Finite Group Databasebeta

← Group #66367

Character table — Group #66367

Order 324.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111111333333333333333333333333333333333121212121212121212121212121212121212
order133333333233333366666666666666666666666666999999999999999999
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1+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
χ3111111111111111111111111111111111111111111−1−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
χ41111111111−1+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−i32−1−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
χ51111111111−1+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−i32−1−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
χ61111111111−1+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−i32−1−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
χ71111111111−1−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+i32−1+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
χ81111111111−1−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+i32−1+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
χ91111111111−1−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+i32−1+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−i3211−1+i32−1−i321−1+i32−1−i3211−1+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−i32ζζ4ζ7ζζ4ζ7ζζ4ζ7ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8
χ11111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i3211−1+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−i32ζ4ζ7ζζ4ζ7ζζ4ζ7ζζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5
χ12111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i3211−1+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−i32ζ7ζζ4ζ7ζζ4ζ7ζζ4ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2
χ13111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i3211−1+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+i32ζζ4ζ7ζ4ζ7ζζ7ζζ4ζ2ζ5ζ8ζ5ζ8ζ2ζ8ζ2ζ5
χ14111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i3211−1+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+i32ζ4ζ7ζζ7ζζ4ζζ4ζ7ζ8ζ2ζ5ζ2ζ5ζ8ζ5ζ8ζ2
χ15111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1−i321−1+i3211−1+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+i32ζ7ζζ4ζζ4ζ7ζ4ζ7ζζ5ζ8ζ2ζ8ζ2ζ5ζ2ζ5ζ8
χ16111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32111−1+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−i32111ζζ4ζ7ζ7ζζ4ζ4ζ7ζζ2ζ5ζ8ζ8ζ2ζ5ζ5ζ8ζ2
χ17111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32111−1+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−i32111ζ4ζ7ζζζ4ζ7ζ7ζζ4ζ8ζ2ζ5ζ5ζ8ζ2ζ2ζ5ζ8
χ18111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i32111−1+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−i32111ζ7ζζ4ζ4ζ7ζζζ4ζ7ζ5ζ8ζ2ζ2ζ5ζ8ζ8ζ2ζ5
χ19111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i3211−1−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+i32ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ4ζζ7ζ4ζζ7ζ4ζζ7
χ20111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i3211−1−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+i32ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζζ7ζ4ζζ7ζ4ζζ7ζ4
χ21111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i3211−1−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+i32ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ7ζ4ζζ7ζ4ζζ7ζ4ζ
χ22111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32111−1−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+i32111ζ2ζ8ζ5ζ5ζ2ζ8ζ8ζ5ζ2ζ4ζζ7ζ7ζ4ζζζ7ζ4
χ23111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32111−1−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+i32111ζ5ζ2ζ8ζ8ζ5ζ2ζ2ζ8ζ5ζζ7ζ4ζ4ζζ7ζ7ζ4ζ
χ24111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i32111−1−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+i32111ζ8ζ5ζ2ζ2ζ8ζ5ζ5ζ2ζ8ζ7ζ4ζζζ7ζ4ζ4ζζ7
χ25111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i3211−1−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−i32ζ2ζ8ζ5ζ8ζ5ζ2ζ5ζ2ζ8ζ4ζζ7ζζ7ζ4ζ7ζ4ζ
χ26111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i3211−1−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−i32ζ5ζ2ζ8ζ2ζ8ζ5ζ8ζ5ζ2ζζ7ζ4ζ7ζ4ζζ4ζζ7
χ27111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1+i321−1−i3211−1−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−i32ζ8ζ5ζ2ζ5ζ2ζ8ζ2ζ8ζ5ζ7ζ4ζζ4ζζ7ζζ7ζ4
χ28333333333-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ29333333333-1−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000000000
χ30333333333-1−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000000000
χ31333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-13−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i321−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32-1-1-11−i321−i321−i321+i321+i321+i32000000000000000000
χ32333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-1−3+3i32−3−3i323−3−3i323−3+3i32-1-11−i321−i321+i321+i321−i321+i321−i321−i321−i321+i321+i321+i32-1-1-11+i321+i321+i32-1-1-11−i321−i321−i32000000000000000000
χ33333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-1−3−3i323−3+3i32−3+3i32−3−3i323-1-11−i321−i321+i321+i321−i321+i321+i321+i321+i32-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i32-1-1-1000000000000000000
χ34333−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i32-13−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i321+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32-1-1-11+i321+i321+i321−i321−i321−i32000000000000000000
χ35333−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i32-1−3+3i323−3−3i32−3−3i32−3+3i323-1-11+i321+i321−i321−i321+i321−i321−i321−i321−i32-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i32-1-1-1000000000000000000
χ36333−3−3i32−3−3i32−3+3i32−3+3i32−3−3i32−3+3i32-1−3−3i32−3+3i323−3+3i323−3−3i32-1-11+i321+i321−i321−i321+i321−i321+i321+i321+i321−i321−i321−i32-1-1-11−i321−i321−i32-1-1-11+i321+i321+i32000000000000000000
χ373−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i323000000−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32000000000000000000000000000000000000
χ383−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32-10000001−i321+i32-11−i32-11+i321+i321−i322−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000
χ393−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32-10000001−i321+i32-11−i32-11+i321+i321−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3000000000000000000
χ403−3+3i32−3−3i323−3+3i323−3−3i32−3−3i32−3+3i32-10000001−i321+i32-11−i32-11+i321+i321−i32−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32000000000000000000
χ413−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32333000000−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233000000000000000000000000000000000000
χ423−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233-10000001−i321+i321−i321+i321+i321−i32-1-12−1+i3−1−i3−1+i3−1−i32−1−i32−1+i32−1+i3−1−i3−1+i3−1−i32−1−i32−1+i3000000000000000000
χ433−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233-10000001−i321+i321−i321+i321+i321−i32-1-1−1+i3−1−i32−1−i32−1+i32−1+i3−1−i3−1−i32−1+i32−1+i3−1−i3−1+i3−1−i32000000000000000000
χ443−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i3233-10000001−i321+i321−i321+i321+i321−i32-1-1−1−i32−1+i32−1+i3−1−i3−1+i3−1−i32−1+i3−1−i32−1−i32−1+i32−1+i3−1−i3000000000000000000
χ453−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i323000000−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i32000000000000000000000000000000000000
χ463−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i32-10000001−i321+i321+i32-11−i32-11−i321+i322−1+i3−1−i3−1−i32−1+i3−1+i3−1−i322−1+i3−1−i3−1−i32−1+i3−1+i3−1−i32000000000000000000
χ473−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i32-10000001−i321+i321+i32-11−i32-11−i321+i32−1+i3−1−i322−1+i3−1−i3−1−i32−1+i3−1−i32−1+i3−1+i3−1−i322−1+i3−1−i3000000000000000000
χ483−3+3i32−3−3i32−3−3i323−3+3i323−3+3i32−3−3i32-10000001−i321+i321+i32-11−i32-11−i321+i32−1−i32−1+i3−1+i3−1−i322−1+i3−1−i3−1+i3−1−i322−1+i3−1−i3−1−i32−1+i3000000000000000000
χ493−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i323000000−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32000000000000000000000000000000000000
χ503−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32-10000001+i321−i32-11+i32-11−i321−i321+i322−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000
χ513−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32-10000001+i321−i32-11+i32-11−i321−i321+i32−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32000000000000000000
χ523−3−3i32−3+3i323−3−3i323−3+3i32−3+3i32−3−3i32-10000001+i321−i32-11+i32-11−i321−i321+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3000000000000000000
χ533−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i323000000−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i32000000000000000000000000000000000000
χ543−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i32-10000001+i321−i321−i32-11+i32-11+i321−i322−1−i3−1+i3−1+i32−1−i3−1−i3−1+i322−1−i3−1+i3−1+i32−1−i3−1−i3−1+i32000000000000000000
χ553−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i32-10000001+i321−i321−i32-11+i32-11+i321−i32−1+i32−1−i3−1−i3−1+i322−1−i3−1+i3−1−i3−1+i322−1−i3−1+i3−1+i32−1−i3000000000000000000
χ563−3−3i32−3+3i32−3+3i323−3−3i323−3−3i32−3+3i32-10000001+i321−i321−i32-11+i32-11+i321−i32−1−i3−1+i322−1−i3−1+i3−1+i32−1−i3−1+i32−1−i3−1−i3−1+i322−1−i3−1+i3000000000000000000
χ573−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32333000000−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233000000000000000000000000000000000000
χ583−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-10000001+i321−i321+i321−i321−i321+i32-1-12−1−i3−1+i3−1−i3−1+i32−1+i32−1−i32−1−i3−1+i3−1−i3−1+i32−1+i32−1−i3000000000000000000
χ593−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-10000001+i321−i321+i321−i321−i321+i32-1-1−1+i32−1−i32−1−i3−1+i3−1−i3−1+i32−1−i3−1+i32−1+i32−1−i32−1−i3−1+i3000000000000000000
χ603−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i3233-10000001+i321−i321+i321−i321−i321+i32-1-1−1−i3−1+i32−1+i32−1−i32−1−i3−1+i3−1+i32−1−i32−1−i3−1+i3−1−i3−1+i32000000000000000000

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