Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of #67355 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | C3×#67356 |
| Fitting | C3×C7×C9 ⋊ C2×C3 |
| Hall | C3×#4427 ⋊ C2 |
| Hall | D7 ⋊ C3×3−1+2 |
| Sylow | C7 ⋊ C2×C3×3−1+2 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
93 conjugacy classes — view the full character table.
| maximal subgroup of | #72229855, C3×3−1+2×AGL(1,𝔽7), #72229861, … |
| maximal normal subgroup of | #72229855, C3×3−1+2×AGL(1,𝔽7), #72229861, … |
| maximal quotient of | #72229855, #72229861, #72249144 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 139);