Finite Group Databasebeta

← Group #13143321

Character table — Group #13143321

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111222222333333334444444466666666666666668888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order12223446663366666688121224242424999121212121818181818181818182266662424242436363636363672727272727272727272727266661818181818181818181818184488121212122424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-1-1-111111111111111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ6111111111111111111-1-111-1-1-1-111111111111111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ7111111111111111111-1-111-1-1-1-11111111111111111-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11-1-111
χ8111111111111111111-1-111-1-1-1-11111111111111111-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111111-111-1-1
χ91111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111111−1−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+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ101111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32111111−1−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+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-1-11+i321−i321+i321−i32
χ111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1-1−1−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+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ121111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-1-1-1-1-1−1−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+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ131111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-111-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ141111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321-111-1-11+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ151111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-1111+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ161111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11-1-1111+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32
χ171111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111111−1+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−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ181111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32111111−1+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−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-1-11−i321+i321−i321+i32
χ191111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1-1−1+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−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ201111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-1-1-1-1-1−1+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−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ211111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-111-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ221111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321-111-1-11−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ231111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-1111−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ241111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11-1-1111−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32
χ2522222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2622222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000000000
χ27222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-12-222-2-2-2-2-2-2-1-1-1-1-1-111111111111122-2-2-1-1-1-1-1-1111111000000000000000000
χ28222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-22-2-222-2-2-2-2-1-1-1-1-1-1111111111111-2-222111111-1-1-1-1-1-1000000000000000000
χ292222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32222222−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000
χ302222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-2-2-2-2-2-2−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ312222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-2-222-2-2-2-2-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i322-222-2-21+i31+i31−i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000000
χ322222222222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-2-222-2-2-2-2-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32-22-2-2221+i31+i31−i31−i3-11+i321−i32-11+i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
χ332222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i322222222-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32222222−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000
χ342222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i322222222-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-2-2-2-2-2-2−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ352222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-2-222-2-2-2-2-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i322-222-2-21−i31−i31+i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ362222222222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-2-222-2-2-2-2-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32-22-2-2221−i31−i31+i31+i3-11−i321+i32-11−i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ3722222-2-22222222222200-2-20000222-2-2-2-22222222220000000000-2-2-2-2-2-200000000000000000000000000002-2002-22-20000000000
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χ9912121212-6-12-12-6-6-60000000000660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1001212-12-12-600-6660000000000003i6−3i63i6−3i6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1011212-12-12-600-666000000000000−3i63i6−3i63i6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-6006-660000000000003i6−3i6−3i63i6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-1212-12-6006-66000000000000−3i63i63i6−3i6000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212-6-121266-60000000000-660000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.