Finite Group Databasebeta

← Group #13152268

Character table — Group #13152268

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111111111333333333121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212646464646464646464646464646464646464
order1333333332666666664444412121212121212121212121212121212121212121212121212121212121212121212121212121212999999999999999999
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ3111111111111111111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32ζζζζ4ζ4ζ4ζ7ζ7ζ7ζ2ζ2ζ2ζ5ζ5ζ5ζ8ζ8ζ8
χ5111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ4ζ4ζ4ζ7ζ7ζ7ζζζζ8ζ8ζ8ζ2ζ2ζ2ζ5ζ5ζ5
χ6111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ7ζ7ζ7ζζζζ4ζ4ζ4ζ5ζ5ζ5ζ8ζ8ζ8ζ2ζ2ζ2
χ7111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ2ζ2ζ2ζ8ζ8ζ8ζ5ζ5ζ5ζ4ζ4ζ4ζζζζ7ζ7ζ7
χ8111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ5ζ5ζ5ζ2ζ2ζ2ζ8ζ8ζ8ζζζζ7ζ7ζ7ζ4ζ4ζ4
χ9111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ8ζ8ζ8ζ5ζ5ζ5ζ2ζ2ζ2ζ7ζ7ζ7ζ4ζ4ζ4ζζζ
χ101−1+i32−1−i321−1+i321−1−i32−1−i32−1+i321−1+i32−1−i321−1+i321−1−i32−1−i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζζ4ζ7ζζ4ζ7ζζ4ζ7
χ111−1+i32−1−i321−1+i321−1−i32−1−i32−1+i321−1+i32−1−i321−1+i321−1−i32−1−i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ7ζζ4ζ7ζζ4ζ7ζζ4
χ121−1+i32−1−i321−1+i321−1−i32−1−i32−1+i321−1+i32−1−i321−1+i321−1−i32−1−i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32ζ8ζ2ζ5ζ8ζ2ζ5ζ8ζ2ζ5ζ4ζ7ζζ4ζ7ζζ4ζ7ζ
χ131−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32111−1+i32−1−i32−1+i32−1−i32−1−i32−1+i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i321−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32−1−i321−1+i321−1+i32−1−i32−1+i32−1−i321
χ141−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32111−1+i32−1−i32−1+i32−1−i32−1−i32−1+i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i32−1+i32−1−i321−1−i321−1+i321−1+i32−1−i32
χ151−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32111−1+i32−1−i32−1+i32−1−i32−1−i32−1+i321111111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1+i321−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1−i321−1+i32
χ161−1+i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32−1−i32−1−i321−1+i321−1+i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111ζζ4ζ7ζ7ζζ4ζ4ζ7ζζ8ζ2ζ5ζ5ζ8ζ2ζ2ζ5ζ8
χ171−1+i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32−1−i32−1−i321−1+i321−1+i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111ζ4ζ7ζζζ4ζ7ζ7ζζ4ζ5ζ8ζ2ζ2ζ5ζ8ζ8ζ2ζ5
χ181−1+i32−1−i32−1−i321−1+i321−1+i32−1−i321−1+i32−1−i32−1−i321−1+i321−1+i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i3211111ζ7ζζ4ζ4ζ7ζζζ4ζ7ζ2ζ5ζ8ζ8ζ2ζ5ζ5ζ8ζ2
χ191−1−i32−1+i321−1−i321−1+i32−1+i32−1−i321−1−i32−1+i321−1−i321−1+i32−1+i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32ζζ7ζ4ζζ7ζ4ζζ7ζ4ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8
χ201−1−i32−1+i321−1−i321−1+i32−1+i32−1−i321−1−i32−1+i321−1−i321−1+i32−1+i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ4ζζ7ζ4ζζ7ζ4ζζ7ζ2ζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5
χ211−1−i32−1+i321−1−i321−1+i32−1+i32−1−i321−1−i32−1+i321−1−i321−1+i32−1+i32−1−i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32ζ7ζ4ζζ7ζ4ζζ7ζ4ζζ8ζ5ζ2ζ8ζ5ζ2ζ8ζ5ζ2
χ221−1−i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32−1+i32−1+i321−1−i321−1−i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111ζ2ζ8ζ5ζ5ζ2ζ8ζ8ζ5ζ2ζ7ζ4ζζζ7ζ4ζ4ζζ7
χ231−1−i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32−1+i32−1+i321−1−i321−1−i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111ζ5ζ2ζ8ζ8ζ5ζ2ζ2ζ8ζ5ζ4ζζ7ζ7ζ4ζζζ7ζ4
χ241−1−i32−1+i32−1+i321−1−i321−1−i32−1+i321−1−i32−1+i32−1+i321−1−i321−1−i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111ζ8ζ5ζ2ζ2ζ8ζ5ζ5ζ2ζ8ζζ7ζ4ζ4ζζ7ζ7ζ4ζ
χ251−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32111−1−i32−1+i32−1−i32−1+i32−1+i32−1−i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i321−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32−1+i321−1−i321−1−i32−1+i32−1−i32−1+i321
χ261−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32111−1−i32−1+i32−1−i32−1+i32−1+i32−1−i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1−i321−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1+i321−1−i32
χ271−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32111−1−i32−1+i32−1−i32−1+i32−1+i32−1−i321111111−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i3211111−1+i32−1+i32−1+i32−1+i32−1+i3211111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i32−1−i32−1+i321−1+i321−1−i321−1−i32−1+i32
χ283333333333333333333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-1000000000000000000
χ29333333333333333333-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1000000000000000000
χ30333333333333333333-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1000000000000000000
χ31333333333333333333-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1000000000000000000
χ32333333333333333333-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13-1-1-1-13000000000000000000
χ33333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i323-1-1-1-13-1-1-1-13-1-1-1-1−3+3i321−i321−i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i321+i321+i321+i321+i32000000000000000000
χ34333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-13-1-1-1-13-1-1-1-13-1-1-11−i32−3+3i321−i321−i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i321+i321+i321+i32000000000000000000
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χ36333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3+3i32−3−3i32−3−3i32−3+3i32−3−3i32-1-1-13-1-1-1-13-1-1-1-13-11−i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i321−i321−i321−i321−i32−3+3i321−i321+i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i321+i321+i321+i321+i32−3−3i321+i32000000000000000000
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χ73121212121212121212-4-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000
χ74121212−6+6i3−6+6i3−6−6i3−6−6i3−6+6i3−6−6i3-4-4-42−2i32−2i32+2i32+2i32−2i32+2i3000000000000000000000000000000000000000000000000000000000000000
χ75121212−6−6i3−6−6i3−6+6i3−6+6i3−6−6i3−6+6i3-4-4-42+2i32+2i32−2i32−2i32+2i32−2i3000000000000000000000000000000000000000000000000000000000000000
χ7612−6+6i3−6−6i312−6+6i312−6−6i3−6−6i3−6+6i3-42−2i32+2i3-42−2i3-42+2i32+2i32−2i3000000000000000000000000000000000000000000000000000000000000000
χ7712−6+6i3−6−6i3−6+6i3−6−6i3−6−6i3−6+6i31212-42−2i32+2i32−2i32+2i32+2i32−2i3-4-4000000000000000000000000000000000000000000000000000000000000000
χ7812−6+6i3−6−6i3−6−6i312−6+6i312−6+6i3−6−6i3-42−2i32+2i32+2i3-42−2i3-42−2i32+2i3000000000000000000000000000000000000000000000000000000000000000
χ7912−6−6i3−6+6i312−6−6i312−6+6i3−6+6i3−6−6i3-42+2i32−2i3-42+2i3-42−2i32−2i32+2i3000000000000000000000000000000000000000000000000000000000000000
χ8012−6−6i3−6+6i3−6+6i312−6−6i312−6−6i3−6+6i3-42+2i32−2i32−2i3-42+2i3-42+2i32−2i3000000000000000000000000000000000000000000000000000000000000000
χ8112−6−6i3−6+6i3−6−6i3−6+6i3−6+6i3−6−6i31212-42+2i32−2i32+2i32−2i32−2i32+2i3-4-4000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.