Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊(#6923⋊C3)) |
| unambiguous semidirect product | C11⋊(C3⋊(#6923⋊C3)) |
| unambiguous semidirect product | (C3⋊(C11⋊#6923))⋊C3 |
| Fitting, socle, derived | C3×C11×C61 ⋊ C3×C4 |
| Hall | C3×C11×C61⋊C3 ⋊ C4 |
| Hall | C11×C61 ⋊ C3×Dic3 |
| Hall | C3×C61⋊C3 ⋊ Dic11 |
| Sylow | C61 ⋊ C3×Dic33 |
| Sylow | C11 ⋊ C3⋊(#6923⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C61 | C3×C4 |
| prime radical | C3×C11×D61⋊C3 | C2 |
| cosocle | C3×C11×D61 | C2×C3 |
| LCS | G ▷ C3×C11×C61 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2013 |
Polycyclic presentation:
2,3,2,3,11,61|a^2=c,d^a=d^2,e^a=e^10,f^a=f^50,f^b=f^13,f^c=f^60273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 67);