Finite Group DatabasebetaFinite Group Databasebeta| order | 10842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D417 |
| unambiguous semidirect product | C3⋊(C13×D139) |
| unambiguous semidirect product | C139⋊(D3×C13) |
| Fitting, socle, Hall | C3×C13×C139 ⋊ C2 |
| derived, Hall | C3×C139 ⋊ C2×C13 |
| Hall | C13×C139 ⋊ D3 |
| Sylow | C139 ⋊ D3×C13 |
| Hall | C3×C13 ⋊ D139 |
| Sylow | C3 ⋊ C13×D139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D417 |
| commutator, cosocle, hypocenter | C3×C139 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C139 | C2 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
2730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D139, D13×D417, D39⋊D139, … |
| maximal normal subgroup of | D3×C13×D139, D13×D417, D39⋊D139, … |
| maximal quotient of | C13×Dic417, C2×C13×D417, C13×D1251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10842, 10);