Finite Group DatabasebetaFinite Group Databasebeta| order | 810 |
| isoclinism | isoclinic class of AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×D9⋊C9 |
| unambiguous semidirect product | D9⋊(C5×C9) |
| unambiguous semidirect product | (C9⋊C9)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D9)⋊C9 |
| Fitting, Hall | C5×C9⋊C9 ⋊ C2 |
| derived | C9 ⋊ C2×C5×C9 |
| Sylow | C9⋊C9 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | AGL(1,ℤ/9) |
| commutator, hypocenter | C9 | C2×C5×C9 |
| Frattini | C32 | C3×C5×D3 |
| Fitting | C5×C9⋊C9 | C2 |
| socle | C32×C5 | C3×D3 |
| prime radical | C3×C5×D9 | C3 |
| cosocle | C3×C9 | C2×C3×C5 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C3×C5 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D9⋊C9, C2×C5×D9⋊C9, C5×#92265, … |
| maximal normal subgroup of | D5×D9⋊C9, C2×C5×D9⋊C9, C5×#92265 |
| maximal quotient of | C5×Dic9⋊C9, C2×C5×D9⋊C9, C5×AGL(1,ℤ/27) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(810, 17);