Finite Group DatabasebetaFinite Group Databasebeta| order | 10842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1807 |
| Fitting, socle, Hall | C3×C13×C139 ⋊ C2 |
| derived, Hall | C13×C139 ⋊ C2×C3 |
| Hall | C3×C139 ⋊ D13 |
| Sylow | C139 ⋊ C3×D13 |
| Hall | C3×C13 ⋊ D139 |
| Sylow | C13 ⋊ C3×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1807 |
| commutator, cosocle, hypocenter | C13×C139 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C139 | C2 |
| LCS | G ▷ C13×C139 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2715 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D139, D3×D1807, D39⋊D139, … |
| maximal normal subgroup of | C3×D13×D139, D3×D1807, D39⋊D139, … |
| maximal quotient of | C3×Dic1807, C2×C3×D1807, C9×D1807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10842, 8);