Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | S4×C9⋊C9 |
| unambiguous semidirect product | A4⋊(C2×C9⋊C9) |
| unambiguous semidirect product | (C9×S4)⋊C9 |
| Fitting | C22×C9⋊C9 ⋊ D3 |
243 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 243 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) = 324 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#6875, S4×D9⋊C9 |
| maximal normal subgroup of | S4×#6875, S4×D9⋊C9 |
| maximal quotient of | S4×#6875 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2349);