Finite Group Databasebeta

← Group #726

Character table — Group #726

Order 81.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33
size111111111333333333333333333333333
order133333333333333999999999999999999
χ1111111111111111111111111111111111
χ2111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ3111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ5111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32
χ6111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ7111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ8111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ9111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32
χ10111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32ζζ4ζ7ζζ4ζ7ζζ4ζ7ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8
χ11111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32ζ4ζ7ζζ4ζ7ζζ4ζ7ζζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5
χ12111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32ζ7ζζ4ζ7ζζ4ζ7ζζ4ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2
χ13111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32ζζ4ζ7ζ4ζ7ζζ7ζζ4ζ2ζ5ζ8ζ5ζ8ζ2ζ8ζ2ζ5
χ14111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32ζ4ζ7ζζ7ζζ4ζζ4ζ7ζ8ζ2ζ5ζ2ζ5ζ8ζ5ζ8ζ2
χ15111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32ζ7ζζ4ζζ4ζ7ζ4ζ7ζζ5ζ8ζ2ζ8ζ2ζ5ζ2ζ5ζ8
χ16111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321ζζ4ζ7ζ7ζζ4ζ4ζ7ζζ2ζ5ζ8ζ8ζ2ζ5ζ5ζ8ζ2
χ17111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321ζ4ζ7ζζζ4ζ7ζ7ζζ4ζ8ζ2ζ5ζ5ζ8ζ2ζ2ζ5ζ8
χ18111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321ζ7ζζ4ζ4ζ7ζζζ4ζ7ζ5ζ8ζ2ζ2ζ5ζ8ζ8ζ2ζ5
χ19111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ4ζζ7ζ4ζζ7ζ4ζζ7
χ20111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζζ7ζ4ζζ7ζ4ζζ7ζ4
χ21111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ7ζ4ζζ7ζ4ζζ7ζ4ζ
χ22111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321ζ2ζ8ζ5ζ5ζ2ζ8ζ8ζ5ζ2ζ4ζζ7ζ7ζ4ζζζ7ζ4
χ23111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321ζ5ζ2ζ8ζ8ζ5ζ2ζ2ζ8ζ5ζζ7ζ4ζ4ζζ7ζ7ζ4ζ
χ24111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321ζ8ζ5ζ2ζ2ζ8ζ5ζ5ζ2ζ8ζ7ζ4ζζζ7ζ4ζ4ζζ7
χ25111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32ζ2ζ8ζ5ζ8ζ5ζ2ζ5ζ2ζ8ζ4ζζ7ζζ7ζ4ζ7ζ4ζ
χ26111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32ζ5ζ2ζ8ζ2ζ8ζ5ζ8ζ5ζ2ζζ7ζ4ζ7ζ4ζζ4ζζ7
χ27111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32ζ8ζ5ζ2ζ5ζ2ζ8ζ2ζ8ζ5ζ7ζ4ζζ4ζζ7ζζ7ζ4
χ283−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32000000000000000000000000
χ293−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000000000000000000000
χ303−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i32000000000000000000000000
χ313−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32000000000000000000000000
χ323−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i32000000000000000000000000
χ333−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000000000000000000000

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