Finite Group DatabasebetaFinite Group Databasebeta| order | 34916 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic29⋊C7 |
| unambiguous semidirect product | Dic29⋊(C7×C43) |
| derived, Sylow | C29 ⋊ C4×C7×C43 |
| Hall | C43×C29⋊C7 ⋊ C4 |
| Hall | C43×Dic29 ⋊ C7 |
| Hall | C29×C43 ⋊ C4×C7 |
| Hall | C29⋊C7 ⋊ C4×C43 |
| Hall | Dic29 ⋊ C7×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D29⋊C7 |
| commutator, hypocenter | C29 | C4×C7×C43 |
| Frattini | C2 | C43×D29⋊C7 |
| Fitting, socle | C2×C29×C43 | C2×C7 |
| prime radical | C2×C43×C29⋊C7 | C2 |
| cosocle | C2×C29 | C2×C7×C43 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4988 |
1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34916, 26);