Finite Group Databasebeta

← Group #737

Character table — Group #737

Order 81.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33
size111111111333333333333333333333333
order133999999333333339999999999999999
χ1111111111111111111111111111111111
χ211111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111−1−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−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32
χ5111111111−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1−i32−1−i3211−1+i32−1+i32
χ6111111111−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1+i32−1−i32−1−i3211
χ7111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32
χ8111111111−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1−i32−1+i32−1+i3211
χ9111111111−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1+i32−1+i3211−1−i32−1−i32
χ10111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111111−1+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
χ11111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i321−1−i321−1−i3211−1+i321−1+i321−1+i32
χ12111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i321−1+i321−1+i321−1+i32−1−i321−1−i321−1−i321
χ13111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32
χ14111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1−i3211−1+i32−1−i3211−1+i32−1+i32−1−i321−1+i32−1+i32−1−i32−1−i321
χ15111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i3211−1+i321−1+i32−1+i32−1−i32−1−i321−1−i3211−1+i32−1+i32−1−i32
χ16111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321
χ17111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i3211−1+i32−1−i321−1−i321−1+i32−1−i321−1+i321−1+i32−1−i321−1+i32−1−i32
χ18111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32
χ19111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111111−1−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
χ20111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i321−1−i321−1−i321−1−i32−1+i321−1+i321−1+i321
χ21111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i321−1+i321−1+i3211−1−i321−1−i321−1−i32
χ22111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321
χ23111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32
χ24111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1+i32−1−i3211−1−i32−1+i321−1+i321−1−i32−1+i321−1−i321−1−i32−1+i321−1−i32−1+i32
χ25111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32
χ26111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i3211−1−i321−1−i32−1−i32−1+i32−1+i321−1+i3211−1−i32−1−i32−1+i32
χ27111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1+i3211−1−i32−1+i3211−1−i32−1−i32−1+i321−1−i32−1−i32−1+i32−1+i321
χ283−3+3i32−3−3i323ζ3ζ43ζ73ζ23ζ53ζ8000000000000000000000000
χ293−3+3i32−3−3i323ζ43ζ73ζ3ζ83ζ23ζ5000000000000000000000000
χ303−3+3i32−3−3i323ζ73ζ3ζ43ζ53ζ83ζ2000000000000000000000000
χ313−3−3i32−3+3i323ζ23ζ83ζ53ζ43ζ3ζ7000000000000000000000000
χ323−3−3i32−3+3i323ζ53ζ23ζ83ζ3ζ73ζ4000000000000000000000000
χ333−3−3i32−3+3i323ζ83ζ53ζ23ζ73ζ43ζ000000000000000000000000

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