Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
| direct product | C2×SD16×C3⋊(C3⋊D3) |
| Fitting | C2×C33×SD16 ⋊ C2 |
| Sylow | C33 ⋊ C22×SD16 |
4172 conjugacy classes of subgroups; only the 683 normal subgroups are shown.
This group has 4172 conjugacy classes of subgroups — too many to draw. Only its 683 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×SD16×C3⋊D3 |
| maximal normal subgroup of | C2×D3×SD16×C3⋊D3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45946);