Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C5 |
| direct product | C2×C13×C52⋊C9 |
| unambiguous semidirect product | (C2×C52)⋊(C9×C13) |
| derived, Sylow | C52 ⋊ C2×C9×C13 |
| Hall | C2×C52×C13 ⋊ C9 |
| Hall | C52×C13 ⋊ C2×C9 |
| Hall | C2×C52 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | C52⋊C3 |
| commutator, hypocenter | C52 | C2×C9×C13 |
| Frattini | C3 | C2×C13×C52⋊C3 |
| Fitting, socle | C2×C3×C52×C13 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C13 | |
40 conjugacy classes of subgroups.
858 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#11744607, #26043228, Dic13×C52⋊C9, … |
| maximal normal subgroup of | C13×#11744607, #26043228, Dic13×C52⋊C9, … |
| maximal quotient of | C4×C13×C52⋊C9, C22×C13×C52⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 48);