Finite Group Databasebeta

← Group #4178

Character table — Group #4178

Order 162.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22
size1113333336999999999181818
order1339999993266181818181818333
χ11111111111111111111111
χ21111111111-1-1-1-1-1-1-1-1-1111
χ3111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32
χ4111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-1-11−i321−i321−i321+i321+i321+i321−1+i32−1−i32
χ5111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32
χ6111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-1-11+i321+i321+i321−i321−i321−i321−1−i32−1+i32
χ72222222222000000000-1-1-1
χ8222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32000000000-11−i321+i32
χ9222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32000000000-11+i321−i32
χ103−3+3i32−3−3i32ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ501−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8000
χ113−3+3i32−3−3i32ζ+2ζ4ζ−ζ4−2ζ−ζ42ζ2+ζ5−ζ2+ζ5−ζ2−2ζ50-11−i321+i32−ζ−ζ4−ζ7−ζ2−ζ5−ζ8000
χ123−3+3i32−3−3i32ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ501−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2000
χ133−3+3i32−3−3i32ζ−ζ4−2ζ−ζ4ζ+2ζ4−ζ2+ζ5−ζ2−2ζ52ζ2+ζ50-11−i321+i32−ζ7−ζ−ζ4−ζ5−ζ8−ζ2000
χ143−3+3i32−3−3i32−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ501−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5000
χ153−3+3i32−3−3i32−2ζ−ζ4ζ+2ζ4ζ−ζ4−ζ2−2ζ52ζ2+ζ5−ζ2+ζ50-11−i321+i32−ζ4−ζ7−ζ−ζ8−ζ2−ζ5000
χ163−3−3i32−3+3i322ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ401−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4000
χ173−3−3i32−3+3i322ζ2+ζ5−ζ2+ζ5−ζ2−2ζ5ζ−ζ4−2ζ−ζ4ζ+2ζ40-11+i321−i32−ζ5−ζ2−ζ8−ζ−ζ7−ζ4000
χ183−3−3i32−3+3i32−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ401−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ000
χ193−3−3i32−3+3i32−ζ2+ζ5−ζ2−2ζ52ζ2+ζ5−2ζ−ζ4ζ+2ζ4ζ−ζ40-11+i321−i32−ζ8−ζ5−ζ2−ζ7−ζ4−ζ000
χ203−3−3i32−3+3i32−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ401−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7000
χ213−3−3i32−3+3i32−ζ2−2ζ52ζ2+ζ5−ζ2+ζ5ζ+2ζ4ζ−ζ4−2ζ−ζ40-11+i321−i32−ζ2−ζ8−ζ5−ζ4−ζ−ζ7000
χ22666000000-3000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.