Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×3−1+2⋊C4 |
| unambiguous semidirect product | (C16×Dic9)⋊C3 |
| derived | C9 ⋊ C3×C4×C16 |
| Sylow | 3−1+2 ⋊ C4×C16 |
188 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1544);