Finite Group DatabasebetaFinite Group Databasebeta| order | 34916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C4×#22576612 |
| Fitting, Hall | C4×C29×C43 ⋊ C7 |
| derived, Hall | C29×C43 ⋊ C4×C7 |
| Hall | C4×C43 ⋊ C29⋊C7 |
| Hall | C4×C29 ⋊ C43⋊C7 |
| Sylow | C43 ⋊ C4×C29⋊C7 |
| Sylow | C29 ⋊ C4×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22576612 |
| commutator, hypocenter | C29×C43 | C4×C7 |
| Frattini | C2 | C2×#22576612 |
| Fitting | C4×C29×C43 | C7 |
| socle, cosocle | C2×C29×C43 | C2×C7 |
| prime radical | C2×#22576612 | C2 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4988 |
740 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34916, 5);