Finite Group DatabasebetaFinite Group Databasebeta| order | 24244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C11⋊#1181 |
| unambiguous semidirect product | C11⋊(C19×#1181) |
| Fitting, socle, Hall | C11×C19×C29 ⋊ C4 |
| derived, Hall | C11×C29 ⋊ C4×C19 |
| Hall | C19×C29 ⋊ Dic11 |
| Hall | C11×C19 ⋊ #1181 |
| Sylow | C29 ⋊ C19×Dic11 |
| Sylow | C11 ⋊ C19×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C11⋊#1181 |
| commutator, hypocenter | C11×C29 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C29 | C4 |
| prime radical | C11×C19×D29 | C2 |
| cosocle | C11×D29 | C2×C19 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6061 |
1729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24244, 13);