Finite Group DatabasebetaFinite Group Databasebeta| order | 34790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D71⋊C49) |
| unambiguous semidirect product | D355⋊C49 |
| unambiguous semidirect product | (C71⋊C49)⋊D5 |
| derived, Hall | C5×C71 ⋊ C2×C49 |
| Hall | C5×C71⋊C49 ⋊ C2 |
| Hall | C71⋊C49 ⋊ D5 |
| Hall | D355 ⋊ C49 |
| Sylow | C71 ⋊ D5×C49 |
| Sylow | C5 ⋊ D71⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C5⋊(D71⋊C7) |
| commutator, hypocenter | C5×C71 | C2×C49 |
| Fitting, socle, cosocle | C5×C7×C71 | C2×C7 |
| prime radical | C7×D355 | C7 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17395 |
Polycyclic presentation:
2,5,7,71,7|c^7=e,b^a=b^4,d^a=d^70,d^c=d^45371 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34790, 14);