Finite Group Databasebeta

← Group #85597

Character table — Group #85597

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111444444446611114444444466222288888888121222228888888812122222888888881212
order1244336612121212242244666612121212242244666612121212242244666612121212244444121212121212121244
χ11111111111111111111111111111111111111111111111111111111111111111111111
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+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−i3211
χ411-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-11
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−i32-11
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+i32-11
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−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−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−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−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−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−ζ11ζ1100
χ13333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1333300000000-1-1
χ1433-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-133-3-3000000001-1
χ15111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111−1−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+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1
χ171111−1+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−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1
χ1811-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-1-1-111-1-1-1-111111-1
χ1911-1-1−1−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−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1
χ2011-1-1−1+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+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1
χ212-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii00-22−2i2i11-1-1−ii−ii00
χ222-22i−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−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700
χ232-22i−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−ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100
χ242-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii00-222i−2i11-1-1i−ii−i00-222i−2i11-1-1i−ii−i00
χ252-2−2i2i1+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−ζ7ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700
χ262-2−2i2i1−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−ζ11ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100
χ27333300000000-1-1333300000000-1-1333300000000-1-1-3-3-3-30000000011-3-3-3-30000000011
χ2833-3-3000000001-133-3-3000000001-133-3-3000000001-1-3-33300000000-11-3-33300000000-11
χ291111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111−1−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−i32111111−1+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
χ3211-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-1
χ3311-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1111-1-1−1−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+i32-1111-1-1−1+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−i002-22i−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−ζ7002-22i−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
χ372-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100
χ382-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii00-222i−2i11-1-1i−ii−i002-2−2i2i-1-111−ii−ii00-222i−2i11-1-1i−ii−i00
χ392-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700
χ402-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100
χ41333300000000-1-1333300000000-1-1-3-3-3-30000000011333300000000-1-1-3-3-3-30000000011
χ4233-3-3000000001-133-3-3000000001-1-3-33300000000-1133-3-3000000001-1-3-33300000000-11
χ431111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ441111−1−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+i3211-1-1-1-11+i321−i321+i321−i321+i321+i321−i321−i32-1-1-1-1-1-11+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
χ451111−1+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−i3211-1-1-1-11−i321+i321−i321+i321−i321−i321+i321+i32-1-1-1-1-1-11−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
χ4611-1-11111-1-1-1-1-1111-1-11111-1-1-1-1-11-1-111-1-1-1-111111-1-1-111-1-1-1-111111-111-1-11111-1-1-1-1-11
χ4711-1-1−1−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−i32-11-1-1111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321-1-1-1111+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
χ4811-1-1−1+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+i32-11-1-1111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321-1-1-1111−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
χ492-22i−2i-1-111i−ii−i002-22i−2i-1-111i−ii−i00-22−2i2i11-1-1−ii−ii00-22−2i2i11-1-1−ii−ii002-22i−2i-1-111i−ii−i00
χ502-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ700-22−2i2i−1−i32−1+i321+i321−i32−ζ11ζ11−ζ7ζ7002-22i−2i1+i321−i32−1−i32−1+i32ζ11−ζ11ζ7−ζ700
χ512-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ1100-22−2i2i−1+i32−1−i321−i321+i32−ζ7ζ7−ζ11ζ11002-22i−2i1−i321+i32−1+i32−1−i32ζ7−ζ7ζ11−ζ1100
χ522-2−2i2i-1-111−ii−ii002-2−2i2i-1-111−ii−ii00-222i−2i11-1-1i−ii−i00-222i−2i11-1-1i−ii−i002-2−2i2i-1-111−ii−ii00
χ532-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ700-222i−2i−1−i32−1+i321+i321−i32ζ11−ζ11ζ7−ζ7002-2−2i2i1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ7ζ700
χ542-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ1100-222i−2i−1+i32−1−i321−i321+i32ζ7−ζ7ζ11−ζ11002-2−2i2i1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ11ζ1100
χ55333300000000-1-1333300000000-1-1-3-3-3-30000000011-3-3-3-30000000011333300000000-1-1
χ5633-3-3000000001-133-3-3000000001-1-3-33300000000-11-3-33300000000-1133-3-3000000001-1
χ5722222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000
χ582222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322-2-2-2-21+i31−i31+i31−i31+i31+i31−i31−i3-2-2000000000000000000000000000000000000000000
χ592222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i322-2-2-2-21−i31+i31−i31+i31−i31−i31+i31+i3-2-2000000000000000000000000000000000000000000
χ6022-2-22222-2-2-2-2-22-2-222-2-2-2-222222-2000000000000000000000000000000000000000000
χ6122-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3-22-2-2221+i31−i31+i31−i3−1−i3−1−i3−1+i3−1+i32-2000000000000000000000000000000000000000000
χ6222-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3-22-2-2221−i31+i31−i31+i3−1+i3−1+i3−1−i3−1−i32-2000000000000000000000000000000000000000000
χ634-44i−4i-2-2222i−2i2i−2i00-44−4i4i22-2-2−2i2i−2i2i00000000000000000000000000000000000000000000
χ644-44i−4i1+i31−i3−1−i3−1+i32ζ11−2ζ112ζ7−2ζ700-44−4i4i−1−i3−1+i31+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000000000000000000000
χ654-44i−4i1−i31+i3−1+i3−1−i32ζ7−2ζ72ζ11−2ζ1100-44−4i4i−1+i3−1−i31−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000000000000000000
χ664-4−4i4i-2-222−2i2i−2i2i00-444i−4i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000
χ674-4−4i4i1+i31−i3−1−i3−1+i3−2ζ112ζ11−2ζ72ζ700-444i−4i−1−i3−1+i31+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000000000000000000000
χ684-4−4i4i1−i31+i3−1+i3−1−i3−2ζ72ζ7−2ζ112ζ1100-444i−4i−1+i3−1−i31−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000000000000000000
χ69666600000000-2-2-6-6-6-60000000022000000000000000000000000000000000000000000
χ7066-6-6000000002-2-6-66600000000-22000000000000000000000000000000000000000000

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