Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C1 |
| direct product | D3×C7×3−1+2 |
| unambiguous semidirect product | C3⋊(C2×C7×3−1+2) |
| unambiguous semidirect product | (D3×C9)⋊(C3×C7) |
| Fitting, Hall | C3×C7×3−1+2 ⋊ C2 |
| Sylow | C3×3−1+2 ⋊ C2×C7 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#92265, D3×ΓL(1,𝔽8)×3−1+2, D3×C7×AGL(1,ℤ/9), … |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×3−1+2, D3×C7×AGL(1,ℤ/9), D3×D7×3−1+2, … |
| maximal quotient of | C7×#92265 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 208);