Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | #126×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×#126) |
| Fitting | 3−1+2×#126 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×#126 |
768 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19309);