Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D75 |
| unambiguous semidirect product | C3⋊(C9×D25) |
| unambiguous semidirect product | C25⋊(D3×C9) |
| Fitting, Hall | C3×C9×C25 ⋊ C2 |
| derived | C3×C25 ⋊ C2×C9 |
| Sylow | C3×C9 ⋊ D25 |
| Sylow | C25 ⋊ D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D75 |
| commutator, hypocenter | C3×C25 | C2×C9 |
| Frattini | C3×C5 | C3×D15 |
| Fitting | C3×C9×C25 | C2 |
| socle | C32×C5 | C3×D5 |
| prime radical | C3×D75 | C3 |
| cosocle | C32×C25 | C2×C3 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C9 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 450 |
351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 12);