Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×D9⋊C9 |
| unambiguous semidirect product | (A4×D9)⋊C9 |
| Fitting | C22×C9⋊C9 ⋊ C2×C3 |
| derived | C22×C9 ⋊ C2×C3×C9 |
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | A4×AGL(1,ℤ/27), S4×D9⋊C9 |
| maximal normal subgroup of | S4×D9⋊C9 |
| maximal quotient of | A4×AGL(1,ℤ/27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2532);