Finite Group DatabasebetaFinite Group Databasebeta| order | 10686 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C137 · Schur multiplier (H2) = C1 |
| direct product | D3×C13×C137 |
| unambiguous semidirect product | C3⋊(C2×C13×C137) |
| Fitting, socle, Hall | C3×C13×C137 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C13×C137 |
| Hall | C3×C137 ⋊ C2×C13 |
| Hall | C3×C13 ⋊ C2×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C137 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C13×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C137 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C13×C137 | |
16 conjugacy classes of subgroups.
5343 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D137, D3×D13×C137, D3×D1781, … |
| maximal normal subgroup of | D3×C13×D137, D3×D13×C137, D3×D1781, … |
| maximal quotient of | Dic3×C13×C137, C2×D3×C13×C137, C13×D9×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10686, 6);