Finite Group DatabasebetaFinite Group Databasebeta| order | 20826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1157 |
| unambiguous semidirect product | C89⋊(C9×D13) |
| Fitting, Hall | C9×C13×C89 ⋊ C2 |
| derived, Hall | C13×C89 ⋊ C2×C9 |
| Hall | C9×C89 ⋊ D13 |
| Hall | C9×C13 ⋊ D89 |
| Sylow | C89 ⋊ C9×D13 |
| Sylow | C13 ⋊ C9×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1157 |
| commutator, hypocenter | C13×C89 | C2×C9 |
| Frattini | C3 | C3×D1157 |
| Fitting | C9×C13×C89 | C2 |
| socle, cosocle | C3×C13×C89 | C2×C3 |
| prime radical | C3×D1157 | C3 |
| LCS | G ▷ C13×C89 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10413 |
5220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20826, 5);