Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D71⋊C5 |
| unambiguous semidirect product | (C49×D71)⋊C5 |
| Fitting, Hall | C49×C71 ⋊ C2×C5 |
| derived, Sylow | C71 ⋊ C2×C5×C49 |
| Hall | C49×C71⋊C5 ⋊ C2 |
| Hall | C49×D71 ⋊ C5 |
| Hall | C71⋊C5 ⋊ C2×C49 |
| Hall | D71 ⋊ C5×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D71⋊C5 |
| commutator, hypocenter | C71 | C2×C5×C49 |
| Frattini | C7 | C7×D71⋊C5 |
| Fitting | C49×C71 | C2×C5 |
| socle, cosocle | C7×C71 | C2×C5×C7 |
| prime radical | C7×D71⋊C5 | C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3479 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 15);