Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×D3×C7⋊C9 |
| unambiguous semidirect product | C3⋊(C2×C3×C7⋊C9) |
| unambiguous semidirect product | (C3×D3×C7)⋊C9 |
| derived | C3×C7 ⋊ C2×C3×C9 |
| Hall | C32×C7⋊C9 ⋊ C2 |
| Sylow | C7 ⋊ C3×D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D3×ΓL(1,𝔽8) |
| commutator, hypocenter | C3×C7 | C2×C3×C9 |
| Frattini | C3 | C3×D3×ΓL(1,𝔽8) |
| Fitting, socle | C33×C7 | C2×C3 |
| prime radical | C32×D3×C7 | C3 |
| cosocle | C32×C7 | C2×C32 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C32 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 156);