Finite Group Databasebeta

← Group #12939

Character table — Group #12939

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12224444224488888888888844448816161616161616161616161616161616224488884488
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111ii−i−i11-1-111-1-1ii−i−ii−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111ii−i−i11-1-111-1-1ii−i−ii−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-111ii−i−i11-1-111-1-1ii−i−ii−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111ii−i−i11-1-111-1-1ii−i−ii−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-111−i−iii11-1-111-1-1−i−iii−ii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1-1-111−i−iii11-1-111-1-1−i−iii−ii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-1-1-111−i−iii11-1-111-1-1−i−iii−ii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-1-1-111−i−iii11-1-111-1-1−i−iii−ii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ1922222222-2-2-2-22222000000000000-2-222−2−222−2−222−2−222−2−2000000000000
χ2022222222-2-2-2-22222000000000000-2-2−2−222−2−222−2−222−2−222000000000000
χ2122222222-2-2-2-2-2-2-2-20000000000002222−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-2-2-2-2-2-2-200000000000022−2−222−2−22222−2−222−2−2000000000000
χ232222-2-2-2-222-2-22i2i−2i−2i000000000000−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ242222-2-2-2-222-2-22i2i−2i−2i000000000000−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ252222-2-2-2-222-2-2−2i−2i2i2i0000000000002i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ262222-2-2-2-222-2-2−2i−2i2i2i0000000000002i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ272222-2-2-2-2-2-2222i2i−2i−2i-2-222-2-222−2i−2i2i2i2i−2i0000000000000000000000000000
χ282222-2-2-2-2-2-222−2i−2i2i2i-2-222-2-2222i2i−2i−2i−2i2i0000000000000000000000000000
χ2922-2-22i−2i2i−2i00002ζ2−2ζ22ζ6−2ζ62−2i2−i22−2i2−i21+i−1−i1−i−1+i00ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ3022-2-22i−2i2i−2i00002ζ2−2ζ22ζ6−2ζ62−2i2−i22−2i2−i21+i−1−i1−i−1+i00−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ3122-2-22i−2i2i−2i00002ζ2−2ζ22ζ6−2ζ6−22−i2i2−22−i2i2−1−i1+i−1+i1−i00ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ3222-2-22i−2i2i−2i00002ζ2−2ζ22ζ6−2ζ6−22−i2i2−22−i2i2−1−i1+i−1+i1−i00−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ3322-2-22i−2i2i−2i0000−2ζ22ζ2−2ζ62ζ62−2i2−i22−2i2−i2−1−i1+i−1+i1−i00ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ3422-2-22i−2i2i−2i0000−2ζ22ζ2−2ζ62ζ62−2i2−i22−2i2−i2−1−i1+i−1+i1−i00−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ3522-2-22i−2i2i−2i0000−2ζ22ζ2−2ζ62ζ6−22−i2i2−22−i2i21+i−1−i1−i−1+i00ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ3622-2-22i−2i2i−2i0000−2ζ22ζ2−2ζ62ζ6−22−i2i2−22−i2i21+i−1−i1−i−1+i00−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ3722-2-2−2i2i−2i2i00002ζ6−2ζ62ζ2−2ζ22−2−i2i22−2−i2i2−1+i1−i−1−i1+i00ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ3822-2-2−2i2i−2i2i00002ζ6−2ζ62ζ2−2ζ22−2−i2i22−2−i2i2−1+i1−i−1−i1+i00−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ3922-2-2−2i2i−2i2i00002ζ6−2ζ62ζ2−2ζ2−22i2−i2−22i2−i21−i−1+i1+i−1−i00ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ4022-2-2−2i2i−2i2i00002ζ6−2ζ62ζ2−2ζ2−22i2−i2−22i2−i21−i−1+i1+i−1−i00−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ4122-2-2−2i2i−2i2i0000−2ζ62ζ6−2ζ22ζ22−2−i2i22−2−i2i21−i−1+i1+i−1−i00ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ4222-2-2−2i2i−2i2i0000−2ζ62ζ6−2ζ22ζ22−2−i2i22−2−i2i21−i−1+i1+i−1−i00−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ4322-2-2−2i2i−2i2i0000−2ζ62ζ6−2ζ22ζ2−22i2−i2−22i2−i2−1+i1−i−1−i1+i00ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ4422-2-2−2i2i−2i2i0000−2ζ62ζ6−2ζ22ζ2−22i2−i2−22i2−i2−1+i1−i−1−i1+i00−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ452-2-2222-2-22-2-2200002222-2-2-2-200000000000000000000002-22-200000000
χ462-2-2222-2-22-2-2200002222-2-2-2-20000000000000000000000-22-2200000000
χ472-2-2222-2-22-2-220000-2-2-2-22222000000000000000000000000002i−2i2i−2i0000
χ482-2-2222-2-22-2-220000-2-2-2-2222200000000000000000000000000−2i2i−2i2i0000
χ492-2-22-2-222-22-22000022-2-2-2-22200000000000000000000002-2-2200000000
χ502-2-22-2-222-22-22000022-2-2-2-2220000000000000000000000-222-200000000
χ512-2-22-2-222-22-220000-2-22222-2-2000000000000000000000000002-2-220000
χ522-2-22-2-222-22-220000-2-22222-2-200000000000000000000000000-222-20000
χ534-44-44i−4i−4i4i0000000022−222i2−2i2−2222−2i22i20000000000000000000000000000000000
χ544-44-44i−4i−4i4i00000000−2222−2i22i222−222i2−2i20000000000000000000000000000000000
χ554-44-4−4i4i4i−4i0000000022−22−2i22i2−22222i2−2i20000000000000000000000000000000000
χ564-44-4−4i4i4i−4i00000000−22222i2−2i222−22−2i22i20000000000000000000000000000000000
χ574-4-4444-4-4-444-40000000000000000000000000000000000000000000000
χ584-4-44-4-4444-44-40000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.