Finite Group DatabasebetaFinite Group Databasebeta| order | 6021 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C223⋊C27 |
| derived, Sylow | C223 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C223⋊C3 |
| commutator, hypocenter | C223 | C27 |
| Fitting | C9×C223 | C3 |
| socle | C3×C223 | C9 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3^3,223|a^3=b,b^3=c,d^a=d^183693 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C223⋊C3, C3×C223⋊C27, #31825584, … |
| maximal normal subgroup of | C27×C223⋊C3, C3×C223⋊C27, #31825584, … |
| maximal quotient of | C223⋊C81, C3×C223⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6021, 6);