Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×C9×D9 |
| Fitting, Hall | C7×C92 ⋊ C2 |
| derived | C9 ⋊ C2×C7×C9 |
| Sylow | C92 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C9 | D9 |
| commutator, hypocenter | C9 | C2×C7×C9 |
| Frattini | C32 | C3×D3×C7 |
| Fitting | C7×C92 | C2 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×C7×D9 | C3 |
| cosocle | C3×C9 | C2×C3×C7 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C7×C9 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#92265, C9×D9×ΓL(1,𝔽8), #72229913, … |
| maximal normal subgroup of | C7×#92265, C9×D9×ΓL(1,𝔽8), #72229913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 88);