Finite Group Databasebeta

← Group #13152244

Character table — Group #13152244

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111111133333333666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212484848484848484848484848484848484848484848484848
order1222336666669918181818181822666618181818181818181818181844441212121212121212363636363636363636363636363636363636363636363636336666669999181818181818181818181818
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+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+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−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+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−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−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
χ5111111111111−1+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+i32−1−i32−1−i32−1−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−i32−1−i32−1−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−i32−1−i32111111−1+i32−1+i32−1+i32
χ6111111111111−1+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+i32−1−i32−1−i32−1−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−i32−1−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−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111
χ7111111111111−1−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−i32−1+i32−1+i32−1+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+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
χ8111111111111−1−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−i32−1+i32−1+i32−1+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+i32−1+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+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111
χ9111111111111−1−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−i32−1+i32−1+i32−1+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+i32−1+i32−1+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+i32−1+i32111111−1−i32−1−i32−1−i32
χ1022-2-22222-2-2-2-22222-2-2-2-22-222-2-2222-2-2-2222-2-2-2000000000000000000000000000000000000-1-111-111-1-1-1-1-111-111-111-111-1
χ1122-2-22222-2-2-2-22222-2-2-2-22-222-2-2222-2-2-2222-2-2-20000000000000000000000000000000000001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ1222-2-22222-2-2-2-22222-2-2-2-22-222-2-2222-2-2-2222-2-2-20000000000000000000000000000000000001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ1322-2-22222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-222-2-2−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000000000000000000000000000-1-111-111-11−i321+i321−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ1422-2-22222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-222-2-2−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000000000000000000000000000001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32-1-11−i32−1−i32−1−i321+i3211-111-1−1+i32−1+i321−i32
χ1522-2-22222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i32-222-2-2−1+i3−1+i3−1+i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000000000000000000000000000001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32-11−i321+i32-111-1−1+i32−1+i321−i32−1−i32−1−i321+i3211-1
χ1622-2-22222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-222-2-2−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000000000000000000000000000-1-111-111-11+i321−i321+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ1722-2-22222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-222-2-2−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000000000000000000000000000001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32-11+i321−i32-111-1−1−i32−1−i321+i32−1+i32−1+i321−i3211-1
χ1822-2-22222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i32-222-2-2−1−i3−1−i3−1−i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000000000000000000000000000001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32-1-11+i32−1+i32−1+i321−i3211-111-1−1−i32−1−i321+i32
χ1933333333333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2033333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-133-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1000000000000000000000000
χ2133333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1000000000000000000000000
χ2233333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-133-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333-1-1-1000000000000000000000000
χ2333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1333000000000000000000000000
χ24333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32333333−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000000000000000
χ25333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i323-1-1-133-1-1-1-1-1-1−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000000000000000
χ26333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-13-1-1-1-133-1-1-1-11−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i32000000000000000000000000
χ27333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-13-1-1-1-1-133-1-11−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i32000000000000000000000000
χ28333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-1-13-1-1-1-1-1-1331−i321−i321−i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i32000000000000000000000000
χ29333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32333333−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000000000000000
χ30333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i323-1-1-133-1-1-1-1-1-1−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000000000000000
χ31333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-13-1-1-1-133-1-1-1-11+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i321+i321+i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i321−i321−i32000000000000000000000000
χ32333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-13-1-1-1-1-133-1-11+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321+i321+i321+i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i321−i321−i321−i32000000000000000000000000
χ33333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-1-13-1-1-1-1-1-1331+i321+i321+i321+i321+i321+i321+i321+i321+i32−3−3i32−3−3i32−3−3i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−3+3i32−3+3i32−3+3i32000000000000000000000000
χ343333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i320000000000003333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000000000000000
χ353333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ8000000000000000000000000
χ363333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i322ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ5000000000000000000000000
χ373333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i322ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ72ζ2ζ42ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ22ζ52ζ82ζ2000000000000000000000000
χ383333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000-1-11−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ83-1-1-1−3+3i32−3−3i321−i321+i321−i321+i321−i321+i320002ζ2ζ42ζ72ζ42ζ72ζ2ζ72ζ2ζ40002ζ22ζ52ζ82ζ82ζ22ζ52ζ52ζ82ζ2000000000000000000000000
χ393333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000-1-11−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ8-13-1-11−i321+i32−3+3i32−3−3i321−i321+i321−i321+i322ζ2ζ42ζ70002ζ72ζ2ζ42ζ42ζ72ζ2ζ22ζ52ζ80002ζ52ζ82ζ22ζ82ζ22ζ5000000000000000000000000
χ403333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000-1-11−i321+i321−i321+i322ζ2ζ42ζ72ζ2ζ42ζ72ζ22ζ52ζ82ζ22ζ52ζ8-1-13-11−i321+i321−i321+i32−3+3i32−3−3i321−i321+i322ζ42ζ72ζ2ζ72ζ2ζ40002ζ2ζ42ζ72ζ82ζ22ζ52ζ52ζ82ζ20002ζ22ζ52ζ8000000000000000000000000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.