Finite Group DatabasebetaFinite Group Databasebeta| order | 9720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×AGL(1,ℤ/27) |
| Fitting, Hall | C5×#6875 ⋊ C2×C4 |
| derived | C5×C27 ⋊ C2×C4×C9 |
| Sylow | #6875 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×AGL(1,ℤ/27) |
216 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
155 conjugacy classes — view the full character table.
| holomorph of | C5×C27 |
Past the SmallGroups library coverage — no SmallGroups id.