Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | (D9⋊A4)⋊C9 |
| unambiguous semidirect product | ((C9⋊A4)⋊C9)⋊C2 |
| Fitting | C22×C9⋊C9 ⋊ C2×C3 |
| derived | C22×C9 ⋊ C2×C3×C9 |
204 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^3,2^2,3^2|c^3=d,g^3=h,g^a=g^2h^2,h^a=h^2,e^b=ef,f^b=e,g^b=gh^2,g^c=gh^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2533);