Finite Group DatabasebetaFinite Group Databasebeta| order | 35055 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | #4294×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×#4294) |
| unambiguous semidirect product | (C41×#4294)⋊C5 |
| derived, Hall | C19×C41 ⋊ C5×C9 |
| Hall | C41×#4294 ⋊ C5 |
| Hall | C19×C41⋊C5 ⋊ C9 |
| Sylow | C41 ⋊ C5×#4294 |
| Sylow | C19 ⋊ C9×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×C41⋊C5 |
| commutator, hypocenter | C19×C41 | C5×C9 |
| Fitting, socle, cosocle | C3×C19×C41 | C3×C5 |
| prime radical | C3×C19×C41⋊C5 | C3 |
| LCS | G ▷ C19×C41 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7011 |
351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35055, 4);