2ζ32ζ−2ζ00000000000000
χ534-44-40000000−4i4i000−2i22i222−22002i−2i00-2200000000002ζ3−2ζ32ζ−2ζ00000000000000
χ544-44-40000000−4i4i000−2i22i222−2200−2i2i002-20000000000−2ζ32ζ3−2ζ2ζ00000000000000
χ558-8-88000000800-8000000000000000000000000000000000000000000
χ568-8-88000000-8008000000000000000000000000000000000000000000

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