Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | D3×#63436 |
| Fitting | C3×C42×C9 ⋊ C22 |
| Sylow | C3×C9 ⋊ C2×#127 |
1602 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9×#127 |
| maximal normal subgroup of | D3×D9×#127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13770);