Finite Group DatabasebetaFinite Group Databasebeta| order | 6039 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C61⋊C9 |
| unambiguous semidirect product | C61⋊(C9×C11) |
| unambiguous semidirect product | (C11×C61)⋊C9 |
| derived, Sylow | C61 ⋊ C9×C11 |
| Hall | C11×C61 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C61⋊C3 |
| commutator, hypocenter | C61 | C9×C11 |
| Frattini | C3 | C11×C61⋊C3 |
| Fitting, socle | C3×C11×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C11 | |
12 conjugacy classes of subgroups.
759 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11×C61⋊C9, C11×D61⋊C9, D11×C61⋊C9, … |
| maximal normal subgroup of | C2×C11×C61⋊C9, C11×D61⋊C9, D11×C61⋊C9, … |
| maximal quotient of | C2×C11×C61⋊C9, C11×C22⋊(C61⋊C9), C5×C11×C61⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6039, 2);