Finite Group DatabasebetaFinite Group Databasebeta| order | 6021 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C223⋊C3 |
| unambiguous semidirect product | C223⋊C33 |
| unambiguous semidirect product | (C3×C223)⋊C32 |
| Fitting, socle | C32×C223 ⋊ C3 |
| derived, Sylow | C223 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C223⋊C3 |
| commutator, hypocenter | C223 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C223 | C3 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
693 conjugacy classes — view the full character table.
| maximal subgroup of | (C3×C223⋊C3)⋊C9, #31825587, #31825589, … |
| maximal normal subgroup of | (C3×C223⋊C3)⋊C9, #31825587, #31825589, … |
| maximal quotient of | C3×C9×C223⋊C3, C32×C223⋊C9, H(3,𝔽3)×C223⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6021, 13);