Finite Group Databasebeta

← Group #72259725

Character table — Group #72259725

Order 3888.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size1122233334666666661212121818181818181818181818181818181818181818272727272727363636363636363636363636363636363654545454545454545454545454545454545454545454545454108108108108108108108108108108108108
order1234633661233366612121212122233366699912121212121218181822666666999181818363636363636363636224666666666666661212121212121212666666181818181818
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3111111111111111111111-1-1111111111111111111111111-1-1111111111111111-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ511111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i3211−1−i32−1−i32−1+i32−1+i32
χ611111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ711111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-111+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ811111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ911111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+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−i3211−1+i32−1+i32−1−i32−1−i32
χ1011111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1111111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-111−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ1211111−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ13111-111111-1111111-1-1-1-1-11-1111111111-1-1-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-1-11-1-11-11-11-11-1111111-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ14111-111111-1111111-1-1-1-1-11-1111111111-1-1-1-1-1-1111-1-1-1-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1111-11-1-11-11-1-1-1-1-1-111111111-11-11-111-11-11-1
χ15111-111111-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111-11111111-1-1-1-1-1-1-1-1-1-11-1-11-11-11-11111111-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ16111-111111-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11-11-11-111-11-1-1-1-1-1-1-1111111111-11-11-1-11-11-11
χ17111-11−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321−1−i32−1+i321+i321−i32-11+i321−i321-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-11−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i321-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i321-1−1−i321+i32−1+i321−i321-1−1−i321+i32−1+i321−i32
χ18111-11−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321−1−i32−1+i321+i321−i32-11+i321−i321-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i321-11−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-111−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i321-1−1−i321+i32−1+i321−i32
χ19111-11−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321−1−i32−1+i321+i321−i32-11+i321−i32-111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-111−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-11-11+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-111+i32−1−i321−i32−1+i32
χ20111-11−1−i32−1+i32−1−i32−1+i32-11−1−i32−1+i321−1−i32−1+i321+i321−i32-11+i321−i32-111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32-1-11+i321+i321−i321−i321−1−i32−1+i32-1-11+i321+i321−i321−i32-111−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i321-111+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32-111+i32−1−i321−i32−1+i32
χ21111-11−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−1+i32−1−i321−i321+i32-11−i321+i321-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-11−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i321-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i321-1−1+i321−i32−1−i321+i321-1−1+i321−i32−1−i321+i32
χ22111-11−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−1+i32−1−i321−i321+i32-11−i321+i321-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i321-11−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-111−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i321-1−1+i321−i32−1−i321+i32
χ23111-11−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−1+i32−1−i321−i321+i32-11−i321+i32-111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-111−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-11-11−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-111−i32−1+i321+i32−1−i32
χ24111-11−1+i32−1−i32−1+i32−1−i32-11−1+i32−1−i321−1+i32−1−i321−i321+i32-11−i321+i32-111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32-1-11−i321−i321+i321+i321−1+i32−1−i32-1-11−i321−i321+i321+i32-111−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i321-111−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32-111−i32−1+i321+i32−1−i32
χ2522222222222222222222200-1-1-1-1-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1222-1-1-1-1-1-100200000000-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ2622222222222222222222200-1-1-1-1-1-1222-1-1-1-1-1-1222-2-2-2-2-2-200-1-1-1-1-1-1222-1-1-1-1-1-100-200000000111111-2-2111111000000000000
χ2722222222222222222222222222222-1-1-1222222-1-1-100000022-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10002222000000000000000000000000-1-1-1-1-1-1
χ28222222222222222222222-2-2222222-1-1-1222222-1-1-1000000-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-2-2-2-2000000000000000000000000111111
χ2922222−1−i3−1+i3−1−i3−1+i322−1−i3−1+i32−1−i3−1+i3−1−i3−1+i32−1−i3−1+i300-11+i321−i32-11+i321−i322−1−i3−1+i3-1-11+i321+i321−i321−i322−1−i3−1+i322−1−i3−1−i3−1+i3−1+i300-11+i321−i32-11+i321−i322−1−i3−1+i3-1-11+i321+i321−i321−i3200200000000-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000
χ3022222−1−i3−1+i3−1−i3−1+i322−1−i3−1+i32−1−i3−1+i3−1−i3−1+i32−1−i3−1+i300-11+i321−i32-11+i321−i322−1−i3−1+i3-1-11+i321+i321−i321−i322−1−i3−1+i3-2-21+i31+i31−i31−i300-11+i321−i32-11+i321−i322−1−i3−1+i3-1-11+i321+i321−i321−i3200-20000000011−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000
χ3122222−1−i3−1+i3−1−i3−1+i322−1−i3−1+i32−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3222−1−i3−1+i32−1−i3−1+i3-11+i321−i3222−1−i3−1−i3−1+i3−1+i3-11+i321−i3200000022-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i32000−1−i3−1−i3−1+i3−1+i3000000000000000000000000-1-11+i321+i321−i321−i32
χ3222222−1−i3−1+i3−1−i3−1+i322−1−i3−1+i32−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3-2-22−1−i3−1+i32−1−i3−1+i3-11+i321−i3222−1−i3−1−i3−1+i3−1+i3-11+i321−i32000000-2-2-11+i321−i32-11+i321−i32-11+i321−i32-1-11+i321+i321−i321−i320001+i31+i31−i31−i300000000000000000000000011−1−i32−1−i32−1+i32−1+i32
χ3322222−1+i3−1−i3−1+i3−1−i322−1+i3−1−i32−1+i3−1−i3−1+i3−1−i32−1+i3−1−i300-11−i321+i32-11−i321+i322−1+i3−1−i3-1-11−i321−i321+i321+i322−1+i3−1−i322−1+i3−1+i3−1−i3−1−i300-11−i321+i32-11−i321+i322−1+i3−1−i3-1-11−i321−i321+i321+i3200200000000-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000
χ3422222−1+i3−1−i3−1+i3−1−i322−1+i3−1−i32−1+i3−1−i3−1+i3−1−i32−1+i3−1−i300-11−i321+i32-11−i321+i322−1+i3−1−i3-1-11−i321−i321+i321+i322−1+i3−1−i3-2-21−i31−i31+i31+i300-11−i321+i32-11−i321+i322−1+i3−1−i3-1-11−i321−i321+i321+i3200-20000000011−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000
χ3522222−1+i3−1−i3−1+i3−1−i322−1+i3−1−i32−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3222−1+i3−1−i32−1+i3−1−i3-11−i321+i3222−1+i3−1+i3−1−i3−1−i3-11−i321+i3200000022-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i32000−1+i3−1+i3−1−i3−1−i3000000000000000000000000-1-11−i321−i321+i321+i32
χ3622222−1+i3−1−i3−1+i3−1−i322−1+i3−1−i32−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3-2-22−1+i3−1−i32−1+i3−1−i3-11−i321+i3222−1+i3−1+i3−1−i3−1−i3-11−i321+i32000000-2-2-11−i321+i32-11−i321+i32-11−i321+i32-1-11−i321−i321+i321+i320001−i31−i31+i31+i300000000000000000000000011−1+i32−1+i32−1−i32−1−i32
χ37222-222222-2222222-2-2-2-2-200-1-1-1-1-1-122211111122222222200-1-1-1-1-1-1-2-2-211111100-200000000-1-1-1-1-1-1-2-2111111000000000000
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χ9612-12120-12−6+6i3−6−6i36−6i36+6i30-63−3i33+3i36−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ971818-918-90000-90000000000066000000000000000000000000-3-30000000000000000000000000000000000000000000000000000
χ981818-918-90000-900000000000-6-6000000000000000000000000330000000000000000000000000000000000000000000000000000
χ991818-9-18-900009000000000006-6000000000000000000000000-330000000000000000000000000000000000000000000000000000
χ1001818-9-18-90000900000000000-660000000000000000000000003-30000000000000000000000000000000000000000000000000000
χ10136-36-18018000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.