Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊(C3⋊#6923) |
| unambiguous semidirect product | C3⋊(C11×C3⋊#6923) |
| Fitting, socle, Hall | C32×C11×C61 ⋊ C4 |
| derived, Hall | C32×C61 ⋊ C4×C11 |
| Hall | C11×C61 ⋊ C3⋊Dic3 |
| Hall | C32×C11 ⋊ #6923 |
| Sylow | C61 ⋊ C11×C3⋊Dic3 |
| Sylow | C32 ⋊ C11×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C3⋊#6923) |
| commutator, hypocenter | C32×C61 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C61 | C4 |
| prime radical | C32×C11×D61 | C2 |
| cosocle | C32×D61 | C2×C11 |
| LCS | G ▷ C32×C61 | |
| UCS | C1 ◁ C11 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
1617 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 108);