Finite Group Databasebeta

← Group #265263

Character table — Group #265263

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222224444444444888888888888888816161616161616161616161632323232
order12222222224444444444888824444488888888882244444444884444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1111-1-1-1-1-111-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1111-1-11111-1-1
χ91111111111111111-1-1-1-11111-1-11111-1-111-1-111111-11-1-111-1-1-1-1-11-11-1
χ101111111111111111-1-1-1-11111-1-11111-1-111-1-11111-11-111-1-11-1-1-1-1-11-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-111-11111-11-11
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-111-1-1111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111-1-1-1-11-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-111-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1111-1-1-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-11111-111-1-11-1-11
χ172222222222-2-2-2-2-2-222220000-2-222-2-20000000000000000002-2000000
χ182222222222-2-2-2-2-2-222220000-2-2-2-222000000000000000000-22000000
χ192222222222-2-2-2-2-2-2-2-2-2-200002222-2-2000000000000000000-22000000
χ202222222222-2-2-2-2-2-2-2-2-2-2000022-2-2220000000000000000002-2000000
χ2122222-2-2-22-22-2-222-2000022-2-2000000002-20000000202-200-200000000
χ2222222-2-2-22-22-2-222-2000022-2-2000000002-20000000-20-2200200000000
χ2322222-2-2-22-22-2-222-20000-2-22200000000-22000000020-2200-200000000
χ2422222-2-2-22-22-2-222-20000-2-22200000000-220000000-202-200200000000
χ252222-22-2-2-222-2-22-22000022-2-200000000-2200000020-2002-2000000000
χ262222-22-2-2-222-2-22-22000022-2-200000000-22000000-20200-22000000000
χ272222-22-2-2-222-2-22-220000-2-222000000002-200000020-200-22000000000
χ282222-22-2-2-222-2-22-220000-2-222000000002-2000000-202002-2000000000
χ292222-2-222-2-22222-2-222-2-222222-20000-2-2-2-22200000000000000000000
χ302222-2-222-2-22222-2-222-2-2-2-2-2-22-200002222-2-200000000000000000000
χ312222-2-222-2-22222-2-2-2-2222222-22000022-2-2-2-200000000000000000000
χ322222-2-222-2-22222-2-2-2-222-2-2-2-2-220000-2-2222200000000000000000000
χ332222-2-222-2-2-2-2-2-22222-2-20000-2200000000002i2i−2i−2i00000000002i−2i0000
χ342222-2-222-2-2-2-2-2-22222-2-20000-220000000000−2i−2i2i2i0000000000−2i2i0000
χ352222-2-222-2-2-2-2-2-222-2-22200002-200000000002i2i−2i−2i0000000000−2i2i0000
χ362222-2-222-2-2-2-2-2-222-2-22200002-20000000000−2i−2i2i2i00000000002i−2i0000
χ3744444-4-4-44-4-444-4-440000000000000000000000000000000000000000
χ384444-44-4-4-44-444-44-40000000000000000000000000000000000000000
χ3944-4-400000004i−4i00000002i2−2i222−22002-22i−2i0000002ζ−2ζ2ζ3−2ζ30000000000000000
χ4044-4-400000004i−4i00000002i2−2i222−2200-22−2i2i000000−2ζ2ζ−2ζ32ζ30000000000000000
χ4144-4-400000004i−4i0000000−2i22i2−2222002-22i−2i000000−2ζ2ζ−2ζ32ζ30000000000000000
χ4244-4-400000004i−4i0000000−2i22i2−222200-22−2i2i0000002ζ−2ζ2ζ3−2ζ30000000000000000
χ4344-4-40000000−4i4i00000002i2−2i2−2222002-2−2i2i0000002ζ3−2ζ32ζ−2ζ0000000000000000
χ4444-4-40000000−4i4i00000002i2−2i2−222200-222i−2i000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ4544-4-40000000−4i4i0000000−2i22i222−22002-2−2i2i000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ4644-4-40000000−4i4i0000000−2i22i222−2200-222i−2i0000002ζ3−2ζ32ζ−2ζ0000000000000000
χ474-44-4444-4-4-40000000000000000000022−220022−2200000000000000000000
χ484-44-4444-4-4-400000000000000000000−222200−222200000000000000000000
χ494-44-44-4-44-440000004i−4i4i−4i000000000000000000000000000000000000
χ504-44-44-4-44-44000000−4i4i−4i4i000000000000000000000000000000000000
χ514-44-4-44-444-40000004i−4i−4i4i000000000000000000000000000000000000
χ524-44-4-44-444-4000000−4i4i4i−4i000000000000000000000000000000000000
χ534-44-4-4-44-4440000000000000000000022−2200−222200000000000000000000
χ544-44-4-4-44-44400000000000000000000−22220022−2200000000000000000000
χ558-8-88000000800-8000000000000000000000000000000000000000000
χ568-8-88000000-8008000000000000000000000000000000000000000000

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