Finite Group DatabasebetaFinite Group Databasebeta| order | 21186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D963 |
| unambiguous semidirect product | C9⋊(C11×D107) |
| unambiguous semidirect product | C107⋊(C11×D9) |
| Fitting, Hall | C9×C11×C107 ⋊ C2 |
| derived, Hall | C9×C107 ⋊ C2×C11 |
| Hall | C11×C107 ⋊ D9 |
| Sylow | C107 ⋊ C11×D9 |
| Hall | C9×C11 ⋊ D107 |
| Sylow | C9 ⋊ C11×D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D963 |
| commutator, cosocle, hypocenter | C9×C107 | C2×C11 |
| Frattini | C3 | C11×D321 |
| Fitting | C9×C11×C107 | C2 |
| socle | C3×C11×C107 | D3 |
| LCS | G ▷ C9×C107 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10593 |
5313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21186, 6);