Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×D3×C9 |
| unambiguous semidirect product | C3⋊(C2×C52×C9) |
| Fitting, Hall | C3×C52×C9 ⋊ C2 |
| derived | C3 ⋊ C2×C52×C9 |
| Sylow | C3×C9 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C9 | D3 |
| commutator, hypocenter | C3 | C2×C52×C9 |
| Frattini | C3 | C3×C52×D3 |
| Fitting | C3×C52×C9 | C2 |
| socle | C32×C52 | C2×C3 |
| prime radical | C3×C52×D3 | C3 |
| cosocle | C32 | C2×C3×C52 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C52×C9 | |
112 conjugacy classes of subgroups.
| 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, 72);