Finite Group Databasebeta

← Group #263277

Character table — Group #263277

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444488888888888888888888881616161616161616161632323232
order12222244444444448888224444444444888888888824444444888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ41111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ611111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1
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
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-111-1
χ131111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-111-1-1-1-1-11-11
χ141111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111-1-111-1-111-1-11-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1111-1-11
χ172222222-2-2-2222-2-2-200002222-2-2-2-222-2-2000000000000000000000000
χ182222222-2-2-2222-2-2-2000022-2-2-2-222-2-222000000000000000000000000
χ192222222-2-2-2222-2-2-20000-2-22222-2-2-2-222000000000000000000000000
χ202222222-2-2-2222-2-2-20000-2-2-2-2222222-2-2000000000000000000000000
χ21222222-2222-2-2-22-2-22222002-2002-20000-2-200000000000000002-20000
χ22222222-2222-2-2-22-2-2222200-2200-220000-2-20000000000000000-220000
χ23222222-2222-2-2-22-2-2-2-2-2-2002-2002-20000220000000000000000-220000
χ24222222-2222-2-2-22-2-2-2-2-2-200-2200-2200002200000000000000002-20000
χ25222222-2-2-2-2-2-2-2-2220000002-200-220000002i2i−2i−2i2i2i−2i−2i00000000000000
χ26222222-2-2-2-2-2-2-2-2220000002-200-22000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ27222222-2-2-2-2-2-2-2-222000000-22002-20000002i2i−2i−2i−2i−2i2i2i00000000000000
χ28222222-2-2-2-2-2-2-2-222000000-22002-2000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ292222-2-222-2-2-2-2222-222-2-20000000000002-20000000000002-22-2000000
χ302222-2-222-2-2-2-2222-222-2-20000000000002-2000000000000-22-22000000
χ312222-2-222-2-2-2-2222-2-2-222000000000000-220000000000002-2-22000000
χ322222-2-222-2-2-2-2222-2-2-222000000000000-22000000000000-222-2000000
χ332222-2-2-22-2-222-22-2222-2-2000000000000-22000000002-22-20000000000
χ342222-2-2-22-2-222-22-2222-2-2000000000000-2200000000-22-220000000000
χ352222-2-2-22-2-222-22-22-2-2220000000000002-2000000002-2-220000000000
χ362222-2-2-22-2-222-22-22-2-2220000000000002-200000000-222-20000000000
χ374444-4-44-444-4-44-4-440000000000000000000000000000000000000000
χ384444-4-4-4-44444-4-44-40000000000000000000000000000000000000000
χ3944-4-44-440004-4-4000000000000000000000000022−2222−2200000000000000
χ4044-4-44-440004-4-40000000000000000000000000−2222−222200000000000000
χ4144-4-44-4-4000-44400000000000000000000000002i2−2i2−2i22i200000000000000
χ4244-4-44-4-4000-4440000000000000000000000000−2i22i22i2−2i200000000000000
χ4344-4-4-444000-44-400000004-40000000000000000000000000000000000
χ4444-4-4-444000-44-40000000-440000000000000000000000000000000000
χ4544-4-4-44-40004-44000000000004i−4i000000000000000000000000000000
χ4644-4-4-44-40004-4400000000000−4i4i000000000000000000000000000000
χ474-44-400004i−4i0000002i2−2i222−22000000002i−2i2-2002ζ−2ζ2ζ3−2ζ3000000000000000000
χ484-44-400004i−4i0000002i2−2i222−2200000000−2i2i-2200−2ζ2ζ−2ζ32ζ3000000000000000000
χ494-44-400004i−4i000000−2i22i2−2222000000002i−2i2-200−2ζ2ζ−2ζ32ζ3000000000000000000
χ504-44-400004i−4i000000−2i22i2−222200000000−2i2i-22002ζ−2ζ2ζ3−2ζ3000000000000000000
χ514-44-40000−4i4i0000002i2−2i2−2222000000002i−2i-2200−2ζ32ζ3−2ζ2ζ000000000000000000
χ524-44-40000−4i4i0000002i2−2i2−222200000000−2i2i2-2002ζ3−2ζ32ζ−2ζ000000000000000000
χ534-44-40000−4i4i000000−2i22i222−22000000002i−2i-22002ζ3−2ζ32ζ−2ζ000000000000000000
χ544-44-40000−4i4i000000−2i22i222−2200000000−2i2i2-200−2ζ32ζ3−2ζ2ζ000000000000000000
χ558-8-88000800000-8000000000000000000000000000000000000000000
χ568-8-88000-8000008000000000000000000000000000000000000000000

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