Finite Group Databasebeta

← Group #85576

Character table — Group #85576

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size1111444444446611114444444466111144444444661111444444446611114444444466111144444444661111444444446611114444444466
order1244336612121212244444121212121212121244224466661212121224444412121212121212124422446666121212122444441212121212121212442244666612121212244444121212121212121244
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111−1−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+i32111111−1−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+i32111111−1−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+i32111111−1−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+i3211
χ31111−1+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−i32111111−1+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−i32111111−1+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−i32111111−1+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−i3211
χ411-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-11
χ511-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11
χ611-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11
χ72-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i00
χ82-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700
χ92-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100
χ102-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii00
χ112-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700
χ122-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100
χ13333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1
χ1433-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-1
χ1511111111111111iiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i11111111111111iiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ161111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211iiiiζ11ζ7ζ11ζ7ζ11ζ11ζ7ζ7ii-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ11−ζ7−ζ7−i−i1111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211iiiiζ11ζ7ζ11ζ7ζ11ζ11ζ7ζ7ii-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ11−ζ7−ζ7−i−i
χ171111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211iiiiζ7ζ11ζ7ζ11ζ7ζ7ζ11ζ11ii-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ7−ζ11−ζ11−i−i1111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211iiiiζ7ζ11ζ7ζ11ζ7ζ7ζ11ζ11ii-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ7−ζ11−ζ11−i−i
χ1811-1-11111-1-1-1-1-11ii−i−iiiii−i−i−i−i−ii-1-111-1-1-1-111111-1−i−iii−i−i−i−iiiiii−i11-1-11111-1-1-1-1-11ii−i−iiiii−i−i−i−i−ii-1-111-1-1-1-111111-1−i−iii−i−i−i−iiiiii−i
χ1911-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11ii−i−iζ11ζ7ζ11ζ7−ζ11−ζ11−ζ7−ζ7−ii-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1−i−iii−ζ11−ζ7−ζ11−ζ7ζ11ζ11ζ7ζ7i−i11-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11ii−i−iζ11ζ7ζ11ζ7−ζ11−ζ11−ζ7−ζ7−ii-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1−i−iii−ζ11−ζ7−ζ11−ζ7ζ11ζ11ζ7ζ7i−i
χ2011-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11ii−i−iζ7ζ11ζ7ζ11−ζ7−ζ7−ζ11−ζ11−ii-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1−i−iii−ζ7−ζ11−ζ7−ζ11ζ7ζ7ζ11ζ11i−i11-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11ii−i−iζ7ζ11ζ7ζ11−ζ7−ζ7−ζ11−ζ11−ii-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1−i−iii−ζ7−ζ11−ζ7−ζ11ζ7ζ7ζ11ζ11i−i
χ212-22i−2i-1-111i−ii−i002i−2i-22−i−iii-11-1100-22−2i2i11-1-1−ii−ii00−2i2i2-2ii−i−i1-11-1002-22i−2i-1-111i−ii−i002i−2i-22−i−iii-11-1100-22−2i2i11-1-1−ii−ii00−2i2i2-2ii−i−i1-11-100
χ222-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002i−2i-22−ζ11−ζ7ζ11ζ71+i32−1−i321−i32−1+i3200-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700−2i2i2-2ζ11ζ7−ζ11−ζ7−1−i321+i32−1+i321−i32002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002i−2i-22−ζ11−ζ7ζ11ζ71+i32−1−i321−i32−1+i3200-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700−2i2i2-2ζ11ζ7−ζ11−ζ7−1−i321+i32−1+i321−i3200
χ232-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002i−2i-22−ζ7−ζ11ζ7ζ111−i32−1+i321+i32−1−i3200-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100−2i2i2-2ζ7ζ11−ζ7−ζ11−1+i321−i32−1−i321+i32002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002i−2i-22−ζ7−ζ11ζ7ζ111−i32−1+i321+i32−1−i3200-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100−2i2i2-2ζ7ζ11−ζ7−ζ11−1+i321−i32−1−i321+i3200
χ242-2−2i2i-1-111−ii−ii002i−2i2-2−i−iii1-11-100-222i−2i11-1-1i−ii−i00−2i2i-22ii−i−i-11-11002-2−2i2i-1-111−ii−ii002i−2i2-2−i−iii1-11-100-222i−2i11-1-1i−ii−i00−2i2i-22ii−i−i-11-1100
χ252-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002i−2i2-2−ζ11−ζ7ζ11ζ7−1−i321+i32−1+i321−i3200-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700−2i2i-22ζ11ζ7−ζ11−ζ71+i32−1−i321−i32−1+i32002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002i−2i2-2−ζ11−ζ7ζ11ζ7−1−i321+i32−1+i321−i3200-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700−2i2i-22ζ11ζ7−ζ11−ζ71+i32−1−i321−i32−1+i3200
χ262-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002i−2i2-2−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i3200-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100−2i2i-22ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i32002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002i−2i2-2−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i3200-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100−2i2i-22ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i3200
χ27333300000000-1-13i3i3i3i00000000−i−i-3-3-3-30000000011−3i−3i−3i−3i00000000ii333300000000-1-13i3i3i3i00000000−i−i-3-3-3-30000000011−3i−3i−3i−3i00000000ii
χ2833-3-3000000001-13i3i−3i−3i00000000i−i-3-33300000000-11−3i−3i3i3i00000000−ii33-3-3000000001-13i3i−3i−3i00000000i−i-3-33300000000-11−3i−3i3i3i00000000−ii
χ2911111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1
χ311111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1
χ3211-1-11111-1-1-1-1-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-1
χ3311-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1
χ3411-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1
χ352-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii002-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii002-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii002-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii00
χ362-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700
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χ1092-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700−2i2i-22ζ11ζ7−ζ11−ζ71+i32−1−i321−i32−1+i3200-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7002i−2i2-2−ζ11−ζ7ζ11ζ7−1−i321+i32−1+i321−i3200-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7002i−2i2-2−ζ11−ζ7ζ11ζ7−1−i321+i32−1+i321−i32002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700−2i2i-22ζ11ζ7−ζ11−ζ71+i32−1−i321−i32−1+i3200
χ1102-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100−2i2i-22ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i3200-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11002i−2i2-2−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i3200-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11002i−2i2-2−ζ7−ζ11ζ7ζ11−1+i321−i32−1−i321+i32002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100−2i2i-22ζ7ζ11−ζ7−ζ111−i32−1+i321+i32−1−i3200
χ111333300000000-1-1−3i−3i−3i−3i00000000ii-3-3-3-300000000113i3i3i3i00000000−i−i-3-3-3-300000000113i3i3i3i00000000−i−i333300000000-1-1−3i−3i−3i−3i00000000ii
χ11233-3-3000000001-1−3i−3i3i3i00000000−ii-3-33300000000-113i3i−3i−3i00000000i−i-3-33300000000-113i3i−3i−3i00000000i−i33-3-3000000001-1−3i−3i3i3i00000000−ii

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