Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C34 |
| direct product | C3×D7×H(3,𝔽3) |
| Fitting, Hall | C3×C7×H(3,𝔽3) ⋊ C2 |
| Sylow | C7 ⋊ C2×C3×H(3,𝔽3) |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 189 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D7×AΣL(1,𝔽27), D7×3−1+4, D7×#6909, … |
| maximal normal subgroup of | C3×D7×AΣL(1,𝔽27), D7×3−1+4, D7×#6909, … |
| maximal quotient of | C3×D7×AΣL(1,𝔽27), D7×#6909, D7×#6910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 200);