Finite Group DatabasebetaFinite Group Databasebeta| order | 29450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C25 · Schur multiplier (H2) = C1 |
| direct product | C19×D31⋊C25 |
| unambiguous semidirect product | D31⋊(C19×C25) |
| unambiguous semidirect product | (C31⋊C25)⋊(C2×C19) |
| unambiguous semidirect product | (C19×D31)⋊C25 |
| derived, Sylow | C31 ⋊ C2×C19×C25 |
| Hall | C19×C31⋊C25 ⋊ C2 |
| Hall | C19×D31 ⋊ C25 |
| Hall | C31⋊C25 ⋊ C2×C19 |
| Hall | C19×C31 ⋊ C2×C25 |
| Hall | D31 ⋊ C19×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | D31⋊C5 |
| commutator, hypocenter | C31 | C2×C19×C25 |
| Frattini | C5 | C19×D31⋊C5 |
| Fitting, socle | C5×C19×C31 | C2×C5 |
| prime radical | C5×C19×D31 | C5 |
| cosocle | C5×C31 | C2×C5×C19 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14725 |
1235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29450, 10);