Finite Group DatabasebetaFinite Group Databasebeta| order | 34370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D491⋊C7) |
| unambiguous semidirect product | (C491⋊C7)⋊D5 |
| unambiguous semidirect product | D2455⋊C7 |
| Fitting, socle, derived, Hall | C5×C491 ⋊ C2×C7 |
| Hall | C5×C491⋊C7 ⋊ C2 |
| Hall | D2455 ⋊ C7 |
| Hall | C491⋊C7 ⋊ D5 |
| Sylow | C491 ⋊ C7×D5 |
| Sylow | C5 ⋊ D491⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C491 | C2×C7 |
| LCS | G ▷ C5×C491 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2455 |
Polycyclic presentation:
2,5,7,491|b^a=b^4,d^a=d^490,d^c=d^138203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34370, 14);