Finite Group Databasebeta

← Group #13047784

Character table — Group #13047784

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11133333333333333333333333999999999999999999999999999999999999999916161616161648484848484848484848484848484848
order13323344446699999912121212121212126612121212121212121818181818183636363636363636363636363636363636363636363636363333333333999999999999
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ4111111111111−1−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+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
χ5111111111111−1−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+i32−1−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
χ6111111111111−1−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+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ7111111111111−1+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−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
χ8111111111111−1+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−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ9111111111111−1+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−i32−1+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
χ101111−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i3211111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ111111−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i3211111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−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−i32−1+i321−1−i32−1+i321−1+i321−1−i32−1+i321−1−i32
χ121111−1−i32−1+i321111111−1−i32−1+i321−1−i32−1+i3211111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−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+i321−1−i32−1+i321−1−i32−1−i32−1+i321−1−i32−1+i321
χ131111−1−i32−1+i32111111−1−i32−1+i321−1+i321−1−i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ141111−1−i32−1+i32111111−1−i32−1+i321−1+i321−1−i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1+i32−1+i32−1+i32−1+i321111−1−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−i32−1+i321−1−i32−1+i32−1−i32−1+i321
χ151111−1−i32−1+i32111111−1−i32−1+i321−1+i321−1−i3211111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i32
χ161111−1−i32−1+i32111111−1+i321−1−i32−1−i32−1+i32111111111−1−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+i321−1+i32−1+i32−1+i32−1+i321111−1−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+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ171111−1−i32−1+i32111111−1+i321−1−i32−1−i32−1+i32111111111−1−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+i321−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i321−1−i32−1+i32−1+i321−1−i32−1−i32−1+i3211−1−i32−1+i32
χ181111−1−i32−1+i32111111−1+i321−1−i32−1−i32−1+i32111111111−1−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+i321−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1+i321−1−i32
χ191111−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i3211111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ201111−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i3211111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+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−i321−1+i32−1−i321−1+i32−1+i32−1−i321−1+i32−1−i321
χ211111−1+i32−1−i321111111−1+i32−1−i321−1+i32−1−i3211111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+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+i32−1−i321−1+i32−1−i321−1−i321−1+i32−1−i321−1+i32
χ221111−1+i32−1−i32111111−1−i321−1+i32−1+i32−1−i32111111111−1+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−i321−1−i32−1−i32−1−i32−1−i321111−1+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−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ231111−1+i32−1−i32111111−1−i321−1+i32−1+i32−1−i32111111111−1+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−i321−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1−i321−1+i32
χ241111−1+i32−1−i32111111−1−i321−1+i32−1+i32−1−i32111111111−1+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−i321−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i321−1+i32−1−i32−1−i321−1+i32−1+i32−1−i3211−1+i32−1−i32
χ251111−1+i32−1−i32111111−1+i32−1−i321−1−i321−1+i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ261111−1+i32−1−i32111111−1+i32−1−i321−1−i321−1+i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i32
χ271111−1+i32−1−i32111111−1+i32−1−i321−1−i321−1+i3211111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1−i32−1−i32−1−i32−1−i321111−1+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+i32−1−i321−1+i32−1−i32−1+i32−1−i321
χ28333333-1-1-1-133333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ29333333-1-1-1-133−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i320000000000000000000000
χ30333333-1-1-1-133−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i320000000000000000000000
χ313333−3−3i32−3+3i32-1-1-1-1333−3−3i32−3+3i323−3−3i32−3+3i32-1-1-1-1-1-1-1-1−3−3i32−3+3i321+i321+i321+i321+i321−i321−i321−i321−i323−3−3i32−3+3i323−3−3i32−3+3i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i320000000000000000000000
χ323333−3−3i32−3+3i32-1-1-1-133−3−3i32−3+3i323−3+3i323−3−3i32-1-1-1-1-1-1-1-1−3−3i32−3+3i321+i321+i321+i321+i321−i321−i321−i321−i32−3−3i32−3+3i323−3+3i323−3−3i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i320000000000000000000000
χ333333−3−3i32−3+3i32-1-1-1-133−3+3i323−3−3i32−3−3i32−3+3i323-1-1-1-1-1-1-1-1−3−3i32−3+3i321+i321+i321+i321+i321−i321−i321−i321−i32−3+3i323−3−3i32−3−3i32−3+3i3231−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-10000000000000000000000
χ343333−3+3i32−3−3i32-1-1-1-1333−3+3i32−3−3i323−3+3i32−3−3i32-1-1-1-1-1-1-1-1−3+3i32−3−3i321−i321−i321−i321−i321+i321+i321+i321+i323−3+3i32−3−3i323−3+3i32−3−3i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i320000000000000000000000
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χ743−3−3i32−3+3i323003333−3−3i32−3+3i32000000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000−3−3i32−3+3i323−3+3i323−3−3i320000000000000000
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χ829−9−9i32−9+9i32-300−3+6i−3−6i333+3i323−3i320000003ζ2+6ζ116ζ7+3ζ103ζ2−6ζ11−6ζ7+3ζ10−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000000000000000000000000000
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χ849−9+9i32−9−9i32900-3-3-3-3−9+9i32−9−9i320000003−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i3200000000000000000000000000000000000000000000000000000000000000
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χ869−9+9i32−9−9i32-30033−3−6i−3+6i3−3i323+3i32000000−3+3i32−3−3i32−3+3i32−3−3i32−6ζ7+3ζ103ζ2−6ζ116ζ7+3ζ103ζ2+6ζ1100000000000000000000000000000000000000000000000000000000000000
χ879−9+9i32−9−9i32-300−3+6i−3−6i333−3i323+3i320000006ζ7+3ζ103ζ2+6ζ11−6ζ7+3ζ103ζ2−6ζ11−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000000000000000000000000000
χ889−9+9i32−9−9i32-300−3−6i−3+6i333−3i323+3i32000000−6ζ7+3ζ103ζ2−6ζ116ζ7+3ζ103ζ2+6ζ11−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.