Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#6923⋊C9) |
| unambiguous semidirect product | (C11⋊#6923)⋊C9 |
| derived, Hall | C11×C61 ⋊ C4×C9 |
| Hall | C11×C61⋊C9 ⋊ C4 |
| Hall | C11⋊#6923 ⋊ C9 |
| Hall | C61⋊C9 ⋊ Dic11 |
| Sylow | C61 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ #6923⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊(#6923⋊C3) |
| commutator, hypocenter | C11×C61 | C4×C9 |
| Fitting, socle | C3×C11×C61 | C3×C4 |
| prime radical, cosocle | C3×C11×D61 | C2×C3 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
Polycyclic presentation:
2,3,2,11,61,3|a^2=c,b^3=f,d^a=d^10,e^a=e^50,e^b=e^13,e^c=e^60291 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 15);