Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3×C4 |
| direct product | #127×C3⋊D9 |
| Fitting | C3×C9×#127 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#127 |
2490 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 2490 conjugacy classes of subgroups — too many to draw. Only its 339 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | #127×C9⋊D9, #127×C3⋊AGL(1,ℤ/9), #72220062, … |
| maximal normal subgroup of | #127×C3⋊AGL(1,ℤ/9), #72220062, D3×D9×#127 |
| maximal quotient of | #127×C9⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20324);