Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C43⋊C7)⋊C9) |
| unambiguous semidirect product | (C43⋊C7)⋊(C22⋊C9) |
| unambiguous semidirect product | (C22⋊(C43⋊C9))⋊C7 |
| derived, Hall | C22×C43 ⋊ C7×C9 |
| Hall | C22⋊(C43⋊C9) ⋊ C7 |
| Hall | C22×C43⋊C7 ⋊ C9 |
| Hall | C43⋊C7 ⋊ C22⋊C9 |
| Sylow | C43 ⋊ C7×C22⋊C9 |
| Sylow | C22 ⋊ (C43⋊C7)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C43⋊C3)⋊C7) |
| commutator, hypocenter | C22×C43 | C7×C9 |
| Fitting, socle, cosocle | C22×C3×C43 | C3×C7 |
| prime radical | C22×C3×C43⋊C7 | C3 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,2^2,43,3|a^3=f,c^a=d,d^a=cd,e^a=e^36,e^b=e^41108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 35);