Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×#10588043 |
| Fitting | C2×C7×H(3,𝔽3) ⋊ C3 |
| Hall | C2×C7 ⋊ AΣL(1,𝔽27) |
| Sylow | C7 ⋊ C2×AΣL(1,𝔽27) |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 73);