Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#10590189 |
| Fitting | C33×M16 ⋊ C4 |
| Sylow | C33 ⋊ #339 |
396 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23177);