Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C5 |
| direct product | C53×C5⋊D45 |
| unambiguous semidirect product | C5⋊(C53×D45) |
| unambiguous semidirect product | C9⋊(C5⋊D5×C53) |
| Fitting, Hall | C52×C9×C53 ⋊ C2 |
| derived, Hall | C52×C9 ⋊ C2×C53 |
| Hall | C52×C53 ⋊ D9 |
| Hall | C9×C53 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D9×C53 |
| Sylow | C9 ⋊ C5⋊D5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C5⋊D45 |
| commutator, cosocle, hypocenter | C52×C9 | C2×C53 |
| Frattini | C3 | C53×C3⋊(C5⋊D5) |
| Fitting | C52×C9×C53 | C2 |
| socle | C3×C52×C53 | D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C53 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11925 |
6042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 37);