Finite Group DatabasebetaFinite Group Databasebeta| order | 35090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3509 |
| unambiguous semidirect product | C29⋊(C5×D121) |
| Fitting, Hall | C5×C29×C121 ⋊ C2 |
| derived, Hall | C29×C121 ⋊ C2×C5 |
| Hall | C5×C121 ⋊ D29 |
| Hall | C5×C29 ⋊ D121 |
| Sylow | C121 ⋊ C5×D29 |
| Sylow | C29 ⋊ C5×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3509 |
| commutator, cosocle, hypocenter | C29×C121 | C2×C5 |
| Frattini | C11 | C5×D319 |
| Fitting | C5×C29×C121 | C2 |
| socle | C5×C11×C29 | D11 |
| LCS | G ▷ C29×C121 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17545 |
8780 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35090, 5);