Finite Group DatabasebetaFinite Group Databasebeta| order | 24244 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C29×D209 |
| unambiguous semidirect product | (C2×C11)⋊(C29×D19) |
| unambiguous semidirect product | (C2×C19)⋊(D11×C29) |
| Fitting, socle | C2×C11×C19×C29 ⋊ C2 |
| derived, Hall | C11×C19 ⋊ C22×C29 |
| Hall | C11×C19×C29 ⋊ C22 |
| Hall | C19×C29 ⋊ C2×D11 |
| Hall | C11×C29 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D11×C29 |
| Sylow | C11 ⋊ C2×C29×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | D209 |
| commutator, cosocle, hypocenter | C11×C19 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C19×C29 | C2 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C29 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12122 |
6148 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24244, 26);