Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C3×A4×AGL(1,ℤ/9) |
| unambiguous semidirect product | (D9⋊A4)⋊C32 |
| unambiguous semidirect product | (A4×D9)⋊C32 |
| unambiguous semidirect product | (C22×AGL(1,ℤ/9))⋊C32 |
| Fitting | C22×C3×3−1+2 ⋊ C2×C3 |
| derived | C22×C9 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C22×C9 | C2×C33 |
| Frattini | C3 | C32×D3×A4 |
| Fitting | C22×C3×3−1+2 | C2×C3 |
| socle | C22×C32 | C32×D3 |
| LCS | G ▷ C22×C9 | |
| UCS | C1 ◁ C3 | |
622 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4×#4183, A4×#4207⋊C3, A4×#4183⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3634);