Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×C3⋊(C5⋊D65) |
| unambiguous semidirect product | C3⋊(C3×C5⋊D65) |
| unambiguous semidirect product | C5⋊(C3×D195) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C2 |
| derived | C3×C52×C13 ⋊ C2×C3 |
| Hall | C52×C13 ⋊ C3×D3 |
| Hall | C32×C52 ⋊ D13 |
| Hall | C32×C13 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3×C3⋊(C5⋊D5) |
| Sylow | C32 ⋊ C5⋊D65 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C5⋊D65) |
| commutator, hypocenter | C3×C52×C13 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C2 |
| LCS | G ▷ C3×C52×C13 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
1467 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×C3⋊(C5⋊D5), C3×C5⋊D5×D39, C3×D3×C5⋊D65, … |
| maximal normal subgroup of | C3×D13×C3⋊(C5⋊D5), C3×C5⋊D5×D39, C3×D3×C5⋊D65, … |
| maximal quotient of | C3×C3⋊#13049918, C2×C3×C3⋊(C5⋊D65) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 110);