Finite Group DatabasebetaFinite Group Databasebeta| order | 5838 |
| isoclinism | isoclinic class of D139 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D139 |
| Fitting, socle, Hall | C3×C7×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C2×C3×C7 |
| Hall | C7×C139 ⋊ C2×C3 |
| Hall | C3×C139 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D139 |
| commutator, hypocenter | C139 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C3×C7 | |
16 conjugacy classes of subgroups.
1491 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D139, D3×C7×D139, D21×D139, … |
| maximal normal subgroup of | C3×D7×D139, D3×C7×D139, D21×D139, … |
| maximal quotient of | C3×C7×Dic139, C2×C3×C7×D139, C7×C9×D139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5838, 6);