Finite Group Databasebeta

← Group #314997

Character table — Group #314997

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12224444224444448888222444448888884488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-111-1111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111-1-1111-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-111
χ111111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ121111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1111-1-11-1-11111-1-11111-1-111-1-1-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-111-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-111
χ17222222222222-2-2-2-22222002-2-2002-2-200000000000000002-200000000
χ18222222222222-2-2-2-2222200-22200-2-2-20000000000000000-2200000000
χ19222222222222-2-2-2-2-2-2-2-2002-2-2002220000000000000000-2200000000
χ20222222222222-2-2-2-2-2-2-2-200-22200-22200000000000000002-200000000
χ212222-2-2-2-222-2-222-2-200002222-2-2-2-20000002-200000000000000000000
χ222222-2-2-2-222-2-222-2-2000022-2-22-2-22000000-2200000000000000000000
χ232222-2-2-2-222-2-222-2-20000-2-222-222-2000000-2200000000000000000000
χ242222-2-2-2-222-2-222-2-20000-2-2-2-222220000002-200000000000000000000
χ252222-2-2-2-222-2-2-2-2220000002-2200-2002i2i−2i−2i00002i−2i0000000000000000
χ262222-2-2-2-222-2-2-2-2220000002-2200-200−2i−2i2i2i0000−2i2i0000000000000000
χ272222-2-2-2-222-2-2-2-222000000-22-2002002i2i−2i−2i0000−2i2i0000000000000000
χ282222-2-2-2-222-2-2-2-222000000-22-200200−2i−2i2i2i00002i−2i0000000000000000
χ292222-2-2-2-2-2-2222-22-222-2-2000000002-20000000000002i−2i2i−2i0000000000
χ302222-2-2-2-2-2-2222-22-222-2-2000000002-2000000000000−2i2i−2i2i0000000000
χ312222-2-2-2-2-2-2222-22-2-2-22200000000-220000000000002i−2i−2i2i0000000000
χ322222-2-2-2-2-2-2222-22-2-2-22200000000-22000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-2-2-222-22-2222-2-200000000-220000002i−2i002i−2i00000000000000
χ342222-2-2-2-2-2-222-22-2222-2-200000000-22000000−2i2i00−2i2i00000000000000
χ352222-2-2-2-2-2-222-22-22-2-222000000002-20000002i−2i00−2i2i00000000000000
χ362222-2-2-2-2-2-222-22-22-2-222000000002-2000000−2i2i002i−2i00000000000000
χ3744444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ3844444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ3944-4-44i−4i4i−4i000000002i2−2i222−222-20002i−2i0002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4044-4-44i−4i4i−4i000000002i2−2i222−22-22000−2i2i000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4144-4-44i−4i4i−4i00000000−2i22i2−22222-20002i−2i000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4244-4-44i−4i4i−4i00000000−2i22i2−2222-22000−2i2i0002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4344-4-4−4i4i−4i4i000000002i2−2i2−22222-2000−2i2i0002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ4444-4-4−4i4i−4i4i000000002i2−2i2−2222-220002i−2i000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4544-4-4−4i4i−4i4i00000000−2i22i222−222-2000−2i2i000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4644-4-4−4i4i−4i4i00000000−2i22i222−22-220002i−2i0002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ474-4-4444-4-44-44-400000000000000000000000000000000000022−22000000
χ484-4-4444-4-44-44-4000000000000000000000000000000000000−2222000000
χ494-4-4444-4-4-44-440000000000000000000000000000000000000000002i2−2i2
χ504-4-4444-4-4-44-44000000000000000000000000000000000000000000−2i22i2
χ514-4-44-4-4444-4-44000000000000000000000000000000000000000022−2200
χ524-4-44-4-4444-4-440000000000000000000000000000000000000000−222200
χ534-4-44-4-444-444-40000000000000000000000000000000000000022−220000
χ544-4-44-4-444-444-400000000000000000000000000000000000000−22220000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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