Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C9⋊(C5×AGL(1,𝔽5)) |
| Fitting, Hall | C52×C9 ⋊ C4 |
| derived | C5×C9 ⋊ C4×C5 |
| Sylow | C52 ⋊ Dic9 |
| Sylow | C9 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C9 | C4×C5 |
| Frattini | C3 | C5×ΓL(1,𝔽16) |
| Fitting | C52×C9 | C4 |
| socle | C3×C52 | Dic3 |
| prime radical | C3×C5×D5 | D3 |
| cosocle | C9×D5 | C2×C5 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C5 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 55);