Finite Group DatabasebetaFinite Group Databasebeta| order | 34650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×C11×#90646 |
| derived, Hall | C52⋊C9 ⋊ C2×C7×C11 |
| Hall | C7×C11×C52⋊C9 ⋊ C2 |
| Hall | C11×C52⋊C9 ⋊ C2×C7 |
| Hall | C52×C7×C11 ⋊ D9 |
| Hall | C7×C52⋊C9 ⋊ C2×C11 |
| Hall | C52×C11 ⋊ C7×D9 |
| Hall | C52×C7 ⋊ C11×D9 |
| Sylow | C52 ⋊ C7×C11×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | #90646 |
| commutator, cosocle, hypocenter | C52⋊C9 | C2×C7×C11 |
| Frattini | C3 | C7×C11×#3874 |
| Fitting, socle | C3×C52×C7×C11 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C7×C11 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3465 |
1848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34650, 132);