Finite Group DatabasebetaFinite Group Databasebeta| order | 28116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D11×D71 |
| unambiguous semidirect product | (D11×C71)⋊(C2×C9) |
| unambiguous semidirect product | (C11×D71)⋊(C2×C9) |
| unambiguous semidirect product | D781⋊(C2×C9) |
| Fitting, Hall | C9×C11×C71 ⋊ C22 |
| derived, Hall | C11×C71 ⋊ C22×C9 |
| Hall | C9×C71 ⋊ C2×D11 |
| Hall | C9×C11 ⋊ C2×D71 |
| Sylow | C71 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C2×C9×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D11×D71 |
| commutator, hypocenter | C11×C71 | C22×C9 |
| Frattini | C3 | C3×D11×D71 |
| Fitting | C9×C11×C71 | C22 |
| socle, cosocle | C3×C11×C71 | C22×C3 |
| prime radical | C3×D11×D71 | C3 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7029 |
2331 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28116, 10);