Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#67355 |
| Fitting | C3×C7×C9 ⋊ C2×C3 |
| Hall | C3×#4428 ⋊ C2 |
| Sylow | C7 ⋊ D3×3−1+2 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
Polycyclic presentation:
2,3^4,7|c^3=d,e^a=e^2,f^a=f^6,c^b=cd,f^b=f^460 conjugacy classes — view the full character table.
| maximal subgroup of | #72229945, #72229948, 3−1+2×C3⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | 3−1+2×C3⋊AGL(1,𝔽7), D3×#67355, #72230135, … |
| maximal quotient of | #72229945, #72229948 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 164);