Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D325 |
| unambiguous semidirect product | C25⋊(C32×D13) |
| Fitting, Hall | C32×C13×C25 ⋊ C2 |
| derived, Hall | C13×C25 ⋊ C2×C32 |
| Hall | C32×C25 ⋊ D13 |
| Hall | C32×C13 ⋊ D25 |
| Sylow | C25 ⋊ C32×D13 |
| Sylow | C13 ⋊ C32×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D325 |
| commutator, hypocenter | C13×C25 | C2×C32 |
| Frattini | C5 | C32×D65 |
| Fitting | C32×C13×C25 | C2 |
| socle | C32×C5×C13 | D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
1476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#13049908, C32×#13049907, C32×D13×D25, … |
| maximal normal subgroup of | C32×#13049908, C32×#13049907, C32×D13×D25, … |
| maximal quotient of | C32×Dic325, C2×C32×D325 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 24);