Finite Group DatabasebetaFinite Group Databasebeta| order | 29450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D589 |
| unambiguous semidirect product | C19⋊(C25×D31) |
| Fitting, Hall | C19×C25×C31 ⋊ C2 |
| derived, Hall | C19×C31 ⋊ C2×C25 |
| Hall | C25×C31 ⋊ D19 |
| Hall | C19×C25 ⋊ D31 |
| Sylow | C31 ⋊ C25×D19 |
| Sylow | C19 ⋊ C25×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D589 |
| commutator, hypocenter | C19×C31 | C2×C25 |
| Frattini | C5 | C5×D589 |
| Fitting | C19×C25×C31 | C2 |
| socle, cosocle | C5×C19×C31 | C2×C5 |
| prime radical | C5×D589 | C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14725 |
7400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29450, 5);