Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #4169 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×#4169 |
| Fitting, Hall | C7×C32⋊C9 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C7 |
| Sylow | C32⋊C9 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #4169 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C3×C7 |
| Frattini | C32 | C3×D3×C7 |
| Fitting | C7×C32⋊C9 | C2 |
| socle | C32×C7 | C3×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C7 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 90);