Finite Group DatabasebetaFinite Group Databasebeta| order | 10934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D497 |
| unambiguous semidirect product | C7⋊(C11×D71) |
| unambiguous semidirect product | C71⋊(C11×D7) |
| Fitting, socle, Hall | C7×C11×C71 ⋊ C2 |
| derived, Hall | C7×C71 ⋊ C2×C11 |
| Hall | C11×C71 ⋊ D7 |
| Hall | C7×C11 ⋊ D71 |
| Sylow | C71 ⋊ C11×D7 |
| Sylow | C7 ⋊ C11×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D497 |
| commutator, cosocle, hypocenter | C7×C71 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C71 | C2 |
| LCS | G ▷ C7×C71 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D7×D71, D11×D497, D77⋊D71, … |
| maximal normal subgroup of | C11×D7×D71, D11×D497, D77⋊D71, … |
| maximal quotient of | C11×Dic497, C2×C11×D497, C3×C11×D497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10934, 7);