Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | D3×C9×C25 |
| unambiguous semidirect product | C3⋊(C2×C9×C25) |
| Fitting, Hall | C3×C9×C25 ⋊ C2 |
| derived | C3 ⋊ C2×C9×C25 |
| Sylow | C3×C9 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C25 | D3 |
| commutator, hypocenter | C3 | C2×C9×C25 |
| Frattini | C3×C5 | C3×C5×D3 |
| Fitting | C3×C9×C25 | C2 |
| socle, cosocle | C32×C5 | C2×C3×C5 |
| prime radical | C3×C5×D3 | C3×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C9×C25 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 450 |
675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 9);