Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×C32) |
| unambiguous semidirect product | (D9×C32)⋊C3 |
| Fitting | 3−1+2×C32 ⋊ C2 |
| derived | C9 ⋊ C2×C3×C32 |
| Sylow | 3−1+2 ⋊ C2×C32 |
108 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 1310);