Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D477 |
| unambiguous semidirect product | C9⋊(C25×D53) |
| unambiguous semidirect product | C53⋊(D9×C25) |
| Fitting, Hall | C9×C25×C53 ⋊ C2 |
| derived, Hall | C9×C53 ⋊ C2×C25 |
| Hall | C25×C53 ⋊ D9 |
| Hall | C9×C25 ⋊ D53 |
| Sylow | C53 ⋊ D9×C25 |
| Sylow | C9 ⋊ C25×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D477 |
| commutator, hypocenter | C9×C53 | C2×C25 |
| Frattini | C3×C5 | C5×D159 |
| Fitting | C9×C25×C53 | C2 |
| socle | C3×C5×C53 | C5×D3 |
| prime radical | C5×D477 | C5 |
| cosocle | C5×C9×C53 | C2×C5 |
| LCS | G ▷ C9×C53 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11925 |
6000 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 6);