Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of A4⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | A4⋊(D9⋊C9) |
| Fitting | C22×C9⋊C9 ⋊ D3 |
| derived | C9×A4 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4⋊AGL(1,ℤ/9) |
| commutator, hypocenter | C9×A4 | C2×C9 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C9⋊C9 | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| prime radical | C3×C9⋊S4 | C3 |
| cosocle | C3×C9×A4 | C2×C3 |
| LCS | G ▷ C9×A4 | |
| UCS | C1 ◁ C3 | |
211 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3^5,2^2|b^3=c,e^3=f,d^a=d^2,e^a=e^2f^2,f^a=f^2,g^a=gh,e^b=ef^2,g^d=h,h^d=gh93 conjugacy classes — view the full character table.
| maximal subgroup of | #72228977, S4×D9⋊C9, #72229393, … |
| maximal normal subgroup of | S4×D9⋊C9 |
| maximal quotient of | #72228977, #72229393, #72259316 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2409);