Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #4181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4181 |
| Fitting, Hall | C7×C32⋊C9 ⋊ C2 |
| derived, Sylow | C32⋊C9 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | C3⋊D9 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C7 |
| Frattini | C32 | C7×C3⋊D3 |
| Fitting | C7×C32⋊C9 | C2 |
| socle | C32×C7 | C3⋊D3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3×C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#92302, ΓL(1,𝔽8)×#4181, #72249184, … |
| maximal normal subgroup of | C7×#92302, ΓL(1,𝔽8)×#4181, #72249184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 115);