Finite Group Databasebeta

← Group #4629

Character table — Group #4629

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size1333331616133333161613333316161333331616
order124444334444441212224444664444441212
χ111111111111111111111111111111111
χ2111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32111111−1−i32−1+i32
χ3111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32111111−1+i32−1−i32
χ433-1-1-1-10033-1-1-1-10033-1-1-1-10033-1-1-1-100
χ53-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i003-111−1+2i−1−2i00
χ63-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i003-111−1−2i−1+2i00
χ73-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i11003-1−1+2i−1−2i1100
χ83-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i11003-1−1−2i−1+2i1100
χ911111111iiiiiiii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i
χ10111111−1−i32−1+i32iiiiiiζ11ζ7-1-1-1-1-1-11+i321−i32−i−i−i−i−i−i−ζ11−ζ7
χ11111111−1+i32−1−i32iiiiiiζ7ζ11-1-1-1-1-1-11−i321+i32−i−i−i−i−i−i−ζ7−ζ11
χ1233-1-1-1-1003i3i−i−i−i−i00-3-3111100−3i−3iiiii00
χ133-111−1+2i−1−2i003i−iii−2−i2−i00-31-1-11−2i1+2i00−3ii−i−i2+i−2+i00
χ143-111−1−2i−1+2i003i−iii2−i−2−i00-31-1-11+2i1−2i00−3ii−i−i−2+i2+i00
χ153-1−1+2i−1−2i11003i−i−2−i2−iii00-311−2i1+2i-1-100−3ii2+i−2+i−i−i00
χ163-1−1−2i−1+2i11003i−i2−i−2−iii00-311+2i1−2i-1-100−3ii−2+i2+i−i−i00
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ18111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32111111−1−i32−1+i32-1-1-1-1-1-11+i321−i32
χ19111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32111111−1+i32−1−i32-1-1-1-1-1-11−i321+i32
χ2033-1-1-1-100-3-311110033-1-1-1-100-3-3111100
χ213-111−1+2i−1−2i00-31-1-11−2i1+2i003-111−1+2i−1−2i00-31-1-11−2i1+2i00
χ223-111−1−2i−1+2i00-31-1-11+2i1−2i003-111−1−2i−1+2i00-31-1-11+2i1−2i00
χ233-1−1+2i−1−2i1100-311−2i1+2i-1-1003-1−1+2i−1−2i1100-311−2i1+2i-1-100
χ243-1−1−2i−1+2i1100-311+2i1−2i-1-1003-1−1−2i−1+2i1100-311+2i1−2i-1-100
χ2511111111−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiiiiiii
χ26111111−1−i32−1+i32−i−i−i−i−i−i−ζ11−ζ7-1-1-1-1-1-11+i321−i32iiiiiiζ11ζ7
χ27111111−1+i32−1−i32−i−i−i−i−i−i−ζ7−ζ11-1-1-1-1-1-11−i321+i32iiiiiiζ7ζ11
χ2833-1-1-1-100−3i−3iiiii00-3-31111003i3i−i−i−i−i00
χ293-111−1+2i−1−2i00−3ii−i−i2+i−2+i00-31-1-11−2i1+2i003i−iii−2−i2−i00
χ303-111−1−2i−1+2i00−3ii−i−i−2+i2+i00-31-1-11+2i1−2i003i−iii2−i−2−i00
χ313-1−1+2i−1−2i1100−3ii2+i−2+i−i−i00-311−2i1+2i-1-1003i−i−2−i2−iii00
χ323-1−1−2i−1+2i1100−3ii−2+i2+i−i−i00-311+2i1−2i-1-1003i−i2−i−2−iii00

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.