Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2 |
| direct product | M16×C9⋊A4 |
| unambiguous semidirect product | (C9×M16)⋊A4 |
| Fitting | C22×C9×M16 ⋊ C3 |
| Sylow | C22×M16 ⋊ 3−1+2 |
289 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 289 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18203);