Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×A4×C43⋊C7 |
| unambiguous semidirect product | C22⋊(C32×C43⋊C7) |
| unambiguous semidirect product | (C22×C3)⋊(C3×C43⋊C7) |
| unambiguous semidirect product | (C3×A4×C43)⋊C7 |
| Fitting, socle | C22×C3×C43 ⋊ C3×C7 |
| derived, Hall | C22×C43 ⋊ C32×C7 |
| Hall | C3×A4×C43 ⋊ C7 |
| Hall | C22×C43⋊C7 ⋊ C32 |
| Sylow | C43 ⋊ C3×C7×A4 |
| Sylow | C22 ⋊ C32×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×C43⋊C7 |
| commutator, cosocle, hypocenter | C22×C43 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C43 | C3×C7 |
| LCS | G ▷ C22×C43 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 154);