Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C1 |
| direct product | D7×C27⋊C3 |
| Fitting, Hall | C7×C27⋊C3 ⋊ C2 |
| Sylow | C7 ⋊ C2×C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C9 | C32×D7 |
| commutator, socle | C3×C7 | C2×C3×C9 |
| Fitting | C7×C27⋊C3 | C2 |
| prime radical | C32×D7 | C9 |
| cosocle | C7×C9 | C2×C32 |
| hypercenter | C27⋊C3 | D7 |
| hypocenter | C7 | C2×C27⋊C3 |
| LCS | G ▷ C3×C7 ▷ C7 | |
| UCS | C1 ◁ C9 ◁ C27⋊C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×C27⋊C3, D7×#6875, #72249073, … |
| maximal normal subgroup of | AGL(1,𝔽7)×C27⋊C3, D7×#6875, #72249073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 83);