Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | D53×C52⋊C9 |
| unambiguous semidirect product | C53⋊(C2×C52⋊C9) |
| unambiguous semidirect product | (C52×D53)⋊C9 |
| derived, Hall | C52×C53 ⋊ C2×C9 |
| Hall | C53×C52⋊C9 ⋊ C2 |
| Hall | C52×D53 ⋊ C9 |
| Sylow | C53 ⋊ C2×C52⋊C9 |
| Sylow | C52 ⋊ C9×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊C3×D53 |
| commutator, hypocenter | C52×C53 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C53 | C2×C3 |
| prime radical | C3×C52×D53 | C3 |
| LCS | G ▷ C52×C53 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2385 |
924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 26);