Finite Group Databasebeta

← Group #13057416

Character table — Group #13057416

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111224444446666777777771212121212121414141414141414141414141414141424242424282828282828282828282828282828282828282828282828282828282828
order122244224444714141433666666282828282828444412121212121212121212121214142828244444666666121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111111111−1−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
χ41111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321111-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ51111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111111111−1+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
χ61111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321111-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ711111111-1-1-1-1111111111111-1-1-1-111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ811111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111
χ911111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ1011111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-111-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ1111111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i321−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ1211111111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-111-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ13111111-1-11-1-111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ14111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111111111
χ15111111-1-11-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111-1-1-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ16111111-1-11-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1-1-1-1-111111+i321+i321−i321−i321+i321−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+i32−1+i32−1+i32
χ17111111-1-11-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111-1-1-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ18111111-1-11-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1-1-1-1-111111−i321−i321+i321+i321−i321+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−i32−1−i32−1−i32
χ19111111-1-1-111-1111111111111-1-1-1-1111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ20111111-1-1-111-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-111-1-111-1-1
χ21111111-1-1-111-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-1-1-1111+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ22111111-1-1-111-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1111111-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ23111111-1-1-111-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-1-1-1111−i321−i321+i321+i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ24111111-1-1-111-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1111111-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ251111-1-11-111-1-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-11-1-111-11-11-11-1-1-1111-11-111-1-11-11-11-11-1
χ261111-1-11-111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-11-1-11-111-11-111111-11-1-1-1-1-1-11-11-11-11
χ271111-1-11-111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-11-1-111-11-1−1−i321+i32−1+i321−i321+i321−i32−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ281111-1-11-111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11-11-1-11-11−1−i321+i32−1+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ291111-1-11-111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-11-1-111-11-1−1+i321−i32−1−i321+i321−i321+i32−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ301111-1-11-111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-11-11-1-11-11−1+i321−i32−1−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ311111-1-11-1-1-111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-1-111-11-1-111-11-111-1-1-11-11-1-1111-1-111-1-11
χ321111-1-11-1-1-111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-11-111-11-11-1-1-1-1-1-11-111111-111-1-111-1
χ331111-1-11-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-1-111-11-1-11−1−i321+i32−1+i321−i32−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i321+i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ341111-1-11-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1-11-11-111-1−1−i321+i32−1+i321−i321+i321−i321+i321−i321+i32−1−i321−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ351111-1-11-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-1-111-11-1-11−1+i321−i32−1−i321+i32−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i321−i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
χ361111-1-11-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1-11-11-111-1−1+i321−i32−1−i321+i321−i321+i321−i321+i321−i32−1+i321+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ371111-1-1-111-11-111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-11-11-11-11-11-11-1-111-11-1111-1-1-11-11-11-11
χ381111-1-1-111-11-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-11-111-11-11-1-11-111111-11-11-1-1-1-11-11-11-11-1
χ391111-1-1-111-11-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-11-11-11-11-111+i32−1−i321−i32−1+i321+i321−i32−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32
χ401111-1-1-111-11-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11-111-11-11-11+i32−1−i321−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i32−1−i321−i32−1+i321+i321−i321+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32
χ411111-1-1-111-11-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-11-11-11-11-111−i32−1+i321+i32−1−i321−i321+i32−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32
χ421111-1-1-111-11-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11-111-11-11-11−i32−1+i321+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i32−1+i321+i32−1−i321−i321+i321−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32
χ431111-1-1-11-11-11111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-111-11-1-111-1-11-1111-1-11-11-1-1-111-111-1-111-1
χ441111-1-1-11-11-11111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111-1-111-1-11-11-11-1-1-1-11-11-111111-1-111-1-11
χ451111-1-1-11-11-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-111-11-1-111-11+i32−1−i321−i32−1+i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i321+i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32
χ461111-1-1-11-11-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111-1-111-1-111+i32−1−i321−i32−1+i321+i321−i321+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32
χ471111-1-1-11-11-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-111-11-1-111-11−i32−1+i321+i32−1−i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i321−i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32
χ481111-1-1-11-11-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111-1-111-1-111−i32−1+i321+i32−1−i321−i321+i321−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32
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χ572-22-2-220000002-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000-222i−2i−2i2i2ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ791+i3−1−i31−i3−1+i3−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000000000000000000000000000000
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χ592-22-2-220000002-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000-222i−2i−2i2i2ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ831−i3−1+i31+i3−1−i3−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.