Finite Group Databasebeta

← Group #13152134

Character table — Group #13152134

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11133333333333444444444121212121212121212121212121212121212121212121212121212121212121212121212121212121212484848484848484848484848484848484848484848484848
order13326699181818181818222666666244466121212121212181818181818181818181818363636363636363636363636363636363636336666669999181818181818181818181818
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111−1+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−i32
χ311111111111111111111111111111111111111111111111111111111111111111−1−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+i32
χ4111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111111-1-1-1-111-1-1-1-1
χ5111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ6111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ711111111111111-11-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-11-1-11-11111-1-111-1-1-1-111-1-1
χ811111111111111-11-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32
χ911111111111111-11-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32
χ1011111111111111-1-11-1-1-1-111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-11-1-111111-1-1-1-111-1-1-1-111
χ1111111111111111-1-11-1-1-1-111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ1211111111111111-1-11-1-1-1-111-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ13111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111−1+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−i32−1+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
χ14111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111−1+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−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−i3211−1+i32−1−i321−1−i321−1−i3211−1+i321−1+i321−1+i32
χ15111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111111−1+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−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+i321−1+i32−1−i3211−1+i321−1+i321−1+i32−1−i321−1−i321−1−i321
χ16111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-111-1-1-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32111-1-11-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32
χ17111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-111-1-1-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1−i3211−1+i32−1−i3211+i32-11+i32-11−1+i32-11−i32-11−i32
χ18111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-111-1-1-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321−1+i32−1−i3211−1+i32-11−i32-11−i32−1−i3211+i32-11+i32-1
χ19111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11-1-1-111-1-1-111-1-1-11111-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i3211-11-1-11-1−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i32
χ20111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11-1-1-111-1-1-111-1-1-11111-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32−1−i3211−1+i321+i32-1−1−i3211+i32-1-11−i321−1+i32-11−i32
χ21111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11-1-1-111-1-1-111-1-1-11111-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i321−1+i32−1−i321-11−i321−1+i32-11−i321+i32-1−1−i3211+i32-1
χ22111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-1-1-1-111-11-11-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-11-1-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ23111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-1-1-1-111-11-11-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1−i3211−1+i321+i32-11+i32-1−1−i321-11−i32-11−i321−1+i32
χ24111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-1-1-1-111-11-11-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321−1+i32−1−i321-11−i32-11−i321−1+i321+i32-11+i32-1−1−i321
χ25111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111−1−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+i32−1−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
χ26111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111−1−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+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−i321−1−i32−1+i3211−1−i321−1−i321−1−i32−1+i321−1+i321−1+i321
χ27111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111111−1−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+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+i3211−1−i32−1+i321−1+i321−1+i3211−1−i321−1−i321−1−i32
χ28111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-111-1-1-1-111-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32111-1-11-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32
χ29111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-111-1-1-1-111-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321−1−i32−1+i3211−1−i32-11+i32-11+i32−1+i3211−i32-11−i32-1
χ30111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-111-1-1-1-111-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1+i3211−1−i32−1+i3211−i32-11−i32-11−1−i32-11+i32-11+i32
χ31111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11-1-1-111-1-1-111-1-1-11111-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i3211-11-1-11-1−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32
χ32111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11-1-1-111-1-1-111-1-1-11111-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i321−1−i32−1+i321-11+i321−1−i32-11+i321−i32-1−1+i3211−i32-1
χ33111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11-1-1-111-1-1-111-1-1-11111-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32−1+i3211−1−i321−i32-1−1+i3211−i32-1-11+i321−1−i32-11+i32
χ34111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11-1-1-1-111-11-11-1-111-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-11-1-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ35111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11-1-1-1-111-11-11-1-111-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−1−i32−1+i321-11+i32-11+i321−1−i321−i32-11−i32-1−1+i321
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.