Finite Group DatabasebetaFinite Group Databasebeta| order | 22446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D261 |
| unambiguous semidirect product | C9⋊(C43×D29) |
| unambiguous semidirect product | C29⋊(D9×C43) |
| Fitting, Hall | C9×C29×C43 ⋊ C2 |
| derived, Hall | C9×C29 ⋊ C2×C43 |
| Hall | C29×C43 ⋊ D9 |
| Hall | C9×C43 ⋊ D29 |
| Sylow | C29 ⋊ D9×C43 |
| Sylow | C9 ⋊ C43×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D261 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C43 |
| Frattini | C3 | C43×D87 |
| Fitting | C9×C29×C43 | C2 |
| socle | C3×C29×C43 | D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11223 |
5676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22446, 8);