Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×AGL(1,𝔽5) |
| Fitting, Hall | C52×C9 ⋊ C4 |
| derived | C5 ⋊ C4×C5×C9 |
| Sylow | C52 ⋊ C4×C9 |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 51);