Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #4185 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×#4185 |
| Fitting, Hall | C7×#732 ⋊ C2 |
| derived, Sylow | #732 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #4185 |
| commutator, cosocle, hypocenter | #732 | C2×C7 |
| Frattini | C32 | C7×C3⋊D3 |
| Fitting | C7×#732 | C2 |
| socle | C3×C7 | #272 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C7 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#92333, ΓL(1,𝔽8)×#4185, #72249188, … |
| maximal normal subgroup of | C7×#92333, ΓL(1,𝔽8)×#4185, #72249188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 119);