Finite Group Databasebeta

← Group #317117

Character table — Group #317117

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12224444224444448888224488888888882224444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111-111-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-1-1-1-11111111111-1-1-1-1
χ91111111111111111-1-1-1-111111111-1-1-1-1-1-1-11-1-11-1-1-111-1-11111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-111-1-111-1-111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-111111-1-1-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111-1-1111111-111-1-1-111-1-1-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-11111-1-111111-111-11-1-1-1-111-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-111-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111111-1-11111-1-1-1-111
χ17222222222222-2-2-2-22222000022-2-2-2-200000000002-200000000000000
χ18222222222222-2-2-2-222220000-2-222-2-20000000000-2200000000000000
χ19222222222222-2-2-2-2-2-2-2-2000022-2-2220000000000-2200000000000000
χ20222222222222-2-2-2-2-2-2-2-20000-2-2222200000000002-200000000000000
χ212222-2-2-2-222-2-22-22-2000000002i−2i2i−2i002i2i−2i−2i200-2000000000000000000
χ222222-2-2-2-222-2-22-22-2000000002i−2i2i−2i00−2i−2i2i2i-2002000000000000000000
χ232222-2-2-2-222-2-22-22-200000000−2i2i−2i2i002i2i−2i−2i-2002000000000000000000
χ242222-2-2-2-222-2-22-22-200000000−2i2i−2i2i00−2i−2i2i2i200-2000000000000000000
χ252222-2-2-2-222-2-2-22-22000022-2-22i−2i−2i2i0000000000000000002i−2i00000000
χ262222-2-2-2-222-2-2-22-22000022-2-2−2i2i2i−2i000000000000000000−2i2i00000000
χ272222-2-2-2-222-2-2-22-220000-2-2222i−2i−2i2i000000000000000000−2i2i00000000
χ282222-2-2-2-222-2-2-22-220000-2-222−2i2i2i−2i0000000000000000002i−2i00000000
χ292222-2-2-2-2-2-22222-2-222-2-2000000002-20000000000002i−2i2i−2i0000000000
χ302222-2-2-2-2-2-22222-2-222-2-2000000002-2000000000000−2i2i−2i2i0000000000
χ312222-2-2-2-2-2-22222-2-2-2-22200000000-220000000000002i−2i−2i2i0000000000
χ322222-2-2-2-2-2-22222-2-2-2-22200000000-22000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-2-2-222-2-22222-2-200000000-2200000220-2-20000000000000000
χ342222-2-2-2-2-2-222-2-22222-2-200000000-2200000-2-20220000000000000000
χ352222-2-2-2-2-2-222-2-222-2-222000000002-2000002-20-220000000000000000
χ362222-2-2-2-2-2-222-2-222-2-222000000002-200000-2202-20000000000000000
χ3744444444-4-4-4-44-4-440000000000000000000000000000000000000000
χ3844444444-4-4-4-4-444-40000000000000000000000000000000000000000
χ3944-4-44i4i−4i−4i0000000022−222i2−2i22-22i−2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4044-4-44i4i−4i−4i0000000022−222i2−2i2-22−2i2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4144-4-44i4i−4i−4i00000000−2222−2i22i22-22i−2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4244-4-44i4i−4i−4i00000000−2222−2i22i2-22−2i2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4344-4-4−4i−4i4i4i0000000022−22−2i22i22-2−2i2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4444-4-4−4i−4i4i4i0000000022−22−2i22i2-222i−2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ4544-4-4−4i−4i4i4i00000000−22222i2−2i22-2−2i2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ4644-4-4−4i−4i4i4i00000000−22222i2−2i2-222i−2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ474-4-444-44-44-44-40000000000000000000000000000000000000022−220000
χ484-4-444-44-44-44-400000000000000000000000000000000000000−22220000
χ494-4-444-44-4-44-44000000000000000000000000000000000000000022−2200
χ504-4-444-44-4-44-440000000000000000000000000000000000000000−222200
χ514-4-44-44-444-4-4400000000000000000000000000000000000000000022−22
χ524-4-44-44-444-4-44000000000000000000000000000000000000000000−2222
χ534-4-44-44-44-444-400000000000000000000000000000000000022−22000000
χ544-4-44-44-44-444-4000000000000000000000000000000000000−2222000000
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.