Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D25×C13⋊C9 |
| unambiguous semidirect product | C25⋊(C2×C13⋊C9) |
| unambiguous semidirect product | (C13×D25)⋊C9 |
| derived, Hall | C13×C25 ⋊ C2×C9 |
| Hall | C25×C13⋊C9 ⋊ C2 |
| Hall | C13×D25 ⋊ C9 |
| Sylow | C25 ⋊ C2×C13⋊C9 |
| Sylow | C13 ⋊ C9×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C13⋊C3×D25 |
| commutator, hypocenter | C13×C25 | C2×C9 |
| Frattini | C3×C5 | D5×C13⋊C3 |
| Fitting | C3×C13×C25 | C2×C3 |
| socle | C3×C5×C13 | C3×D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
294 conjugacy classes — view the full character table.
| maximal subgroup of | #1035×C13⋊C9, #13049906⋊C9, D25×D13⋊C9, … |
| maximal normal subgroup of | #1035×C13⋊C9, #13049906⋊C9, D25×D13⋊C9, … |
| maximal quotient of | Dic25×C13⋊C9, C2×D25×C13⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 3);