Finite Group DatabasebetaFinite Group Databasebeta| order | 23850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C53⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C53⋊(C3×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C5⋊D265)⋊C32 |
| unambiguous semidirect product | (C3×C5⋊D265)⋊C3 |
| Fitting, socle | C3×C52×C53 ⋊ C2×C3 |
| derived, Hall | C52×C53 ⋊ C2×C32 |
| Hall | C3×C53×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D265 ⋊ C32 |
| Hall | C3×C52⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C32×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C53⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C52×C53 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C53 | C2×C3 |
| LCS | G ▷ C52×C53 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2385 |
888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23850, 44);