Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×D3×C7×C9 |
| unambiguous semidirect product | C3⋊(C2×C3×C7×C9) |
| Fitting, Hall | C32×C7×C9 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C7×C9 |
| Sylow | C32×C9 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C9 | D3 |
| commutator, hypocenter | C3 | C2×C3×C7×C9 |
| Frattini | C3 | C32×D3×C7 |
| Fitting | C32×C7×C9 | C2 |
| socle | C33×C7 | C2×C3 |
| prime radical | C32×D3×C7 | C3 |
| cosocle | C32 | C2×C32×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C7×C9 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 204);