Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D9×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D9×C7⋊C9 |
| derived | C7×C9 ⋊ C2×C9 |
| Hall | C9×C7⋊C9 ⋊ C2 |
| Sylow | C7 ⋊ C9×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D9×ΓL(1,𝔽8) |
| commutator, hypocenter | C7×C9 | C2×C9 |
| Frattini | C32 | D3×ΓL(1,𝔽8) |
| Fitting, cosocle | C3×C7×C9 | C2×C3 |
| socle | C32×C7 | C3×D3 |
| prime radical | C3×C7×D9 | C3 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C3 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D9×ΓL(1,𝔽8), #72229906, #72229909, … |
| maximal normal subgroup of | C9×D9×ΓL(1,𝔽8), #72229906, #72229909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 32);