Finite Group DatabasebetaFinite Group Databasebeta| order | 648 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×Dic3) |
| unambiguous semidirect product | (C3×AGL(1,ℤ/9))⋊C4 |
| unambiguous semidirect product | (Dic3×D9)⋊C3 |
| derived | C3×C9 ⋊ C2×C3×C4 |
| Sylow | C3×3−1+2 ⋊ C2×C4 |
133 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 133 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×AGL(1,ℤ/9), #88641⋊C3, #88634⋊C3, … |
| maximal normal subgroup of | Dic6×AGL(1,ℤ/9), #88641⋊C3, #88634⋊C3, … |
| maximal quotient of | C3⋊C8×AGL(1,ℤ/9), #88413⋊C3, Dic3×3−1+2⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(648, 380);