Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C11⋊(#6923⋊C3) |
| unambiguous semidirect product | C11⋊(C3×#6923⋊C3) |
| unambiguous semidirect product | (C11⋊#6923)⋊C32 |
| unambiguous semidirect product | (C3×C11⋊#6923)⋊C3 |
| Fitting, socle | C3×C11×C61 ⋊ C3×C4 |
| derived, Hall | C11×C61 ⋊ C32×C4 |
| Hall | C3×C11×C61⋊C3 ⋊ C4 |
| Hall | C11⋊#6923 ⋊ C32 |
| Hall | C3×C61⋊C3 ⋊ Dic11 |
| Sylow | C61 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ C3×#6923⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊(#6923⋊C3) |
| commutator, hypocenter | C11×C61 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C3×C4 |
| prime radical | C3×C11×D61⋊C3 | C2 |
| cosocle | C11×D61 | C2×C32 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2013 |
291 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 63);