Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic43⋊C7)⋊C9 |
| unambiguous semidirect product | (Dic43⋊C9)⋊C7 |
| unambiguous semidirect product | ((C43⋊C7)⋊C9)⋊C4 |
| derived, Sylow | C43 ⋊ C4×C7×C9 |
| Hall | (C43⋊C7)⋊C9 ⋊ C4 |
| Hall | Dic43⋊C9 ⋊ C7 |
| Hall | Dic43⋊C7 ⋊ C9 |
| Hall | C43⋊C9 ⋊ C4×C7 |
| Hall | C43⋊C7 ⋊ C4×C9 |
| Hall | Dic43 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | AGL(1,𝔽43) |
| commutator, hypocenter | C43 | C4×C7×C9 |
| Fitting, socle, cosocle | C2×C3×C43 | C2×C3×C7 |
| prime radical | C2×C3×C43⋊C7 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,43,2,3|a^2=e,b^3=f,d^a=d^42,d^b=d^6,d^c=d^35258 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 2);