Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | D8×3−1+2⋊C4 |
| unambiguous semidirect product | (D8×Dic9)⋊C3 |
| Sylow | 3−1+2 ⋊ C4×D8 |
440 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9379);