Finite Group DatabasebetaFinite Group Databasebeta| order | 10686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D137 |
| unambiguous semidirect product | C137⋊(C2×C13⋊C3) |
| unambiguous semidirect product | (C13×D137)⋊C3 |
| Fitting, socle, derived, Hall | C13×C137 ⋊ C2×C3 |
| Hall | C13⋊C3×C137 ⋊ C2 |
| Hall | C13×D137 ⋊ C3 |
| Sylow | C137 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ C3×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C137 | C2×C3 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10686, 10);