Finite Group DatabasebetaFinite Group Databasebeta| order | 10934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D71⋊C7 |
| unambiguous semidirect product | D71⋊(C7×C11) |
| unambiguous semidirect product | (C71⋊C7)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D71)⋊C7 |
| Fitting, socle, Hall | C11×C71 ⋊ C2×C7 |
| derived, Sylow | C71 ⋊ C2×C7×C11 |
| Hall | C11×C71⋊C7 ⋊ C2 |
| Hall | C11×D71 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C11 |
| Hall | D71 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
209 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D71⋊C7, C2×C11×D71⋊C7, C3×C11×D71⋊C7, … |
| maximal normal subgroup of | D11×D71⋊C7, C2×C11×D71⋊C7, C3×C11×D71⋊C7 |
| maximal quotient of | C11×Dic71⋊C7, C2×C11×D71⋊C7, C3×C11×D71⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10934, 10);