Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(((C43⋊C3)⋊C4)⋊C7) |
| unambiguous semidirect product | ((C43⋊C3)⋊C7)⋊Dic3 |
| unambiguous semidirect product | (C3⋊((C43⋊C3)⋊C4))⋊C7 |
| unambiguous semidirect product | (C3⋊(Dic43⋊C7))⋊C3 |
| derived | C3×C43 ⋊ C3×C4×C7 |
| Hall | C3×(C43⋊C3)⋊C7 ⋊ C4 |
| Hall | C3⋊((C43⋊C3)⋊C4) ⋊ C7 |
| Hall | C3×C43⋊C3 ⋊ C4×C7 |
| Hall | C43⋊C7 ⋊ C3×Dic3 |
| Sylow | C43 ⋊ C3×C7×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊AGL(1,𝔽43) |
| commutator, hypocenter | C3×C43 | C3×C4×C7 |
| Fitting, socle, cosocle | C2×C3×C43 | C2×C3×C7 |
| prime radical | C2×C3×(C43⋊C3)⋊C7 | C2 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,3,43,2|a^2=f,d^a=d^2,e^a=e^42,e^b=e^36,e^c=e^41132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 82);