Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C3 |
| direct product | C61×C11⋊#157 |
| unambiguous semidirect product | C11⋊(#157×C61) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C4 |
| derived, Hall | C32×C11 ⋊ C4×C61 |
| Hall | C11×C61 ⋊ #157 |
| Hall | C32×C61 ⋊ Dic11 |
| Sylow | C11 ⋊ #157×C61 |
| Sylow | C32 ⋊ Dic11×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C11⋊#157 |
| commutator, hypocenter | C32×C11 | C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C4 |
| prime radical | C11×C3⋊D3×C61 | C2 |
| cosocle | C11×C3⋊D3 | C2×C61 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C61 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4026 |
2196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 84);