Finite Group DatabasebetaFinite Group Databasebeta| order | 34370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D491⋊C5) |
| unambiguous semidirect product | (C491⋊C5)⋊D7 |
| unambiguous semidirect product | D3437⋊C5 |
| Fitting, socle, derived, Hall | C7×C491 ⋊ C2×C5 |
| Hall | C7×C491⋊C5 ⋊ C2 |
| Hall | D3437 ⋊ C5 |
| Hall | C491⋊C5 ⋊ D7 |
| Sylow | C491 ⋊ C5×D7 |
| Sylow | C7 ⋊ D491⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C491 | C2×C5 |
| LCS | G ▷ C7×C491 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3437 |
Polycyclic presentation:
2,5,7,491|c^a=c^6,d^a=d^490,d^b=d^381368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34370, 17);