Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | SD32×C3⋊D9 |
| Fitting | C3×C9×SD32 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×SD32 |
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 10273);