Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of D27⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D27⋊C3 |
| unambiguous semidirect product | D27⋊(C3×C7) |
| unambiguous semidirect product | (C27⋊C3)⋊(C2×C7) |
| Fitting, Hall | C7×C27⋊C3 ⋊ C2 |
| derived | C27 ⋊ C2×C3×C7 |
| Sylow | C27⋊C3 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D27⋊C3 |
| commutator, cosocle, hypocenter | C27 | C2×C3×C7 |
| Frattini | C9 | C3×D3×C7 |
| Fitting | C7×C27⋊C3 | C2 |
| socle | C3×C7 | C3×D9 |
| LCS | G ▷ C27 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D27⋊C3, ΓL(1,𝔽8)×D27⋊C3, C7×AGL(1,ℤ/27), … |
| maximal normal subgroup of | D7×D27⋊C3, ΓL(1,𝔽8)×D27⋊C3, C7×AGL(1,ℤ/27), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 94);