Finite Group Databasebeta

← Group #11680

Character table — Group #11680

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order12224444444444888888882488881616161616161616161616161616161622448888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i
χ611111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii
χ711111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii
χ811111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i
χ91111-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-1
χ101111-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11
χ111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11
χ121111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1
χ131111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ1822222222-2-222-2-222222222-2-2-2-2-2-2000000000000000000000000
χ19222222-2-222-2-2-2-200000000-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ20222222-2-222-2-2-2-200000000-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ21222222-2-2-2-2-2-222000000002-2000022−2−222−2−2−2−222−2−22200000000
χ22222222-2-2-2-2-2-222000000002-20000−2−222−2−22222−2−222−2−200000000
χ232222-2-22222-2-2-2-2000000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ242222-2-22222-2-2-2-2000000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ252222-2-222-2-2-2-22200000000-22000022−2−2−2−222−2−22222−2−200000000
χ262222-2-222-2-2-2-22200000000-220000−2−22222−2−222−2−2−2−22200000000
χ272222-2-2-2-22222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ282222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-222000000000000000000000000
χ2922-2-200002i−2i2-22i−2i00002i2i−2i−2i002-20000002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ00000000
χ3022-2-200002i−2i2-22i−2i00002i2i−2i−2i002-2000000−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ00000000
χ3122-2-200002i−2i2-22i−2i0000−2i−2i2i2i00-22002ζ3−2ζ32ζ3−2ζ300002ζ−2ζ2ζ−2ζ000000000000
χ3222-2-200002i−2i2-22i−2i0000−2i−2i2i2i00-2200−2ζ32ζ3−2ζ32ζ30000−2ζ2ζ−2ζ2ζ000000000000
χ3322-2-200002i−2i-22−2i2i2i2i−2i−2i000000002-21+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i00000000
χ3422-2-200002i−2i-22−2i2i2i2i−2i−2i000000002-2−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i00000000
χ3522-2-200002i−2i-22−2i2i−2i−2i2i2i00000000-221+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i00000000
χ3622-2-200002i−2i-22−2i2i−2i−2i2i2i00000000-22−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i00000000
χ3722-2-20000−2i2i2-2−2i2i00002i2i−2i−2i00-22002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ3000000000000
χ3822-2-20000−2i2i2-2−2i2i00002i2i−2i−2i00-2200−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ3000000000000
χ3922-2-20000−2i2i2-2−2i2i0000−2i−2i2i2i002-20000002ζ−2ζ2ζ−2ζ00002ζ3−2ζ32ζ3−2ζ300000000
χ4022-2-20000−2i2i2-2−2i2i0000−2i−2i2i2i002-2000000−2ζ2ζ−2ζ2ζ0000−2ζ32ζ3−2ζ32ζ300000000
χ4122-2-20000−2i2i-222i−2i2i2i−2i−2i00000000-221−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i00000000
χ4222-2-20000−2i2i-222i−2i2i2i−2i−2i00000000-22−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i00000000
χ4322-2-20000−2i2i-222i−2i−2i−2i2i2i000000002-21−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i00000000
χ4422-2-20000−2i2i-222i−2i−2i−2i2i2i000000002-2−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i00000000
χ454-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ464-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ474-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ484-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ494-4-44004-400000022−22−222222−22−2222000000000000000000000000000000
χ504-4-44004-4000000−222222−22−222222−22000000000000000000000000000000
χ514-4-4400-4400000022−22−2222−222222−22000000000000000000000000000000
χ524-4-4400-44000000−222222−2222−22−2222000000000000000000000000000000

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