Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| direct product | D3×#4430 |
| unambiguous semidirect product | C3⋊(C2×#4430) |
| Hall | C3×#4430 ⋊ C2 |
| Sylow | C7 ⋊ D3×3−1+2 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | #72229906, D3×ΓL(1,𝔽8)×3−1+2, D3×#4430⋊C2 |
| maximal normal subgroup of | D3×ΓL(1,𝔽8)×3−1+2, D3×#4430⋊C2 |
| maximal quotient of | #72229906 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 157);