Finite Group Databasebeta

← Group #264933

Character table — Group #264933

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444888888888888888888161616161616161616161616161616163232
order12222244444444448888444444448888888888244444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1-11111-111-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-111-1-11111111111-11-1-1-11-1-11111-1-1-1-1-1-1
χ41111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-11-1-111-11-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1111111111111-1-1-1-11-1-11-1-1-1-11111-1-1
χ611111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-111111111111-111-1-11-1-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1111-1111111-1-111-1-1
χ91111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1111-1
χ101111111111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11-11111-1-111-1-1-1-1-11
χ111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1111-1-111-1-1-11
χ121111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-11-1-1-1-11111111-1
χ131111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-11-1-1-1-1-1-111-1-111-11
χ141111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-111-1-1111-1-1-1-1-1-11-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-111-11-111-1-11111-1-11-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-1-11-111-1-11111-11
χ172222222-2-2-2-2222-2-222-2-22200220000002-200000-2000-2000000000000
χ182222222-2-2-2-2222-2-222-2-2-2-200-2-20000002-20000020002000000000000
χ192222222-2-2-2-2222-2-2-2-2222200-2-2000000-22000002000-2000000000000
χ202222222-2-2-2-2222-2-2-2-222-2-20022000000-2200000-20002000000000000
χ21222222-2-2-2-2-2-2-2-2220000002-2002-22i2i−2i−2i000000000000000000002i−2i00
χ22222222-2-2-2-2-2-2-2-2220000002-2002-2−2i−2i2i2i00000000000000000000−2i2i00
χ23222222-2-2-2-2-2-2-2-222000000-2200-222i2i−2i−2i00000000000000000000−2i2i00
χ24222222-2-2-2-2-2-2-2-222000000-2200-22−2i−2i2i2i000000000000000000002i−2i00
χ252222-2-22-2-222-2-22-220000002200-2-200000022-2-20000200-20000000000
χ262222-2-22-2-222-2-22-220000002200-2-2000000-2-2220000-20020000000000
χ272222-2-22-2-222-2-22-22000000-2-2002200000022-2-20000-20020000000000
χ282222-2-22-2-222-2-22-22000000-2-20022000000-2-2220000200-20000000000
χ292222-2-2-222-2-222-2-222222002-200-220000-2-200000000000000002-20000
χ302222-2-2-222-2-222-2-22222200-22002-20000-2-20000000000000000-220000
χ312222-2-2-222-2-222-2-22-2-2-2-2002-200-220000220000000000000000-220000
χ322222-2-2-222-2-222-2-22-2-2-2-200-22002-200002200000000000000002-20000
χ332222-2-2-2-2-22222-22-222-2-2000000000000-220000202-200-200000000000
χ342222-2-2-2-2-22222-22-222-2-2000000000000-220000-20-2200200000000000
χ352222-2-2-2-2-22222-22-2-2-2220000000000002-2000020-2-200200000000000
χ362222-2-2-2-2-22222-22-2-2-2220000000000002-20000-202200-200000000000
χ37444444-44444-4-4-4-4-40000000000000000000000000000000000000000
χ384444-4-4444-4-4-4-444-40000000000000000000000000000000000000000
χ3944-4-44-4400004-4-4000000000000000000000000000000000022−22000000
χ4044-4-44-4400004-4-40000000000000000000000000000000000−2222000000
χ4144-4-44-4-40000-44400000000004i−4i000000000000000000000000000000
χ4244-4-44-4-40000-4440000000000−4i4i000000000000000000000000000000
χ4344-4-4-4440000-44-40000004-40000000000000000000000000000000000
χ4444-4-4-4440000-44-4000000-440000000000000000000000000000000000
χ4544-4-4-44-400004-44000000000000000000000000000000002i2−2i200000000
χ4644-4-4-44-400004-4400000000000000000000000000000000−2i22i200000000
χ474-4-440004i−4i00000002i2−2i222−22000000002ζ−2ζ2ζ3−2ζ3002-22i−2i000000000000000000
χ484-4-440004i−4i00000002i2−2i222−2200000000−2ζ2ζ−2ζ32ζ300-22−2i2i000000000000000000
χ494-4-440004i−4i0000000−2i22i2−2222000000002ζ−2ζ2ζ3−2ζ300-22−2i2i000000000000000000
χ504-4-440004i−4i0000000−2i22i2−222200000000−2ζ2ζ−2ζ32ζ3002-22i−2i000000000000000000
χ514-4-44000−4i4i00000002i2−2i2−2222000000002ζ3−2ζ32ζ−2ζ002-2−2i2i000000000000000000
χ524-4-44000−4i4i00000002i2−2i2−222200000000−2ζ32ζ3−2ζ2ζ00-222i−2i000000000000000000
χ534-4-44000−4i4i0000000−2i22i222−22000000002ζ3−2ζ32ζ−2ζ00-222i−2i000000000000000000
χ544-4-44000−4i4i0000000−2i22i222−2200000000−2ζ32ζ3−2ζ2ζ002-2−2i2i000000000000000000
χ558-88-8000008-8000000000000000000000000000000000000000000000
χ568-88-800000-88000000000000000000000000000000000000000000000

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