Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(Dic61⋊C9) |
| unambiguous semidirect product | Dic671⋊C9 |
| derived, Hall | C11×C61 ⋊ C4×C9 |
| Hall | C11×C61⋊C9 ⋊ C4 |
| Hall | Dic671 ⋊ C9 |
| Hall | C61⋊C9 ⋊ Dic11 |
| Sylow | C61 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ Dic61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C11⋊(D61⋊C3) |
| commutator, hypocenter | C11×C61 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C11×C61 | C2×C3 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24156 |
Polycyclic presentation:
2,3,11,61,2,3|a^2=e,b^3=f,c^a=c^10,d^a=d^60,d^b=d^47786 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 12);