Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×C5⋊AGL(1,ℤ/9) |
| Fitting, Hall | C52×3−1+2 ⋊ C2×C4 |
| derived | C52×C9 ⋊ C2×C3×C4 |
| Sylow | 3−1+2 ⋊ D5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C4×AGL(1,ℤ/9) |
217 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×AGL(1,𝔽5)×AGL(1,ℤ/9) |
| maximal normal subgroup of | D5×AGL(1,𝔽5)×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.