Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C9×C3⋊AGL(1,ℤ/9) |
| unambiguous semidirect product | C3⋊(C9×AGL(1,ℤ/9)) |
| Fitting, Sylow | C3×C9×3−1+2 ⋊ C2 |
| derived | C3×C9 ⋊ C2×C3×C9 |
437 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1442);