Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D12×Q8⋊C9 |
| unambiguous semidirect product | C4⋊(D3×Q8⋊C9) |
| unambiguous semidirect product | (Q8×D12)⋊C9 |
380 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13270);