Finite Group DatabasebetaFinite Group Databasebeta| order | 24244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C19⋊#1181) |
| unambiguous semidirect product | C19⋊(C11⋊#1181) |
| Fitting, socle, derived, Hall | C11×C19×C29 ⋊ C4 |
| Hall | C19×C29 ⋊ Dic11 |
| Hall | C11×C29 ⋊ Dic19 |
| Hall | C11×C19 ⋊ #1181 |
| Sylow | C29 ⋊ Dic209 |
| Sylow | C19 ⋊ C11⋊#1181 |
| Sylow | C11 ⋊ C19⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C19×C29 | C4 |
| prime radical, cosocle | C11×C19×D29 | C2 |
| LCS | G ▷ C11×C19×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6061 |
Polycyclic presentation:
2^2,11,19,29|a^2=b,c^a=c^10,d^a=d^18,e^a=e^17,e^b=e^281675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24244, 15);