Finite Group DatabasebetaFinite Group Databasebeta| order | 5838 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#15668589 |
| Fitting, socle, Hall | C2×C7×C139 ⋊ C3 |
| derived, Hall | C7×C139 ⋊ C2×C3 |
| Hall | C2×C139 ⋊ ΓL(1,𝔽8) |
| Sylow | C139 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C139⋊C3 |
| Sylow | C7 ⋊ C2×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #15668589 |
| commutator, hypocenter | C7×C139 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C139 | C3 |
| LCS | G ▷ C7×C139 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
654 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15668589, #26043014, #26043018, … |
| maximal normal subgroup of | C4×#15668589, #26043014, #26043018, … |
| maximal quotient of | C4×#15668589, C22×#15668589, C2×#22576805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5838, 4);