Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×#4475 |
| Fitting | C3×C9×#100 ⋊ C2 |
| Sylow | C3×C9 ⋊ AΣL(1,𝔽16) |
328 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 63 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, 1413);