Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C11⋊#6923 |
| unambiguous semidirect product | C11⋊(C32×#6923) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C4 |
| derived, Hall | C11×C61 ⋊ C32×C4 |
| Hall | C32×C61 ⋊ Dic11 |
| Hall | C32×C11 ⋊ #6923 |
| Sylow | C61 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C32×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C11⋊#6923 |
| commutator, hypocenter | C11×C61 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C4 |
| prime radical | C32×C11×D61 | C2 |
| cosocle | C11×D61 | C2×C32 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
1611 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 88);