Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
| direct product | C3×D9×3−1+2 |
| Fitting, Sylow | C3×C9×3−1+2 ⋊ C2 |
458 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#6900, C3×3−1+2×AGL(1,ℤ/9), #72243185, … |
| maximal normal subgroup of | D9×#6900, C3×3−1+2×AGL(1,ℤ/9), #72243185, … |
| maximal quotient of | D9×#6900, C9×D9×3−1+2, D9×#6894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1443);