Finite Group DatabasebetaFinite Group Databasebeta| order | 24244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D11×D551 |
| unambiguous semidirect product | (C19×D11)⋊D29 |
| unambiguous semidirect product | (D11×C29)⋊D19 |
| Fitting, socle, derived, Hall | C11×C19×C29 ⋊ C22 |
| Hall | C19×C29 ⋊ C2×D11 |
| Hall | C11×C29 ⋊ C2×D19 |
| Hall | C11×C19 ⋊ C2×D29 |
| Sylow | C29 ⋊ D11×D19 |
| Sylow | C19 ⋊ D11×D29 |
| Sylow | C11 ⋊ C2×D551 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C19×C29 | C22 |
| LCS | G ▷ C11×C19×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6061 |
1939 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24244, 19);