Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | S4×AΣL(1,𝔽27) |
| unambiguous semidirect product | A4⋊(C2×AΣL(1,𝔽27)) |
| Fitting | C22×AΣL(1,𝔽27) ⋊ D3 |
306 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | C3×S4×AΣL(1,𝔽27), S4×#6909 |
| maximal normal subgroup of | C3×S4×AΣL(1,𝔽27), S4×#6909 |
| maximal quotient of | C3×S4×AΣL(1,𝔽27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2352);