Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | D5×C71⋊C49 |
| unambiguous semidirect product | C5⋊(C2×C71⋊C49) |
| unambiguous semidirect product | (D5×C71)⋊C49 |
| derived, Hall | C5×C71 ⋊ C2×C49 |
| Hall | C5×C71⋊C49 ⋊ C2 |
| Hall | D5×C71 ⋊ C49 |
| Sylow | C71 ⋊ D5×C49 |
| Sylow | C5 ⋊ C2×C71⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | D5×C71⋊C7 |
| commutator, hypocenter | C5×C71 | C2×C49 |
| Fitting, socle, cosocle | C5×C7×C71 | C2×C7 |
| prime radical | C7×D5×C71 | C7 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17395 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 13);