Finite Group Databasebeta

← Group #13164659

Character table — Group #13164659

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111111222222333333666666666666666121212121212121212121212121212161616161616161616161616181818181818181818181818181818323232323232323232323232484848484848484848484848
order12336633366644121212122224466666612121212666666666121212121212999999181818181818224446666121212121212999999181818181818363636363636363636363636
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−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
χ3111111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+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
χ4111111111111-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1-1-1111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−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
χ6111111111111-1-1-1-1-1-1111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+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+i3211−1−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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ3411111−1−i32−1−i32−1+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+i3211−1−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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ3411111−1−i32−1−i32−1+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+i3211−1−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+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ2211111−1−i32−1−i32−1+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+i32-1-11+i321+i321−i321−i3211111−1−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+i3211−1−i32−1−i32−1+i32−1+i32ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34ζ14+ζ26−ζ26−ζ14−ζ22ζ22+ζ34−ζ34-1-1-1-1-11+i321+i321−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+i32-1-11+i321+i321−i321−i3211111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34−ζ26−ζ14ζ14+ζ26−ζ34−ζ22ζ22+ζ34-1-1-1-1-11+i321+i321−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+i32-1-11+i321+i321−i321−i3211111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22−ζ14ζ14+ζ26−ζ26ζ22+ζ34−ζ34−ζ22-1-1-1-1-11+i321+i321−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−i3211−1+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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ1411111−1+i32−1+i32−1−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−i3211−1+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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ2611111−1+i32−1+i32−1−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−i3211−1+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−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ2611111−1+i32−1+i32−1−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−i32-1-11−i321−i321+i321+i3211111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14−ζ22−ζ34ζ22+ζ34−ζ26ζ14+ζ26−ζ14-1-1-1-1-11−i321−i321+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−i32-1-11−i321−i321+i321+i3211111−1+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−i3211−1+i32−1+i32−1−i32−1−i32ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26ζ22+ζ34−ζ22−ζ34ζ14+ζ26−ζ14−ζ26-1-1-1-1-11−i321−i321+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−i32-1-11−i321−i321+i321+i3211111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26−ζ34ζ22+ζ34−ζ22−ζ14−ζ26ζ14+ζ26-1-1-1-1-11−i321−i321+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
χ19222222-1-1-1-1-1-1000000222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222000000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222-1-1-1-1-1-1000000222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000000000000001+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i32000000000000
χ21222222-1-1-1-1-1-1000000222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000000000000001−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−i3200000022222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321−i321−i322ζ14+2ζ26−2ζ26−2ζ14−2ζ222ζ22+2ζ34−2ζ342ζ14+2ζ26−2ζ26−2ζ14−2ζ222ζ22+2ζ34−2ζ34000000000000000−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34−ζ14−ζ26ζ26ζ14ζ22−ζ22−ζ34ζ34000000000000
χ2322−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i3200000022222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321−i321−i32−2ζ26−2ζ142ζ14+2ζ26−2ζ34−2ζ222ζ22+2ζ34−2ζ26−2ζ142ζ14+2ζ26−2ζ34−2ζ222ζ22+2ζ34000000000000000ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34ζ26ζ14−ζ14−ζ26ζ34ζ22−ζ22−ζ34000000000000
χ2422−1−i3−1+i3−1−i3−1+i3-11+i321−i32-11+i321−i3200000022222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-11+i321+i321−i321−i32−2ζ142ζ14+2ζ26−2ζ262ζ22+2ζ34−2ζ34−2ζ22−2ζ142ζ14+2ζ26−2ζ262ζ22+2ζ34−2ζ34−2ζ22000000000000000ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22ζ14−ζ14−ζ26ζ26−ζ22−ζ34ζ34ζ22000000000000
χ2522−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i3200000022222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321+i321+i32−2ζ22−2ζ342ζ22+2ζ34−2ζ262ζ14+2ζ26−2ζ14−2ζ22−2ζ342ζ22+2ζ34−2ζ262ζ14+2ζ26−2ζ14000000000000000ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14ζ22ζ34−ζ22−ζ34ζ26−ζ14−ζ26ζ14000000000000
χ2622−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i3200000022222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321+i321+i322ζ22+2ζ34−2ζ22−2ζ342ζ14+2ζ26−2ζ14−2ζ262ζ22+2ζ34−2ζ22−2ζ342ζ14+2ζ26−2ζ14−2ζ26000000000000000−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26−ζ22−ζ34ζ22ζ34−ζ14−ζ26ζ14ζ26000000000000
χ2722−1+i3−1−i3−1+i3−1−i3-11−i321+i32-11−i321+i3200000022222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-11−i321−i321+i321+i32−2ζ342ζ22+2ζ34−2ζ22−2ζ14−2ζ262ζ14+2ζ26−2ζ342ζ22+2ζ34−2ζ22−2ζ14−2ζ262ζ14+2ζ26000000000000000ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26ζ34−ζ22−ζ34ζ22ζ14ζ26−ζ14−ζ26000000000000
χ283333333333333333333-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-1000000000000-1-13-1-1-1-1-1-13-1-13-1-1000000000000000000000000
χ29333333333333333333-13-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1000000000000-1-1-13-1-1-1-1-1-13-1-13-1000000000000000000000000
χ30333333333333333333-1-13-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-1000000000000-1-1-1-13-1-1-1-1-1-13-1-13000000000000000000000000
χ31333333333333333333-1-1-13-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-13-10000000000003-1-1-1-13-13-1-1-1-1-1-1-1000000000000000000000000
χ32333333333333333333-1-1-1-13-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-13000000000000-13-1-1-1-13-13-1-1-1-1-1-1000000000000000000000000
χ33333333333333-3-3-3-3-3-33-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1-100000000000011-3111111-311-311000000000000000000000000
χ34333333333333-3-3-3-3-3-3-13-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-1-1000000000000111-3111111-311-31000000000000000000000000
χ35333333333333-3-3-3-3-3-3-1-13-1-1-1-13-1-13-1-1-1-1-1-13-1-13-1-13-1-1-1-1-1-10000000000001111-3111111-311-3000000000000000000000000
χ36333333333333-3-3-3-3-3-3-1-1-13-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-13-1000000000000-31111-31-31111111000000000000000000000000
χ37333333333333-3-3-3-3-3-3-1-1-1-13-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-1-1-13-13-130000000000001-31111-31-3111111000000000000000000000000
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Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.