Finite Group Databasebeta

← Group #8607

Character table — Group #8607

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222444422444444444488888888244488888888888888888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ121111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ131111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ141111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ151111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ161111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ172222222222-2-222-2-2-2-2-2-2000000000000000000002i−2i2i−2i00000000
χ182222222222-2-222-2-2-2-2-2-200000000000000000000−2i2i−2i2i00000000
χ1922222222-2-222-2-2-2-2-2-222000000002-22-200000000000000000000
χ2022222222-2-222-2-2-2-2-2-22200000000-22-2200000000000000000000
χ2122222222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000
χ2222222222-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000
χ232222-2-2-2-222-2-2-2-222-2-222000000000000000000002i−2i−2i2i00000000
χ242222-2-2-2-222-2-2-2-222-2-22200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-2-2-2222222-2-2-2-2000000002-2-2200000000000000000000
χ262222-2-2-2-2-2-2222222-2-2-2-200000000-222-200000000000000000000
χ272222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-222000000000000000000000000
χ282222-2-2-2-2-2-2-2-222-2-22222-2-22222-2-2000000000000000000000000
χ2922-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i00000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ3022-2-22i2i−2i−2i2-22-22i−2i2i−2i2-22i−2i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ3122-2-22i2i−2i−2i2-2-222i−2i−2i2i-22−2i2i0000000000002ζ−2ζ2ζ3−2ζ30000000000000000
χ3222-2-22i2i−2i−2i2-2-222i−2i−2i2i-22−2i2i000000000000−2ζ2ζ−2ζ32ζ30000000000000000
χ3322-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i00000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ3422-2-22i2i−2i−2i-222-2−2i2i−2i2i-222i−2i0000000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ3522-2-22i2i−2i−2i-22-22−2i2i2i−2i2-2−2i2i0000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3622-2-22i2i−2i−2i-22-22−2i2i2i−2i2-2−2i2i000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3722-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i00000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ3822-2-2−2i−2i2i2i2-22-2−2i2i−2i2i2-2−2i2i0000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ3922-2-2−2i−2i2i2i2-2-22−2i2i2i−2i-222i−2i0000000000002ζ3−2ζ32ζ−2ζ0000000000000000
χ4022-2-2−2i−2i2i2i2-2-22−2i2i2i−2i-222i−2i000000000000−2ζ32ζ3−2ζ2ζ0000000000000000
χ4122-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ4222-2-2−2i−2i2i2i-222-22i−2i2i−2i-22−2i2i0000000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ4322-2-2−2i−2i2i2i-22-222i−2i−2i2i2-22i−2i0000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4422-2-2−2i−2i2i2i-22-222i−2i−2i2i2-22i−2i000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ454-44-44-44-4000000000000002i2−2i2002i2−2i2000000000000000000000000
χ464-44-44-44-400000000000000−2i22i200−2i22i2000000000000000000000000
χ474-44-4-44-44000000000000002i2−2i200−2i22i2000000000000000000000000
χ484-44-4-44-4400000000000000−2i22i2002i2−2i2000000000000000000000000
χ494-4-444i−4i−4i4i00000000000022−22002i2−2i200000000000000000000000000
χ504-4-444i−4i−4i4i000000000000−222200−2i22i200000000000000000000000000
χ514-4-44−4i4i4i−4i00000000000022−2200−2i22i200000000000000000000000000
χ524-4-44−4i4i4i−4i000000000000−2222002i2−2i200000000000000000000000000

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