Finite Group DatabasebetaFinite Group Databasebeta| order | 10686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1781 |
| unambiguous semidirect product | C137⋊(C3×D13) |
| Fitting, socle, Hall | C3×C13×C137 ⋊ C2 |
| derived, Hall | C13×C137 ⋊ C2×C3 |
| Hall | C3×C137 ⋊ D13 |
| Sylow | C137 ⋊ C3×D13 |
| Hall | C3×C13 ⋊ D137 |
| Sylow | C13 ⋊ C3×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1781 |
| commutator, cosocle, hypocenter | C13×C137 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C137 | C2 |
| LCS | G ▷ C13×C137 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2676 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20297117, C3×#20297118, C3×D13×D137, … |
| maximal normal subgroup of | C3×#20297117, C3×#20297118, C3×D13×D137, … |
| maximal quotient of | C3×Dic1781, C2×C3×D1781, C9×D1781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10686, 5);