Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D671 |
| unambiguous semidirect product | (D3×C11)⋊(C3×D61) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C22 |
| derived | C3×C11×C61 ⋊ C22×C3 |
| Hall | C11×C61 ⋊ C2×C3×D3 |
| Hall | C32×C61 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D61 |
| Sylow | C61 ⋊ C3×D3×D11 |
| Sylow | C11 ⋊ C3×D3×D61 |
| Sylow | C32 ⋊ C2×D671 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D671 |
| commutator, cosocle, hypocenter | C3×C11×C61 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C22 |
| LCS | G ▷ C3×C11×C61 | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4026 |
3033 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 96);