Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16813406 |
| derived | C3×C7×C43 ⋊ C3×C4 |
| Hall | C3×#11744748 ⋊ C4 |
| Hall | C7×C43 ⋊ C3×Dic3 |
| Sylow | C43 ⋊ C3⋊(ΓL(1,𝔽8)⋊C4) |
| Sylow | C7 ⋊ C3⋊((C43⋊C3)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#14268593 |
| commutator, hypocenter | C3×C7×C43 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C7×C43 | C2×C3 |
| prime radical | C2×C3×#11744748 | C2 |
| LCS | G ▷ C3×C7×C43 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,43,2|a^2=f,c^a=c^2,d^a=d^6,e^a=e^42,d^b=d^2,e^b=e^6318 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 111);