Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of C5⋊AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C5⋊AGL(1,ℤ/9) |
| unambiguous semidirect product | C5⋊(C3×AGL(1,ℤ/9)) |
| unambiguous semidirect product | D45⋊C32 |
| unambiguous semidirect product | (C3×D45)⋊C3 |
| Fitting, Hall | C3×C5×3−1+2 ⋊ C2 |
| derived | C5×C9 ⋊ C2×C32 |
| Sylow | C3×3−1+2 ⋊ D5 |
| Sylow | C5 ⋊ C3×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C5×C9 | C2×C32 |
| Frattini | C3 | C32×D15 |
| Fitting | C3×C5×3−1+2 | C2 |
| socle | C32×C5 | C3×D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C3 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 77);