Finite Group DatabasebetaFinite Group Databasebeta| order | 34370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D491⋊C5)⋊C7 |
| unambiguous semidirect product | (D491⋊C7)⋊C5 |
| unambiguous semidirect product | ((C491⋊C5)⋊C7)⋊C2 |
| Fitting, socle, derived, Sylow | C491 ⋊ C2×C5×C7 |
| Hall | (C491⋊C5)⋊C7 ⋊ C2 |
| Hall | D491⋊C7 ⋊ C5 |
| Hall | D491⋊C5 ⋊ C7 |
| Hall | C491⋊C7 ⋊ C2×C5 |
| Hall | C491⋊C5 ⋊ C2×C7 |
| Hall | D491 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C491 | C2×C5×C7 |
| LCS | G ▷ C491 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 491 |
Polycyclic presentation:
2,5,7,491|d^a=d^490,d^b=d^381,d^c=d^13877 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34370, 18);