Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C22⋊C9×(C2×D3)⋊C4 |
| unambiguous semidirect product | (C2×D3)⋊(C4×C22⋊C9) |
| unambiguous semidirect product | (C22×(C2×D3)⋊C4)⋊C9 |
674 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 85 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, 13326);