Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | 3−1+2×AGL(1,𝔽7) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C2×3−1+2) |
| Fitting | C7×3−1+2 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×3−1+2 ⋊ C2 |
| Hall | D7 ⋊ C3×3−1+2 |
| Sylow | C7 ⋊ C2×C3×3−1+2 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 63 |
77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 143);