Finite Group Databasebeta

← Group #13164655

Character table — Group #13164655

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111111222222333333333333666666666666666666999999121212121212121212121212161616161616161616161616181818181818181818181818323232323232323232323232484848484848484848484848
order1233663336662244666612121212444466666612121212121212124412121212121212121212121212121212999999181818181818222266666666999999181818181818363636363636363636363636
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111−1−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
χ3111111111111111111111111111111111111111111111111111111111111−1+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
χ411111111111111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32
χ611111111111111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32
χ711−1−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+i32111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ341111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26ζ14+ζ26−ζ26−ζ26−ζ14−ζ14−ζ22−ζ22ζ22+ζ34ζ22+ζ34−ζ34−ζ34
χ811−1−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+i32111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ341111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ26−ζ14−ζ14ζ14+ζ26ζ14+ζ26−ζ34−ζ34−ζ22−ζ22ζ22+ζ34ζ22+ζ34
χ911−1−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+i32111111−1−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+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ221111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14−ζ14ζ14+ζ26ζ14+ζ26−ζ26−ζ26ζ22+ζ34ζ22+ζ34−ζ34−ζ34−ζ22−ζ22
χ1011−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34−ζ14−ζ26−ζ14−ζ26ζ26ζ26ζ14ζ14ζ22ζ22−ζ22−ζ34−ζ22−ζ34ζ34ζ34
χ1111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34ζ26ζ26ζ14ζ14−ζ14−ζ26−ζ14−ζ26ζ34ζ34ζ22ζ22−ζ22−ζ34−ζ22−ζ34
χ1211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22ζ14ζ14−ζ14−ζ26−ζ14−ζ26ζ26ζ26−ζ22−ζ34−ζ22−ζ34ζ34ζ34ζ22ζ22
χ1311−1+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−i32111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ141111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ22−ζ34−ζ34ζ22+ζ34ζ22+ζ34−ζ26−ζ26ζ14+ζ26ζ14+ζ26−ζ14−ζ14
χ1411−1+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−i32111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ261111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34ζ22+ζ34−ζ22−ζ22−ζ34−ζ34ζ14+ζ26ζ14+ζ26−ζ14−ζ14−ζ26−ζ26
χ1511−1+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−i32111111−1+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−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ261111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34−ζ34ζ22+ζ34ζ22+ζ34−ζ22−ζ22−ζ14−ζ14−ζ26−ζ26ζ14+ζ26ζ14+ζ26
χ1611−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14ζ22ζ22ζ34ζ34−ζ22−ζ34−ζ22−ζ34ζ26ζ26−ζ14−ζ26−ζ14−ζ26ζ14ζ14
χ1711−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26−ζ22−ζ34−ζ22−ζ34ζ22ζ22ζ34ζ34−ζ14−ζ26−ζ14−ζ26ζ14ζ14ζ26ζ26
χ1811−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26ζ34ζ34−ζ22−ζ34−ζ22−ζ34ζ22ζ22ζ14ζ14ζ26ζ26−ζ14−ζ26−ζ14−ζ26
χ19222222-1-1-1-1-1-12200222200002222-1-1-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1222222222222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222-1-1-1-1-1-12200222200002222-1-1-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000000001+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32000000000000
χ21222222-1-1-1-1-1-12200222200002222-1-1-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000000001−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i32000000000000
χ2222−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i322200−1−i3−1−i3−1+i3−1+i300002222-1-11+i321+i321−i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3000000-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i322ζ14+2ζ26−2ζ26−2ζ14−2ζ222ζ22+2ζ34−2ζ342ζ14+2ζ26−2ζ26−2ζ14−2ζ222ζ22+2ζ34−2ζ34000000000000−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34000000000000
χ2322−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i322200−1−i3−1−i3−1+i3−1+i300002222-1-11+i321+i321−i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3000000-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−2ζ26−2ζ142ζ14+2ζ26−2ζ34−2ζ222ζ22+2ζ34−2ζ26−2ζ142ζ14+2ζ26−2ζ34−2ζ222ζ22+2ζ34000000000000ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34000000000000
χ2422−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i322200−1−i3−1−i3−1+i3−1+i300002222-1-11+i321+i321−i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3000000-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−2ζ142ζ14+2ζ26−2ζ262ζ22+2ζ34−2ζ34−2ζ22−2ζ142ζ14+2ζ26−2ζ262ζ22+2ζ34−2ζ34−2ζ22000000000000ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22000000000000
χ2522−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i322200−1+i3−1+i3−1−i3−1−i300002222-1-11−i321−i321+i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3000000-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−2ζ22−2ζ342ζ22+2ζ34−2ζ262ζ14+2ζ26−2ζ14−2ζ22−2ζ342ζ22+2ζ34−2ζ262ζ14+2ζ26−2ζ14000000000000ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14000000000000
χ2622−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i322200−1+i3−1+i3−1−i3−1−i300002222-1-11−i321−i321+i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3000000-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i322ζ22+2ζ34−2ζ22−2ζ342ζ14+2ζ26−2ζ14−2ζ262ζ22+2ζ34−2ζ22−2ζ342ζ14+2ζ26−2ζ14−2ζ26000000000000−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26000000000000
χ2722−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i322200−1+i3−1+i3−1−i3−1−i300002222-1-11−i321−i321+i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3000000-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−2ζ342ζ22+2ζ34−2ζ22−2ζ14−2ζ262ζ14+2ζ26−2ζ342ζ22+2ζ34−2ζ22−2ζ14−2ζ262ζ14+2ζ26000000000000ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26000000000000
χ282-222-2-2222-2-2-22-22i−2i2-22-22i−2i2i−2i00002-22-22-2000000002i−2i2i−2i2i−2i000000000000-1-1-1-1-1-1111111000000000000-1-1-1-1-1-1111111i−ii−ii−ii−ii−ii−i
χ292-222-2-2222-2-2-22-22i−2i2-22-22i−2i2i−2i00002-22-22-2000000002i−2i2i−2i2i−2i0000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i320000000000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−ζ15ζ15−ζ15ζ15−ζ15ζ15−ζ3ζ3−ζ3ζ3−ζ3ζ3
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Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.