Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C9⋊AGL(1,𝔽5) |
| Fitting, Hall | C5×C92 ⋊ C4 |
| derived | C5×C9 ⋊ C4×C9 |
| Sylow | C92 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ C9×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C9⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C9 | C4×C9 |
| Frattini | C32 | C3×ΓL(1,𝔽16) |
| Fitting | C5×C92 | C4 |
| socle | C32×C5 | C3×Dic3 |
| prime radical | C32×D5 | C3×D3 |
| cosocle | C3×C9×D5 | C2×C3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C9 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72222360, C9×D9×AGL(1,𝔽5), D9×C9⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #72222360, C9×D9×AGL(1,𝔽5), D9×C9⋊AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 81);