Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C13⋊C3×C5⋊D5 |
| unambiguous semidirect product | C5⋊(C3×D5×C13⋊C3) |
| Fitting, socle | C3×C52×C13 ⋊ C2×C3 |
| derived, Hall | C52×C13 ⋊ C2×C32 |
| Hall | C3×C52×C13⋊C3 ⋊ C2 |
| Hall | C13×C5⋊D5 ⋊ C32 |
| Sylow | C52 ⋊ C2×C3×C13⋊C3 |
| Sylow | C13 ⋊ C32×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C13⋊C3×C5⋊D5 |
| commutator, hypocenter | C52×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C3 | |
192 conjugacy classes of subgroups.
294 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16839083, C3×C13⋊C3×#1043, C3×#13049932⋊C3, … |
| maximal normal subgroup of | C3×#16839083, C3×C13⋊C3×#1043, C3×#13049932⋊C3, … |
| maximal quotient of | C3×C13⋊C3×#1039, C2×C3×C13⋊C3×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 72);