Finite Group DatabasebetaFinite Group Databasebeta| order | 21868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | Dic11×C71⋊C7 |
| unambiguous semidirect product | C11⋊(C4×C71⋊C7) |
| unambiguous semidirect product | (Dic11×C71)⋊C7 |
| derived, Hall | C11×C71 ⋊ C4×C7 |
| Hall | C11×C71⋊C7 ⋊ C4 |
| Hall | Dic11×C71 ⋊ C7 |
| Sylow | C71 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ C4×C71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D11×C71⋊C7 |
| commutator, hypocenter | C11×C71 | C4×C7 |
| Fitting, socle, cosocle | C2×C11×C71 | C2×C7 |
| prime radical | C2×C11×C71⋊C7 | C2 |
| LCS | G ▷ C11×C71 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3124 |
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21868, 11);