Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(C11⋊#6923)) |
| unambiguous semidirect product | C11⋊(C3⋊(C3⋊#6923)) |
| Fitting, socle, derived, Hall | C32×C11×C61 ⋊ C4 |
| Hall | C11×C61 ⋊ C3⋊Dic3 |
| Hall | C32×C61 ⋊ Dic11 |
| Hall | C32×C11 ⋊ #6923 |
| Sylow | C61 ⋊ C3⋊Dic33 |
| Sylow | C11 ⋊ C3⋊(C3⋊#6923) |
| Sylow | C32 ⋊ C11⋊#6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C11×C61 | C4 |
| prime radical, cosocle | C32×C11×D61 | C2 |
| LCS | G ▷ C32×C11×C61 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
Polycyclic presentation:
2^2,3^2,11,61|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^50,f^b=f^601587 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 110);