Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×D3×AΣL(1,𝔽27) |
| unambiguous semidirect product | C3⋊(C23×AΣL(1,𝔽27)) |
| unambiguous semidirect product | (C2×C3)⋊(C22×AΣL(1,𝔽27)) |
| Fitting | C22×C3×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ C23 |
855 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 855 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2873);