Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C5⋊D65 |
| unambiguous semidirect product | C5⋊(C32×D65) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C2 |
| derived, Hall | C52×C13 ⋊ C2×C32 |
| Hall | C32×C52 ⋊ D13 |
| Hall | C32×C13 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C32×D13 |
| Sylow | C13 ⋊ C32×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C5⋊D65 |
| commutator, hypocenter | C52×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C2 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C32 | |
192 conjugacy classes of subgroups.
1476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#13049928, C32×#13049927, C32×#13049931, … |
| maximal normal subgroup of | C32×#13049928, C32×#13049927, C32×#13049931, … |
| maximal quotient of | C32×#13049918, C2×C32×C5⋊D65 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 104);