Finite Group Databasebeta

← Group #67992

Character table — Group #67992

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size1333333366666662424242424242424128
order1244888848888882488161616163
χ1111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-11
χ322222222222222200000000-1
χ43333-1-1-1-13-1-1-1-1-1-11111-1-1-1-10
χ53333-1-1-1-13-1-1-1-1-1-1-1-1-1-111110
χ633-1-1−1+2i−1+2i−1−2i−1−2i-1−1+2i−1−2i111111-1-1ii−i−i0
χ733-1-1−1+2i−1+2i−1−2i−1−2i-1−1+2i−1−2i1111-1-111−i−iii0
χ833-1-1−1−2i−1−2i−1+2i−1+2i-1−1−2i−1+2i111111-1-1−i−iii0
χ933-1-1−1−2i−1−2i−1+2i−1+2i-1−1−2i−1+2i1111-1-111ii−i−i0
χ103-1−1+2i−1−2i2ζ−i−2ζ−ii+2ζ3i−2ζ31i−i1+21−2−1+i2−1−i21-1i−iζ−ζζ3−ζ30
χ113-1−1+2i−1−2i2ζ−i−2ζ−ii+2ζ3i−2ζ31i−i1+21−2−1+i2−1−i2-11−ii−ζζ−ζ3ζ30
χ123-1−1+2i−1−2i−2ζ−i2ζ−ii−2ζ3i+2ζ31i−i1−21+2−1−i2−1+i21-1i−i−ζζ−ζ3ζ30
χ133-1−1+2i−1−2i−2ζ−i2ζ−ii−2ζ3i+2ζ31i−i1−21+2−1−i2−1+i2-11−iiζ−ζζ3−ζ30
χ143-1−1−2i−1+2ii+2ζ3i−2ζ32ζ−i−2ζ−i1−ii1−21+2−1+i2−1−i21-1−iiζ3−ζ3ζ−ζ0
χ153-1−1−2i−1+2ii+2ζ3i−2ζ32ζ−i−2ζ−i1−ii1−21+2−1+i2−1−i2-11i−i−ζ3ζ3−ζζ0
χ163-1−1−2i−1+2ii−2ζ3i+2ζ3−2ζ−i2ζ−i1−ii1+21−2−1−i2−1+i21-1−ii−ζ3ζ3−ζζ0
χ173-1−1−2i−1+2ii−2ζ3i+2ζ3−2ζ−i2ζ−i1−ii1+21−2−1−i2−1+i2-11i−iζ3−ζ3ζ−ζ0
χ1866-2-22222-222-2-2-2-2000000000
χ196-2222+222−222−222+22-2-2-2−222200000000000
χ206-2222−222+222+222−22-2-2-222−2200000000000
χ216-222−2+2i2−2−2i2−2+2i2−2−2i2-22200−2i22i2000000000
χ226-222−2−2i2−2+2i2−2−2i2−2+2i2-222002i2−2i2000000000
χ236-2−2+4i−2−4i2i2i−2i−2i2−2i2i-2-222000000000
χ246-2−2−4i−2+4i−2i−2i2i2i22i−2i-2-222000000000

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