Finite Group Databasebeta

← Group #13136841

Character table — Group #13136841

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size11226661212121212121212121212121212121212121212121236364848484896969696144144144144216
order1236291824666121218181818181818181836363636363622336699181866664
χ111111111111111111111111111111111111111111111
χ21111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321
χ31111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321
χ411111111111111111111111111111-1-111111111-1-1-1-1-1
χ511111111111111111111111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32-1
χ611111111111111111111111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32-1
χ722222-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002222-1-1-1-100000
χ822222-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i3200000
χ922222-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i3200000
χ103333333-1-13-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133000000000000-1
χ113333333-1-13-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-30000000000001
χ124-44-404-400000000000000000000002-211-1-111-1-11-11-10
χ134-44-404-400000000000000000000002-2−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i320
χ144-44-404-400000000000000000000002-2−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i320
χ154-44-404-40000000000000000000000-2211-1-111-1-1-11-110
χ164-44-404-40000000000000000000000-22−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i320
χ174-44-404-40000000000000000000000-22−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i320
χ1866666-3-3-2-26-2-2-2-2-3-3-3111111111111000000000000000
χ196666-2662-2-222-2-2-2-2-2222222-2-2-2-2-2-2000000000000000
χ206666-266-22-2-2-222-2-2-2-2-2-2-2-2-2222222000000000000000
χ216666-2-3-32-2-222-2-2111−1+2i3−1+2i3−1+2i3−1−2i3−1−2i3−1−2i3111111000000000000000
χ226666-2-3-32-2-222-2-2111−1−2i3−1−2i3−1−2i3−1+2i3−1+2i3−1+2i3111111000000000000000
χ236666-2-3-3-22-2-2-222111111111−1+2i3−1+2i3−1+2i3−1−2i3−1−2i3−1−2i3000000000000000
χ246666-2-3-3-22-2-2-222111111111−1−2i3−1−2i3−1−2i3−1+2i3−1+2i3−1+2i3000000000000000
χ2566-3-360066-3-3-3-3-3000000000000000000000000000000
χ2666-3-3600-2-2-311110002ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ5000000000000000
χ2766-3-3600-2-2-311110002ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ8000000000000000
χ2866-3-3600-2-2-311110002ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ2+2ζ7000000000000000
χ2966-3-3-2002-21−1+2i3−1−2i3112ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2ζ72ζ42ζ82ζ22ζ52ζ2+2ζ42ζ+2ζ52ζ7+2ζ82ζ5+2ζ72ζ4+2ζ82ζ+2ζ2000000000000000
χ3066-3-3-2002-21−1+2i3−1−2i3112ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ72ζ42ζ2ζ22ζ52ζ82ζ+2ζ52ζ7+2ζ82ζ2+2ζ42ζ4+2ζ82ζ+2ζ22ζ5+2ζ7000000000000000
χ3166-3-3-2002-21−1+2i3−1−2i3112ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ42ζ2ζ72ζ52ζ82ζ22ζ7+2ζ82ζ2+2ζ42ζ+2ζ52ζ+2ζ22ζ5+2ζ72ζ4+2ζ8000000000000000
χ3266-3-3-2002-21−1−2i3−1+2i3112ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ82ζ22ζ52ζ2ζ72ζ42ζ5+2ζ72ζ4+2ζ82ζ+2ζ22ζ2+2ζ42ζ+2ζ52ζ7+2ζ8000000000000000
χ3366-3-3-2002-21−1−2i3−1+2i3112ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ22ζ52ζ82ζ72ζ42ζ2ζ4+2ζ82ζ+2ζ22ζ5+2ζ72ζ+2ζ52ζ7+2ζ82ζ2+2ζ4000000000000000
χ3466-3-3-2002-21−1−2i3−1+2i3112ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ52ζ82ζ22ζ42ζ2ζ72ζ+2ζ22ζ5+2ζ72ζ4+2ζ82ζ7+2ζ82ζ2+2ζ42ζ+2ζ5000000000000000
χ3566-3-3-200-22111−1+2i3−1−2i32ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ2+2ζ42ζ+2ζ52ζ7+2ζ82ζ5+2ζ72ζ4+2ζ82ζ+2ζ22ζ2ζ72ζ42ζ82ζ22ζ5000000000000000
χ3666-3-3-200-22111−1+2i3−1−2i32ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ+2ζ52ζ7+2ζ82ζ2+2ζ42ζ4+2ζ82ζ+2ζ22ζ5+2ζ72ζ72ζ42ζ2ζ22ζ52ζ8000000000000000
χ3766-3-3-200-22111−1+2i3−1−2i32ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ7+2ζ82ζ2+2ζ42ζ+2ζ52ζ+2ζ22ζ5+2ζ72ζ4+2ζ82ζ42ζ2ζ72ζ52ζ82ζ2000000000000000
χ3866-3-3-200-22111−1−2i3−1+2i32ζ+2ζ82ζ2+2ζ72ζ4+2ζ52ζ5+2ζ72ζ4+2ζ82ζ+2ζ22ζ2+2ζ42ζ+2ζ52ζ7+2ζ82ζ82ζ22ζ52ζ2ζ72ζ4000000000000000
χ3966-3-3-200-22111−1−2i3−1+2i32ζ2+2ζ72ζ4+2ζ52ζ+2ζ82ζ4+2ζ82ζ+2ζ22ζ5+2ζ72ζ+2ζ52ζ7+2ζ82ζ2+2ζ42ζ22ζ52ζ82ζ72ζ42ζ000000000000000
χ4066-3-3-200-22111−1−2i3−1+2i32ζ4+2ζ52ζ+2ζ82ζ2+2ζ72ζ+2ζ22ζ5+2ζ72ζ4+2ζ82ζ7+2ζ82ζ2+2ζ42ζ+2ζ52ζ52ζ82ζ22ζ42ζ2ζ7000000000000000
χ418-88-80-4400000000000000000000000022-2-2-1-11100000
χ428-88-80-44000000000000000000000000−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i3200000
χ438-88-80-44000000000000000000000000−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i3200000
χ4424-24-12120000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.