Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C9⋊C8)⋊C27 |
| unambiguous semidirect product | (C9⋊C27)⋊C8 |
| derived | C9 ⋊ C8×C27 |
| Sylow | C9⋊C27 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C9 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C8×C27 |
| Frattini | C3×C4×C9 | C3×D3 |
| Fitting | C4×C9⋊C27 | C2 |
| socle, prime radical | C2×C32 | C9×Dic3 |
| cosocle | C4×C92 | C2×C3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C4×C9 | |
69 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3,2,3,2,3^3|a^2=c,b^3=d,c^2=e,d^3=f,g^3=h,g^a=g^2h^2,h^a=h^2,g^b=gh^2360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 39);