Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D585 |
| unambiguous semidirect product | C5⋊(C5×D117) |
| unambiguous semidirect product | C9⋊(C5×D65) |
| unambiguous semidirect product | C13⋊(C5×D45) |
| Fitting, Hall | C52×C9×C13 ⋊ C2 |
| derived | C5×C9×C13 ⋊ C2×C5 |
| Hall | C52×C13 ⋊ D9 |
| Hall | C52×C9 ⋊ D13 |
| Hall | C9×C13 ⋊ C5×D5 |
| Sylow | C52 ⋊ D117 |
| Sylow | C13 ⋊ C5×D45 |
| Sylow | C9 ⋊ C5×D65 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D585 |
| commutator, hypocenter | C5×C9×C13 | C2×C5 |
| Frattini | C3 | C5×D195 |
| Fitting | C52×C9×C13 | C2 |
| socle | C3×C52×C13 | D3 |
| LCS | G ▷ C5×C9×C13 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
1470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D45, C5×D5×D117, C5×D9×D65, … |
| maximal normal subgroup of | C5×D13×D45, C5×D5×D117, C5×D9×D65, … |
| maximal quotient of | C5×Dic585, C2×C5×D585 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 58);