Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C3×C9×AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×C3×C9) |
| Fitting | C3×C7×C9 ⋊ C2×C3 |
| derived, Sylow | C7 ⋊ C2×C32×C9 |
| Hall | C3×C9×ΓL(1,𝔽8) ⋊ C2 |
| Hall | D7 ⋊ C32×C9 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 137);