Finite Group Databasebeta

← Group #13057485

Character table — Group #13057485

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11222222222444666666667777121212121212121212121212141414141414141414141414141414141414282828282828282828282828282828282828282828282828282828282828
order12222444488888714282856565656336614141428282856565656565666666612121212121212122424242422224444666666661212121212121212242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ31111111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+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+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ41111111111111111111111−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11+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
χ51111111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−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−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ61111111111111111111111−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11−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
χ7111111111-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111111111111111-1-1-1-1111-11-1-1-1111-1111-11-1-1-11-1-1-1-1-1-1-1-1-1
χ8111111111-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-11-1111-1-1-11-1-1-11-1111-1111-1-1-1-1-1-1
χ9111111111-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1-1-1−1−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−i321−i32111-11-1-1-1−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1−i321+i321+i321+i32−1+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32
χ10111111111-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1-1-1−1−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−i321−i32-1-1-11-11111+i321+i321+i32−1−i321−i321−i321−i32−1+i321+i32−1−i32−1−i32−1−i321−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ11111111111-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1-1-1−1+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+i321+i32111-11-1-1-1−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1+i321−i321−i321−i32−1−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32
χ12111111111-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1-1-1−1+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+i321+i32-1-1-11-11111−i321−i321−i32−1+i321+i321+i321+i32−1−i321−i32−1+i32−1+i32−1+i321+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ13111-1-11-1-11111-1-11111111111111-1-11-1-111-1-1-1-11-1-11-1-11-1-11-1-111111111-1-1-111-111-1-111-1-1-111-1-111-11-1-11-1-1
χ14111-1-11-1-11111-1-11111111111111-1-11-1-111-1-1-1-11-1-11-1-11-1-11-1-1111111-1-1111-1-11-1-111-1-1111-1-111-1-111-1-11-1-1
χ15111-1-11-1-11111-1-111111111−1−i32−1+i32−1−i32−1+i321-1-11-1-111-1-1-1-1−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-111-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1+i321−i321−i32
χ16111-1-11-1-11111-1-111111111−1−i32−1+i32−1−i32−1+i321-1-11-1-111-1-1-1-1−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1111-1-111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ17111-1-11-1-11111-1-111111111−1+i32−1−i32−1+i32−1−i321-1-11-1-111-1-1-1-1−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-111-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1−i321+i321+i32
χ18111-1-11-1-11111-1-111111111−1+i32−1−i32−1+i32−1−i321-1-11-1-111-1-1-1-1−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1111-1-111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ19111-1-11-1-11-1-1-1111111-1-1-1-111111-1-11-1-1-1-111111-1-11-1-11-1-11-1-111-1-1-1-111-11-1-1-1111-1111-11-1-1-11-1-1-11-111-111
χ20111-1-11-1-11-1-1-1111111-1-1-1-111111-1-11-1-1-1-111111-1-11-1-11-1-11-1-111-1-1-1-1-1-11-1111-1-1-11-1-1-11-1111-1111-1-111-111
χ21111-1-11-1-11-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i3211-11-1-1-11−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i321+i321+i321+i32−1−i321−i321−i321−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ22111-1-11-1-11-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32-1-11-1111-11+i321+i32−1−i321+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ23111-1-11-1-11-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i3211-11-1-1-11−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i321−i321−i321−i32−1+i321+i321+i321+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ24111-1-11-1-11-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32-1-11-1111-11−i321−i32−1+i321−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ2511-11-1-11-1111-11-1111111111111-11-1-11-1-1-111-1-1-11-1-11-1-11-1-11-11111111-11-1-11-111-11-11-11-1-11-11-11-11-11-1-11-1
χ2611-11-1-11-1111-11-1111111111111-11-1-11-1-1-111-1-1-11-1-11-1-11-1-11-1111111-11-111-11-1-11-11-11-111-11-11-11-1-11-1-11-1
χ2711-11-1-11-1111-11-111111111−1−i32−1+i32−1−i32−1+i32-11-1-11-1-1-111-1-11+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-1-11-11−1−i321+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+i321−i32−1+i321−i32
χ2811-11-1-11-1111-11-111111111−1−i32−1+i32−1−i32−1+i32-11-1-11-1-1-111-1-11+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-111-11-11+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32
χ2911-11-1-11-1111-11-111111111−1+i32−1−i32−1+i32−1−i32-11-1-11-1-1-111-1-11−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-1-11-11−1+i321−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−i321+i32−1−i321+i32
χ3011-11-1-11-1111-11-111111111−1+i32−1−i32−1+i32−1−i32-11-1-11-1-1-111-1-11−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-111-11-11−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32
χ3111-11-1-11-11-1-11-111111-1-1-1-11111-11-1-11-111-1-111-11-1-11-1-11-1-11-111-1-1-1-11-111-1-11-11-1111-111-1-11-1-1-11-11-111-11
χ3211-11-1-11-11-1-11-111111-1-1-1-11111-11-1-11-111-1-111-11-1-11-1-11-1-11-111-1-1-1-1-11-1-111-11-11-1-1-11-1-111-1111-111-111-11
χ3311-11-1-11-11-1-11-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11-1-11-111-1-1111+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i321-111-1-11-1−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i321+i321+i32−1−i321+i321−i321−i32−1+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ3411-11-1-11-11-1-11-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11-1-11-111-1-1111+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i32−1−i32−1+i321+i321+i321−i321−i32-11-1-111-111+i32−1−i321+i321+i321−i32−1+i321−i321−i32−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ3511-11-1-11-11-1-11-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11-1-11-111-1-1111−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i321-111-1-11-1−1+i321−i32−1+i32−1+i32−1−i321+i32−1−i32−1−i321−i321−i32−1+i321−i321+i321+i32−1−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ3611-11-1-11-11-1-11-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11-1-11-111-1-1111−i32−1+i321−i321+i32−1−i321+i321−i32−1+i321−i321+i32−1−i321+i32−1+i32−1−i321−i321−i321+i321+i32-11-1-111-111−i32−1+i321−i321−i321+i32−1−i321+i321+i32−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ3711-1-11-1-11111-1-11111111111111-1-11-1-11-1-1-1-111-1-11-1-11-1-11-1-111111111-1-1111-1-11-1-111-1-1111-1-111-1-1-1-11-1-11
χ3811-1-11-1-11111-1-11111111111111-1-11-1-11-1-1-1-111-1-11-1-11-1-11-1-11111111-111-1-1-111-111-1-111-1-1-111-1-111-1-11-1-11
χ3911-1-11-1-11111-1-1111111111−1−i32−1+i32−1−i32−1+i32-1-11-1-11-1-1-1-1111+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1111-1-1−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i321−i321−i32−1+i32
χ4011-1-11-1-11111-1-1111111111−1−i32−1+i32−1−i32−1+i32-1-11-1-11-1-1-1-1111+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111-1-1-1111+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ4111-1-11-1-11111-1-1111111111−1+i32−1−i32−1+i32−1−i32-1-11-1-11-1-1-1-1111−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1111-1-1−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i321+i321+i32−1−i32
χ4211-1-11-1-11111-1-1111111111−1+i32−1−i32−1+i32−1−i32-1-11-1-11-1-1-1-1111−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111-1-1-1111−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ4311-1-11-1-111-1-111-11111-1-1-1-11111-1-11-1-111111-1-1-1-11-1-11-1-11-1-1111-1-1-1-11-1-1-11-1111-1-1-11-1-1-11-1111-11111-111-1
χ4411-1-11-1-111-1-111-11111-1-1-1-11111-1-11-1-111111-1-1-1-11-1-11-1-11-1-1111-1-1-1-1-1111-11-1-1-1111-1111-11-1-1-11-1-111-111-1
χ4511-1-11-1-111-1-111-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-11-1-111111-1-11+i321+i32−1−i321−i321−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321-1-1-11-111−1−i321+i321+i321+i32−1+i321−i321−i321−i32−1−i321+i32−1−i32−1−i32−1+i321−i32−1+i32−1+i32−1−i32−1−i321+i32−1+i32−1+i321−i32
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Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.