Finite Group Databasebeta

← Group #72229255

Character table — Group #72229255

Order 3888.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size11133333333333333333333333333999999999999999999999999999999999999999363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636363636144144144144144144144144144144144144
order1332233666699999918181818181818181818181826666666666661818181818181818181818181818181818181818181818181818272727272727272727272727545454545454545454545454545454545454545454545454545454545454545454545454999999272727272727
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ511111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111
χ611111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ711111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ811111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ911111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111111
χ1011111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1−i321−1+i32−1−i32ζζ4ζ7ζ2ζ5ζ8111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8ζζ4ζ7ζ2ζ5ζ8ζζ4ζ7ζ2ζ5ζ8
χ1111111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1−i321−1+i32−1−i32ζ4ζ7ζζ8ζ2ζ5111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5ζ4ζ7ζζ8ζ2ζ5ζ4ζ7ζζ8ζ2ζ5
χ1211111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1−i321−1+i32−1−i32ζ7ζζ4ζ5ζ8ζ2111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2ζ7ζζ4ζ5ζ8ζ2ζ7ζζ4ζ5ζ8ζ2
χ1311111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1−i321−1+i32ζζ4ζ7ζ2ζ5ζ8−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8ζ4ζ7ζζ8ζ2ζ5ζ7ζζ4ζ5ζ8ζ2
χ1411111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1−i321−1+i32ζ4ζ7ζζ8ζ2ζ5−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5ζ7ζζ4ζ5ζ8ζ2ζζ4ζ7ζ2ζ5ζ8
χ1511111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1−i321−1+i32ζ7ζζ4ζ5ζ8ζ2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2ζζ4ζ7ζ2ζ5ζ8ζ4ζ7ζζ8ζ2ζ5
χ1611111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1+i32−1−i321ζζ4ζ7ζ2ζ5ζ8−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8ζ7ζζ4ζ5ζ8ζ2ζ4ζ7ζζ8ζ2ζ5
χ1711111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1+i32−1−i321ζ4ζ7ζζ8ζ2ζ5−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5ζζ4ζ7ζ2ζ5ζ8ζ7ζζ4ζ5ζ8ζ2
χ1811111−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i32111111−1+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−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−i321−1+i32−1+i32−1−i321ζ7ζζ4ζ5ζ8ζ2−1−i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2ζ4ζ7ζζ8ζ2ζ5ζζ4ζ7ζ2ζ5ζ8
χ1911111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1+i321−1−i32−1+i32ζ2ζ8ζ5ζ4ζζ7111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7ζ2ζ8ζ5ζ4ζζ7ζ2ζ8ζ5ζ4ζζ7
χ2011111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1+i321−1−i32−1+i32ζ5ζ2ζ8ζζ7ζ4111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4ζ5ζ2ζ8ζζ7ζ4ζ5ζ2ζ8ζζ7ζ4
χ2111111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1+i321−1−i32−1+i32ζ8ζ5ζ2ζ7ζ4ζ111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζζ8ζ5ζ2ζ7ζ4ζζ8ζ5ζ2ζ7ζ4ζ
χ2211111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1−i32−1+i321ζ2ζ8ζ5ζ4ζζ7−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7ζ5ζ2ζ8ζζ7ζ4ζ8ζ5ζ2ζ7ζ4ζ
χ2311111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1−i32−1+i321ζ5ζ2ζ8ζζ7ζ4−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4ζ8ζ5ζ2ζ7ζ4ζζ2ζ8ζ5ζ4ζζ7
χ2411111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1−i32−1−i32−1+i321ζ8ζ5ζ2ζ7ζ4ζ−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζζ2ζ8ζ5ζ4ζζ7ζ5ζ2ζ8ζζ7ζ4
χ2511111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1+i321−1−i32ζ2ζ8ζ5ζ4ζζ7−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7ζ8ζ5ζ2ζ7ζ4ζζ5ζ2ζ8ζζ7ζ4
χ2611111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1+i321−1−i32ζ5ζ2ζ8ζζ7ζ4−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4ζ2ζ8ζ5ζ4ζζ7ζ8ζ5ζ2ζ7ζ4ζ
χ2711111−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i32111111−1−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+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+i321−1+i321−1−i32ζ8ζ5ζ2ζ7ζ4ζ−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32111−1−i32−1−i32−1−i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζζ5ζ2ζ8ζζ7ζ4ζ2ζ8ζ5ζ4ζζ7
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.