Finite Group DatabasebetaFinite Group Databasebeta| order | 28116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D9×D71 |
| unambiguous semidirect product | (D9×C71)⋊(C2×C11) |
| unambiguous semidirect product | (C9×D71)⋊(C2×C11) |
| unambiguous semidirect product | D639⋊(C2×C11) |
| Fitting, Hall | C9×C11×C71 ⋊ C22 |
| derived, Hall | C9×C71 ⋊ C22×C11 |
| Hall | C11×C71 ⋊ C2×D9 |
| Hall | C9×C11 ⋊ C2×D71 |
| Sylow | C71 ⋊ C2×C11×D9 |
| Sylow | C9 ⋊ C2×C11×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D9×D71 |
| commutator, cosocle, hypocenter | C9×C71 | C22×C11 |
| Frattini | C3 | D3×C11×D71 |
| Fitting | C9×C11×C71 | C22 |
| socle | C3×C11×C71 | C2×D3 |
| LCS | G ▷ C9×C71 | |
| UCS | C1 ◁ C11 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7029 |
2442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28116, 11);