Finite Group Databasebeta

← Group #13060701

Character table — Group #13060701

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11112222223333333344444444444466666666666677777777121212121212121212121212121212121212121212121212141414141414141414141414282828282828282828282828282828282828282828282828
order1222444444771414141414142222244444442828282828282828282828283366666614141414141414141414282828282828282828282828282812121212121212121212121266666666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−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−i32111111111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ411111111111111111111-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1
χ511111111111111111111-1-1-1-111-1-1-1-1111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−1−i32−1−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+i32−1+i32−1+i321−i321−i321−i321+i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ611111111111111111111-1-1-1-111-1-1-1-1111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−1+i32−1+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−i32−1−i32−1−i321+i321+i321+i321−i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ7111111111111111111-1-111-1-1-1-111-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-111-1-1-1-1-111-1-1-1-111-1-1
χ8111111111111111111-1-111-1-1-1-111-1-1111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i321+i321−i321−i32−1+i32−1+i321−i321+i321−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32
χ9111111111111111111-1-111-1-1-1-111-1-1111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i321−i321+i321+i32−1−i32−1−i321+i321−i321+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32
χ10111111111111111111-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1-1-1111-1-1-1-111-1-1-1-111
χ11111111111111111111-1-1-1-111-1-1-1-111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−1−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+i32−1−i321−i321−i321−i321−i32−1+i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ12111111111111111111-1-1-1-111-1-1-1-111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−1+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−i32−1+i321+i321+i321+i321+i32−1−i32−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ13111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-111-1-1-1-111
χ14111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111-1-1-1-1-1-1-1-1-1-1-1-11111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321+i321−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ15111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321−i321+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ16111111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-1111-1-111-1-1-1-111-1-1
χ17111111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-11111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32
χ18111111-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-11111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32
χ19111111-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-111-1-1-1-1
χ20111111-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i32−1−i321−i321−i32−1+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
χ21111111-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i32−1+i321+i321+i32−1−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
χ22111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ23111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1111111111111−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+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+i32−1+i32−1+i32−1+i32−1+i32
χ24111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1111111111111−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32
χ251111-1-111-1-1111111111-11-11-11-11-11-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-111-1-111-1-11-11-111-11-11-1-11-11-11-11-11-11-1
χ261111-1-111-1-1111111111-11-11-11-11-11-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-111-1-111-1-111-1-111-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1+i321+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ271111-1-111-1-1111111111-11-11-11-11-11-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-111-1-111-1-111-1-111-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1−i321−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ281111-1-111-1-1111111111-1-11-111-1-11-11-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-11-1-11-11-1-11-1111-1-11-111-1-11-11
χ291111-1-111-1-1111111111-1-11-111-1-11-11-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-111-1-11111-1-1-1-111-1-1111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i321+i32−1+i321−i321−i32−1+i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ301111-1-111-1-1111111111-1-11-111-1-11-11-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-111-1-11111-1-1-1-111-1-1111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i321−i32−1−i321+i321+i32−1−i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ311111-1-111-1-111111111-111-1-11-111-1-11-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-111-1-1-111-1-111-111-1-11-111-1-11
χ321111-1-111-1-111111111-111-1-11-111-1-11-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11111-1-1-1-111-1-11111-1-1-1-1111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ331111-1-111-1-111111111-111-1-11-111-1-11-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11111-1-1-1-111-1-11111-1-1-1-1111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ341111-1-111-1-111111111-11-111-1-11-111-1-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-1-11-111-11-111-1-1-11-111-1-11-111-1
χ351111-1-111-1-111111111-11-111-1-11-111-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-11111-1-1-1-111-1-11111-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321+i32−1−i32−1−i321−i32−1+i321−i32−1+i32−1+i321+i321−i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ361111-1-111-1-111111111-11-111-1-11-111-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-11111-1-1-1-111-1-11111-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321−i32−1+i32−1+i321+i32−1−i321+i32−1−i32−1−i321−i321+i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ371111-1-1-1-111111111111-11-1-11-11-111-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1111-11-1-11-11-1-111-11-111-1-11-111-1
χ381111-1-1-1-111111111111-11-1-11-11-111-1-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-1-1-111-1-111-1-11111-1-11+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1−i321+i321+i32−1+i321−i32−1+i321−i321−i32−1−i32−1+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ391111-1-1-1-111111111111-11-1-11-11-111-1-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-1-1-111-1-111-1-11111-1-11−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1+i321−i321−i32−1−i321+i32−1−i321+i321+i32−1+i32−1−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.