Finite Group DatabasebetaFinite Group Databasebeta| order | 19350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D25×C43⋊C9 |
| unambiguous semidirect product | C25⋊(C2×C43⋊C9) |
| unambiguous semidirect product | (C43×D25)⋊C9 |
| derived, Hall | C25×C43 ⋊ C2×C9 |
| Hall | C25×C43⋊C9 ⋊ C2 |
| Hall | C43×D25 ⋊ C9 |
| Sylow | C43 ⋊ C9×D25 |
| Sylow | C25 ⋊ C2×C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×C43⋊C3 |
| commutator, hypocenter | C25×C43 | C2×C9 |
| Frattini | C3×C5 | D5×C43⋊C3 |
| Fitting, cosocle | C3×C25×C43 | C2×C3 |
| socle | C3×C5×C43 | C3×D5 |
| prime radical | C3×C43×D25 | C3 |
| LCS | G ▷ C25×C43 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9675 |
714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19350, 3);