Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C32×#4474 |
| Fitting | C33×#99 ⋊ C2 |
| Sylow | C33 ⋊ #353 |
724 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11839);