Finite Group DatabasebetaFinite Group Databasebeta| order | 24854 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D43×C289 |
| unambiguous semidirect product | C43⋊(C2×C289) |
| Fitting, Hall | C43×C289 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D43 |
| commutator, hypocenter | C43 | C2×C289 |
| Frattini | C17 | C17×D43 |
| Fitting | C43×C289 | C2 |
| socle, cosocle | C17×C43 | C2×C17 |
| prime radical | C17×D43 | C17 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12427 |
6647 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24854, 3);