Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22 |
| direct product | C3×D4⋊AGL(1,𝔽9) |
| unambiguous semidirect product | D4⋊(C3×AGL(1,𝔽9)) |
| Fitting | C33×D4 ⋊ C8 |
| Sylow | C33 ⋊ D4⋊C8 |
234 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 32258);