Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C9×(C2×S4)⋊C4 |
| unambiguous semidirect product | (C2×S4)⋊(C4×C9) |
| Fitting | C23×C4×C9 ⋊ D3 |
461 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 461 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 12840);