Finite Group DatabasebetaFinite Group Databasebeta| order | 1782 |
| isoclinism | isoclinic class of C3⋊(C11⋊AGL(1,ℤ/9)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C11⋊AGL(1,ℤ/9)) |
| unambiguous semidirect product | C11⋊(C3⋊AGL(1,ℤ/9)) |
| Fitting, Hall | C3×C11×3−1+2 ⋊ C2 |
| derived | C3×C9×C11 ⋊ C2×C3 |
| Sylow | C3×3−1+2 ⋊ D11 |
| Sylow | C11 ⋊ C3⋊AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C9×C11 | C2×C3 |
| Frattini | C3 | C3×C3⋊D33 |
| Fitting | C3×C11×3−1+2 | C2 |
| socle | C32×C11 | C3×D3 |
| LCS | G ▷ C3×C9×C11 | |
| UCS | C1 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 297 |
Polycyclic presentation:
2,3^3,11,3|d^3=f^2,c^a=c^2,d^a=d^2f,e^a=e^10,f^a=f^2,d^b=df186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1782, 90);