Finite Group DatabasebetaFinite Group Databasebeta| order | 34342 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1561 |
| unambiguous semidirect product | C7⋊(C11×D223) |
| unambiguous semidirect product | C223⋊(C11×D7) |
| Fitting, socle, Hall | C7×C11×C223 ⋊ C2 |
| derived, Hall | C7×C223 ⋊ C2×C11 |
| Hall | C11×C223 ⋊ D7 |
| Sylow | C223 ⋊ C11×D7 |
| Hall | C7×C11 ⋊ D223 |
| Sylow | C7 ⋊ C11×D223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1561 |
| commutator, cosocle, hypocenter | C7×C223 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C223 | C2 |
| LCS | G ▷ C7×C223 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17171 |
8602 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34342, 6);