Finite Group Databasebeta

← Group #8736

Character table — Group #8736

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111222222222222228888888888888888888888888888
order1222222222444444442244444444448888888888888888
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-22222-2-2-2-2000000002i−2i2i−2i0000000000000000
χ18222222-2-2-2-22222-2-2-2-200000000−2i2i−2i2i0000000000000000
χ19222222-2-2-2-2-2-2-2-22222000000002i−2i−2i2i0000000000000000
χ20222222-2-2-2-2-2-2-2-2222200000000−2i2i2i−2i0000000000000000
χ212222-2-222-2-222-2-222-2-200002i−2i2i−2i00000000000000000000
χ222222-2-222-2-222-2-222-2-20000−2i2i−2i2i00000000000000000000
χ232222-2-222-2-2-2-222-2-22200002i−2i−2i2i00000000000000000000
χ242222-2-222-2-2-2-222-2-2220000−2i2i2i−2i00000000000000000000
χ252222-2-2-2-22222-2-2-2-2222-22-2000000000000000000000000
χ262222-2-2-2-22222-2-2-2-222-22-22000000000000000000000000
χ272222-2-2-2-222-2-22222-2-22-2-22000000000000000000000000
χ282222-2-2-2-222-2-22222-2-2-222-2000000000000000000000000
χ2922-2-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3222-2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3322-2-22-2-22-222i−2i2i−2i−2i2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ3422-2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ3522-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000
χ3622-2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ3722-2-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3822-2-2-222-2-222i−2i−2i2i2i−2i−2i2i0000000000000000−2ζ2ζ−2ζ32ζ300000000
χ3922-2-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4022-2-2-222-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4122-2-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4222-2-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000−2ζ2ζ−2ζ32ζ30000
χ4322-2-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4422-2-2-22-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ458-88-8000000000000000000000000000000000000000000
χ468-8-88000000000000000000000000000000000000000000

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