Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4 |
| direct product | C3×D9×#127 |
| Fitting | C3×C9×#127 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#127 |
1602 conjugacy classes of subgroups; only the 314 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 314 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D9×#127, #127×D27⋊C3, #127×D9⋊C9 |
| maximal normal subgroup of | D3×D9×#127, #127×D9⋊C9 |
| maximal quotient of | #127×D27⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19322);