Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | C3⋊D3×AΣL(1,𝔽27) |
| unambiguous semidirect product | C3⋊(D3×AΣL(1,𝔽27)) |
| Fitting, Sylow | C32×AΣL(1,𝔽27) ⋊ C2 |
848 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊D3×AΣL(1,𝔽27), C3⋊D3×#6909 |
| maximal normal subgroup of | C3×C3⋊D3×AΣL(1,𝔽27), C3⋊D3×#6909 |
| maximal quotient of | C3×C3⋊D3×AΣL(1,𝔽27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1643);