Finite Group DatabasebetaFinite Group Databasebeta| order | 20826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D801 |
| unambiguous semidirect product | C9⋊(C13×D89) |
| unambiguous semidirect product | C89⋊(C13×D9) |
| Fitting, Hall | C9×C13×C89 ⋊ C2 |
| derived, Hall | C9×C89 ⋊ C2×C13 |
| Hall | C13×C89 ⋊ D9 |
| Hall | C9×C13 ⋊ D89 |
| Sylow | C89 ⋊ C13×D9 |
| Sylow | C9 ⋊ C13×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D801 |
| commutator, cosocle, hypocenter | C9×C89 | C2×C13 |
| Frattini | C3 | C13×D267 |
| Fitting | C9×C13×C89 | C2 |
| socle | C3×C13×C89 | D3 |
| LCS | G ▷ C9×C89 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10413 |
5226 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20826, 7);