Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊Dic9 |
| unambiguous semidirect product | Dic387⋊C7 |
| derived, Hall | C9×C43 ⋊ C4×C7 |
| Hall | C9×C43⋊C7 ⋊ C4 |
| Hall | Dic387 ⋊ C7 |
| Hall | C43⋊C7 ⋊ Dic9 |
| Sylow | C43 ⋊ C7×Dic9 |
| Sylow | C9 ⋊ Dic43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊(D43⋊C7) |
| commutator, hypocenter | C9×C43 | C4×C7 |
| Frattini | C2×C3 | C3⋊(D43⋊C7) |
| Fitting, cosocle | C2×C9×C43 | C2×C7 |
| socle | C2×C3×C43 | D3×C7 |
| prime radical | C2×C3×C43⋊C7 | D3 |
| LCS | G ▷ C9×C43 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,3,43,2,3|a^2=e,c^3=f^2,c^a=c^2f,d^a=d^42,f^a=f^2,d^b=d^35138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 6);