Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×C4⋊(C3⋊AGL(1,ℤ/9)) |
| unambiguous semidirect product | C4⋊(C3×C3⋊AGL(1,ℤ/9)) |
| Fitting | C32×C4×3−1+2 ⋊ C2 |
| Sylow | C32×3−1+2 ⋊ D4 |
822 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3319);