Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2 |
| direct product | Q16×C9⋊A4 |
| unambiguous semidirect product | (C9×Q16)⋊A4 |
| Fitting | C22×C9×Q16 ⋊ C3 |
| Sylow | C22×Q16 ⋊ 3−1+2 |
255 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18213);