Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×#10596191 |
| Fitting | C33×#127 ⋊ C2 |
| Sylow | C33 ⋊ #560 |
1944 conjugacy classes of subgroups; only the 342 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 342 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45534);